This. So many times i interact with people who don't account for context and just say,"the number don't lie". Of course numbers don't lie, but people can and you have to know the context behind the numbers
@范德萨阿斯顿发大水发大水发阿斯顿发大水发大水发范德萨我和你吻别我爱你他妈的翔宇我和你吻别元的钱破开该 it's certainly a good question to ask but it's also important to mention specifics. His logic seemed sound to me and if you just say "he could be wrong" without pointing to anything specific, it doesn't hold any weight.
@@wizzotizzo No, i didnt. I literally just said something about Biden-Coverage. See for yourself: the channel i named literally covers BOTH THE GOOD AND THE BAD. Yes, i said Both as in 'how unbiased news should work'.
The way I see it, these things are like metal detectors. They're great at finding points of interest, but you have to start digging to see if it's a coin or a bottlecap.
The Dunning-Kruger Effect is a hell of a thing. All the gullible conspiracy theorists who haven't taken a math class in a decade or more are suddenly mathematicians, just like how they're also epidemiologists and economists who clearly know "so much more" than people with degrees in those fields.
You think this guy is an expert? If he were a true unbiased mathematician then he would be arguing that Trumps distribution should follow the same pattern if his theory on the precincts was correct.
These kinds of misunderstandings are, I think, a subset of a larger problem of people getting 'evidence' confused with 'indicators.' One is often the other, but not necessarily so. The indicator should cause you to look closer, but if you look closer and find no evidence you shouldn't continue to tout the indicator.
@@hedgehog3180 depends. I personally think they were just desperate. I thought from the beginning that it would be close if trump won by any margin in 2020, but fewer in my view felt the same in 2016 leading to many not accepting that election for vert much rhe same reason trumpers didn't want to accept 2020. It's like many had selective amnesia when it comes to rhe outcomes they wanted.
Thanks for mentioning my name and my work starting at 3:56 :) I did an analysis of the Maricopa County election results and got pretty much the same patterns. Here's an interesting tidbit... At 2:00 you talk about the populations of the 3,141 counties and Benford's Law. At 13:25 you talk about the digits in pi, .... and, of, course, the first four digits of pi are 3141 :) You went full circle or 2πr.
You've clearly done some seriously good maths work but, honestly, those jokes. Call me irrational, but I love it when a tangent turns into a punch-line.
County precinct groups are too uniform. Benford described the nature of numbers on a larger scale, so if you cherry pick a city block, or man-made precinct and chart the the leading digits, it will fail as bad any of the full state chart by county assessments of in the swing states for Biden counts. Or, blue state, Trump counts. The selective adherence to the law is suspect.
@@poorman-trending nah, more like most people watching the news won’t care abt a mathematician and just arguing over nothing somehow brings in better ratings and views
@@poorman-trending Exactly, and I would guess a mathematician wants nothing to do with politicians for this reason--or maybe they would because they want to show them what the truth actually is?
@@maxwellsequation4887 Pretty sure they do. It just the general public is less likely to listen to a mathematician than a celeb or political figure, thus lower rating for news organization.
I really like that you compared side by side the digit pairs of pi with the last two digits of Biden votes. A very clever way to impartially show the expected variation at that sample size. Without that comparison, people surely would be looking for patterns in the noise, which as we know is a dangerous thing.
If PI is carried to millions of decimal places there are many of what would seem to be improbable strings of numbers such as "1234567890" or "1122334455667788" or "666666666666", but it always breaks out of these patterns.
@@arronaltI always thought that the saying referred to the Tale of Two Cities just because of that scene from the Simpsons. "It was the best of times, it was the...blurst of times?? You stupid monkey!"
I'll just leave my disagreement here. Plenty of stuff you can discuss without a degree. Just because you might get it wrong doesn't mean you shouldn't discuss it
I believe that Mark Twain had an adage, “You have lies, damn lies and statistics.” Based on this it appears you can use several different number sets to argue whichever point you are trying to prove. I have found that looking at the process to outcome is ultimately the only way to actually prove a thing. But as he said, these are only used to determine if something needs to be investigated. It appears that, in the case of Chicago, that a closer look is needed.
Maybe you should revise, because data being random is only relevant when we’re sampling the population so we can make sure it is close to the population, but in this case of election we are looking at the entire population, meaning every single vote. We don’t sample the votes for the election, we count them.
@@anandrai492 yeah, but if the question is "how well does chicago's districts of roughly 100 to 1000 fit Benford's law" the answer is gonna be "not well". Gotta check your data before you try to fit them to something and draw conclusions. (And the question on the exam was about predicting an election based on a survey and finding a rejection region such that alpha, the chance of a type 1 error, is less than some value bla bla - which only worked in the question if you make sure the survey was random and only then can you apply the CLT and estimate it with a Normal)
@@bzboii or you can just focus on something else besides the raw count like second order or summation. www.researchgate.net/publication/319526944_Benford's_Law_The_Second-Order_and_Summation_Tests
@@tangyspy does his nationality affect my statement? I'm making a reference to how he mentions agendas in the video, and how this appears to be a protracted ad for his book 😂
Sure, that also means that, knowing the initial digits, no one has been able to distinguish it from a normal number. The non-randomness would have to be "further down".
It's a standard government/business/PR tactic: present the statistics' results but never reveal how those statistics were derived. As a simple example look at washing-machine detergent adverts (or any other adverts based on provable results rather than aesthetics): they all claim they're the best, but what is 'the best', & under what conditions? You can also move the goalposts by adjusting the size of the sample: '9 out of 10 cats prefer it' sounds great, until you realise that only 10 cats were used to test the food (& they were prolly preselected from certain specialised parameters anyway) :)
@@snafu2350 Interesting concept...I didn't know cats used washing machine detergent! LOL (I have to laugh at my own jokes otherwise there would be complete silence. It's a well known fact that 9 out of 10 comedians laugh at their own jokes... Is it just me or is thing going round and round in circles?)
@@snafu2350 It's something I enjoy about UK adverts - they do have some legal requirements about explaining where the result of the survey comes from, sometimes you even see text like "out of 87 people surveyed" when a shampoo is talking about being preferred. Radio ads are even better as you get someone trying to quickly rattle through all the legal disclaimers etc at the end, but they have to do it slow enough that you can still understand them. Still not a perfect system, and you wish the audience were better educated about sampling error etc, but it's nice to still see it
The takeaway: if you discover an anomoly, you actually have to investigate the source of said anomoly before you can accurately say you know its cause.
Studying the anomalies, rather than the commonalities, might produce some interesting insights. We know some athletes are enormously better than average. We can ask what role does economic status play into their performance?
The problem is that all places where anomalies are accused, seem to lock up and hide the data to substantiate their “certification.” Sort of like Pfizer asking for, what, 95 years or something before disclosing the study data on the vaccine? Quite equally, and scaringly similar when you think about it.. but you probably aren’t concerned or see the analogy ;)
If I understand what you're saying, I agree. For example, the anomaly in the Trump vote tallies compared to the Biden tallies may, I suspect, be explained in several ways, but most of them having to do with the programming of the voting machines, or how the results are calculated after they're input. What algorithms could be used to modify (just assuming hypothetically, not claiming they were) the election results? Would they take into consideration the possibility that some of the data coming in are invalid? How would they handle for example, a massive input illegitimate votes for one candidate over the other? Would it try to compensate by manipulating the data for both candidates to resemble expected outcomes, according to what forensic analysts might expect? The idea being to hide the cheating enough to make it look legit. I'd like to see an analysis like this this one across a larger sample, or better yet, across two larger samples, one of states that reported no "irregularities" compared with a second, of the collection of states that reported substantial irregularities. That would be interesting...
Exactly, another great example of this is his "Perfect Bridge Game" video where he explains away the anomaly of a 1 in 2.2 x10^27 event occurring not just once, but several times.
"AND ELECT ION DATA" To be honest, if there were someone named "Ion Data" running for any position, I'd be very tempted to elect them based on the name alone.
This reminds me of that time an acquaintance called Justin Case blocked me from Facebook because I wouldn't stop unnecessarily tagging him in my comments.
I'm going to use this pinned comment to reply to the most-common questions/complaints. It'll be updated infrequently but I am trying to read everyone comments. - WHY DID YOU ANALYSE DATA FROM CHICAGO NOT A SWING STATE? Good question. It is because the first Benford-Biden theory I was sent was based on the Chicago precinct vote totals (there's a link way down in the video description). So I analysed the same data they did. I did not choose the Chicago dataset: people claiming election fraud did. You are very welcome to analyse data from elsewhere and show us your working. - WHY DOES TRUMPS PLOT MATCH BENFORD'S LAW? It does and it doesn't. I was going to say in the video that Trump's plot is also a bad fit for Benford: there are way too many 1s and then fewer digits from 3 up. That spike of 1s is because Trump got an overwhelming number of vote totals between 10 and 19 and so at a glance it looks like a good fit. I cut that bit though as the video was going to be as long as the election. - SOME PEOPLE ARE CRITICAL OF THAT PAPER YOU QUOTED In terms of legitimate criticism, you are probably thinking of Walter Mebane and I have linked to their papers in the video description. But they specifically disagreed with how 'Benford's Law and the Detection of Election Fraud' (2011) treats the 'second digit' check while still agreeing that "It is widely understood that the first digits of precinct vote counts are not useful for trying to diagnose election frauds." - A STRING OF DISJOINT WORDS AND EMOJIS I'm not sure how to constructively engage with that, but I'm glad you watched the video and wanted to get involved with the comments. I thought I did a pretty good job of being all-math-no-politics in the video but appreciate people are very passionate about these things. Other commenters: I encourage you to engage constructively wherever possible and 'down thumb' anything untoward. - IS THAT TRAILBREAKER ON YOUR SHELF? Yes it is. It is exactly what meets the eye.
I think it would have been more interesting to compare 2020 Biden in Chicago to 2016 Hillary in Chicago than 2020 Biden to 2020 Trump if you are going to use just one city instead of national data. Else, we are comparing apples to oranges. Good explanation otherwise on the precinct size rationale.
Where did you get the 20 mil from? Harris got 75 mil votes, compared to 81 in 2020, trump 77 mil, his margin is barely mediocre. Mate you don't even understand how elections are called, the election was called before even half the votea in California were counted in. Oh you clown 😅
@@Trash_owo millions of Trump hating liberals didnt stay home to let him win. Their names should be on voter roles. So you're saying those millions of liberals were sick of the liberal crap too.?
There's an implicit narrative here that worth making explicit. When it comes to data analytics, the proper question to ask is: why do I have the data that I do? If you simply take your data and analyze it without considering how that data was generated (both collection methodology as well as the phenomenon you wish to understand), you will probably completely misrepresent the actual reality and fail to really understand why you had that data. I suspect this happens *a lot* in practice, especially when companies do data analytics for a myriad of reasons and often have less than stellar data collection methods, let alone failing to consider the real-world process responsible for the data and what, therefore, they should expect to see.
Justin, In Chicago's Graph, Trump's Benford curve shows significantly lower 3's and 4's. That looks like Democrats are THROWING away trump votes in the 300 and 400 and 500 count precincts THUS forcing the 1's in Trumps to be abnormally high. Second, for Biden, those Blue Democrats are PADDING (adding illegal votes) in the 100's, 200"s precinct counts and making them into 300's, 400's and 500's and 600's. There are no examples in elections that show standard bell curve except Blue Democratic cities which have decades of high-level corruption outside of vote counts. Those cities are complete ghettos with decades of declining population.
@@foundingfathers4462 Ghettos with declining populations? Never been to a big city have you now? News flash! Some people hate Trump! In cities with over a couple hundred thousand people, it’s a different world than most red counties. I suggest you go to a big city with your Trump flag and conspiracy theories and see how many times you get cursed out.
@@ThisIsMego From the ignorant analysis in his comment, I don't think he'd understand the video even if he did watch it. A nice example of the Dunning-Kruger effect.
Benford's is an acid test, it can be used as an indicator of places to look, it doesn't mean they are not explainable. For forensic accountants alot of the time the evidence is circumstancial and indirect.
Compared to Bidens normal distribution, Trumps vote counts are best described by a Poisson distribution, which is a pretty sophistacated roundabout way of saying, that Trump just ain't popular in Chigago.
As a retired stats prof (hopefully not Dannycode's), I wanted to thank you for clearly explaining your process and the underlying theories. I'm always (yes, still) looking for interesting examples of phenomena. to use.
As a retired Professor, what did you think of the the presenter in this video using the second digit distribution to justify the Benford result in question for Biden, but then using the Benford result for to justify the second digit distribution in question for Trump.
@@fomori2 most underrated comment so far. I'm an accountant, and elections are perfect use for it. I use it as a litmus test for finding irregularities in bulk data.
@@JamesWolfpacker Did you learn nothing? Stop spreading misleading information as if you're not literally commenting on a video debunking the snake oil you're selling. Shoo now.
@@mangonel I am going to be an annoying pedant here and say that this is technically correct (the best kind of correct), but in reality people collect the data, choose how to analyze it, select the scale on graphs etc. so there is plenty of room for biases to sneak in
I’d like to see Matt upload a video explaining where all the missing votes went. I like this channel and his books, but the dude comes off as a total hack now.
> Would be nice if the media had as much respect for its audience as you do yours. Realistically, the general media is not going to go into a topic at the mathematical depth a math-focused UA-cam channel is going to. That's simply because the audiences are different.
I'm a retired forensic accountant. I'd be happy to explain forensic accounting to anyone who wants to know about it. I should warn you that there's a great deal of statistics involved and attention to detail is mandatory. As a general rule, the only people interested my explanations are other accountants. After a few minutes everyone else discovers that the topic is less fascinating than they thought.
I'm starting out in data and I would frankly love to chat about forensic accounting! I've done some reconciliation and QA and analysis, but none of it really involves intense stats and I'd like to do more than just make pivot tables in excel haha
I do love how you pointed out the unusualness of the data on both sides, presenting it as strange, then showing how it’s not. If you had just done this for one side or the other, and left the undisclosed one up to viewer interpretation, it would have been biased, and not an “impartial step back”
I love how objectively this video is made. No jumping to conclusions, no accusations, no unfounded claims, just mathematics :) and the fact you didn't just answer the question, but started digging deeper into things like the so-called Trump Tower, it really shows why you make such a good teacher!
chi_squared gives you one number to test for significance. Matt's idea (a great one) is to give us a picture of what random data actually looks like. I am very impressed. From mere observation, it looks to have the correct mean and s.d. _ a beautiful illustration.
Fantastic video. Textbook example that a light touch is often better than a heavy hand when engaging with such topics. Many youtubers seem to cripple their own perfectly valid points with unnecessary subjective filler.
Here is a far better video on Benford's Law. See STEP #1 for the video on Benford's Law www.foundingfathers.org/Papers/Politics/BenfordsLaw_n_ElectionFraud.aspx
@@foundingfathers4462 singingbanana, nice yeah, that's a good video, from a great mathematician (also happens to be a friend of Matt Parker) not sure, why it would be far better though, says pretty much the same thing from what I remember. In particular it also says that the data has to span multiple orders of magnitude, which is why you wouldn't be able to use it in this case
@@silversilk8438 anything that could make the video sound like it has an agenda or anything that sounds condescending. It’s an easy way to get people to refuse to accept your points. Even if they’re otherwise accurate.
12:15 "There was a spike at 82 because one employee was claiming their breakfast on their way to work every day, which they weren't allowed to do. You can only claim breakfast when you're on the road for work purposes." *Employee: commuting is for work purposes.*
Love this. You can tell any story you want with data . Digging in an seeing more than 1 aspect of the data is where you start to be able to call out anomalies and ultimately see a holistic view . Well done !
@@standupmaths Sad that only people from Chicago can feel the love here, though I kind of understand why other cities and counties are out of the question.
Sadly, I think the game this year is going to be selecting people to be election observers from the Republican party who are going to be making claims in bad faith to distort the process. I wonder if the Democrats should try to invite UN observers in, though I don't know what can cut through the Republican's echo chamber. All the while places like Fox, OANN and NewsMax are seeding disinformation, a number of the voters aren't going to listen. With 2020, all the claims were easily debunked and coming from dubious places. I hope I'm wrong, but this year my bet would be there are going to be lots of supposed issues reported in count rooms etc - and lots more waste for the American taxpayer...
@@neilbiggs1353 So claims are only false when y ou r enemy is making them. Actions are only crimes when y ou r political enemy is committing (or even just being accused of committing) them. Beliefs are false if y ou r political enemy believes them. And people are not victims unless they agree with y ou r ideology. Do y ou know what a cu lt is?
@@guillermoelnino I know what a cult is - it's when a group of people buy in to everything a pedagogue says without critical analysis. You know, like when they keep trying to claim an election was stolen when the evidence says otherwise, when the lawyers pushing the claims are being sanctioned, disbarred and convicted, when they are paying massive defamation suits... This isn't difficult if you have any ability to parse information...
@@guillermoelnino I love the intersection of ironic or moronic that you represent! Calling people cultists when you are clearly indoctrinated by one of the most incompetent liars in US political history. You'd think the blatant lies that he has been shown to have made in the New York cases would get through, but there are none so blind as people like you that will not see!
I saw a documentary on netflix about Benford's law. I was screaming at my screen when they kept on claiming it was kinda "magical" and no one knew how and why it worked.
@@nmarbletoe8210 maths is a game and those are what the rules say, so. The astonishing thing is the ways in which we can use maths to interpret the world
N Marbletoe There is actually a mathematical explanation on why 1+1=2. But you need to go deep and use set theory for an explanation. 1+1=2 is a mathematical statement that can be proven. Even the existence of zero is actually proven under ZFC.
Right! Which is why I don't trust these "scientists" with their round earth theories. They're tired of me asking them to verify the data according to my needs, say it's a waste of money. I know they're got something to hide.
@@garsm2290 The IRS does that automatically, even more so for those with large finances. The fact that Trump was never charged EVER means his tax history and payments were all lawful. Despite it not being public what anyone owes or has paid in taxes, the IRS and the government does and concerning Trump's business of property and building development much of is in New York, you can't simply not report and you can't just tell the city your building doesn't exist so you don't have to pay that years property tax. I guess a bunch of naive college kids who own nothing and assume mostly everything about much of what they think is true wouldn't really understand this yet or bother to think it out.
@@nlsantiesteban Noel, come on. Your claims of the earth not being round is hardly comparable to either holding or not holding the most powerful office in the world for the next four years.
Scotus has ruled in favor Benford's Law several times including Enron case and it was way more tame then the 4+ deviations we are seeing in some the big cities in swing states
@@Kaoskadosk hope u know Trump's result may have actually been tampered with and that's y I wasn't random anymore... Please do a critical thinking of this, who cheats himself out of an election on a slim chance of winning in court?
I have a lot of respect for the fact that you didn't just stop at "the trump one looks suspicious!" and actually explained why both claims are faulty. That kind of honesty, regardless of where you stand politically, is something we need WAY more of in today's world.
I think that's what Trump is looking for. A validation of EVERY SINGLE LEGALLY cast vote. The only thing I will believe is if they contact every voter to verify their votes.
@@PayNoTax-GetNoVote while that would be great, wouldn’t you say that’s impractical? Should we do that for people who voted in 2016? What if people change their answers over the phone because some guy is haranguingthem? What if people, knowing that race was so close, change their initial vote? Jesus, get real. He lost, hopefully the investigations complete and assure everyone that, yes, that’s true. Assuming he didn’t lose without evidence is conspiracy thinking
@@iMasterchris Also, the way some people are talking now, if some random 'phones my house and asks about my voting, I'd put the phone down and draw the curtains
Thank you for actually explaining the answer to a question a lot of people have. Much more useful than the little warnings social media companies have that "Election fraud is rare according to the AP" or whatever.
Lessons learned from this video: Use Benford's law to detect weird data results and then research why the results are the way they are to find out if anything is wrong. Context people, context matters
Agreed. Statistical models are not definitive last court of appeals. It is as you said, research why they are that way and this Law is still a good rule of thumb. What is good for the gander should be good for the goose, my question in this presentation is but why would Trump's numbers follow Benford's all things being equal it should behave like Biden's too.
@@lpcruz5661 this question is literally answered in the video. Watch the video before commenting. Otherwise, you come across as simply willfully ignorant for asking questions that have already been addressed.
@@LoveJoyPeace4612 I have indeed watched it till the end. I believe my comment is fair. He explains why Biden' does not. Then you can explain to me why Trump follows Benford's? Did he include p-values? He quoted a 2011 paper, well there are recent researches on Benford Law, see this journals.plos.org/plosone/article?id=10.1371/journal.pone.0151235
@@lpcruz5661 Trump's results don't follow Benford's Law either. There's far too many ones and far too few middle numbers. As he showed, that's because half his actual numbers were below 60, and I bet most of those were between 10 and 19.
When I saw Biden's Benford distribution being used on twitter arguments and was googling expert opinions, I was expecting more depressing political articles but instead I discovered this delightful mathematics youtube channel I feel quite lucky to have stumbled here
@@420atheism As a fellow stoner i can only recommend you to take a smoking break for a month and think about your life decisions. Because i think some are not the best
I did one statistics and probability course in my third semester of engineering. All I have ever been doing now is watching statistic videos. I hate this subject. But I love it. Help.
@@ijemand5672 dice are very good at being random.. a 6 sided dice has a uniform distribution to all of its faces, it's pretty good at being random unless its loaded
I trust numbers, but the conclusion of those numbers is something that can differ. Take climate change, 415ppm co2 in the air is 0.04% of the atmosphere. It SOUNDS small, but is it really small? No, it covers perfectly in the holes of water vapor, and is actually quite a huge number relatively. A small number, that has a great impact.
It wasn't an accountant who said that, but a propaganda minister. A German. Some Joseph Goebbels, look him up or watch Der Untergang. And he said: write in the papers that Winston Churchill said this.
@@Khaim.m For this case it is. But removing one case from the set doesn't invalidate Kalpit's hypothesis. I'd be surprised if there's NOT a spike there in human chosen numbers. I'd expect to see a few others in there as well.
@@arfyness Might you know any places where I can find an accurate survey of random numbers? I think analyzing it might be fun before I see what others have to say about it.
Yea usually, people that scream science as proof of their claim don't actually understand how the scientific method really works. It has become quite rampant with the politicization of science.
As a Republican and a Trump voter, I thank you for your video. That really helped me understand the concept. I wanted to check and see if any of the arguments stood up on the other side, and they do. Looking at both sides is so important. Thanks a lot. Love your video.
I don't know English, but I'm wondering, judging by the video, the elections were fair or not? (there are simply no subtitles and I don't understand, but I'm very interested)
LOL - Everyone knows the Dem's cheated> You can't win the house and legislature and lose the presidency. It's impossible. Who would vote for both sides ?
@@adelarsen9776 the house is proportional which means it should fairly closely follow the desires of the people, in this election it did, with the dems leading. The senate is by state, and there are more red states than blue ones, so we should expect too see a slight red lean, and we do. The presidency is by the electoral collage, which leans red compared to actual votes. This is because of a bias towards small states and most small states are red. This is why there has only been one republican president to win the popular vote in the past 5 elections
@@adelarsen9776 Many people (including both Democrats and Republicans) didn't like Biden... but didn't like Trump more. Part of those million of votes weren't for Biden, they were against Trump.
Except it wasn't 15 million. It's less than 7 million. Please stop spreading information that is inaccurate. All that being said they absolutely stole the 2020 election and they tried to do it this time too and this is coming from somebody who didn't vote Republican ever in his life until a few weeks ago.
Where did you get the 15 mil from? Harris got 75 mil votes, compared to 81 in 2020, trump 77 mil, his margin is barely mediocre. Trumps popular vote was less than 50%. Mate you don't even understand how elections are called, the election was called before even half th votea in California were counted in. Oh you clown 😅
It seems to go in spells - you get batches of people who watched and understood, then you get ignorant goons posting sequential word vomit as they get triggered by something being debunked, a few complete morons who beg for the ineffectual law to tested on other states (to prove what exactly has never been revealed...), then some people who would be sued if they tried repeating their baseless claims on TV...
I tried using Benford's Law in my country election a few years ago, grouping by cities (instead of our precincts, which are called "electoral zones"). Cities across the country span several orders of magnitude in population, so it checks that box. Every candidate followed benford's law pretty closely, from what I remember. Of course with this method you have the problem of only looking at the global results of the election, so potentially a localized fraudulent data could be hiding amid all the other genuine data that was generated across the country.
I even remember articles seeing the same nonsense 2016 when Hillary lost but I don't remember people debunking it and insulting and attaching people for not being a statistician. It's amazing that people can died in Iran because of this and people stay silent but when the guy you support has to deal with a legal process it's an outrage.
if only such an approach were even relevant here in the U.S. unfortunately, as the start of the trump presidency indicated (along with 6 other presidential elections since 1980), the popular vote doesn't determine the presidency. because we still rely on a system from when the nation was formed, and which was probably only needed to begin with as a result of half of the country wanting to count 3/5th of their slave population in their political power without actually giving the slaves any say in the matter. As for why we didn't switch to the popular vote after getting rid of slavery, and in doing so also getting rid of the need for the weighted voting system that is the electoral college, I have no clue. probably either because when the amendments at the time were passed banning slavery and extending equal rights, people weren't even considering that the electoral college would become a problem (and every subsequent time the constitution has been amended has been at a point people weren't even considering it to be an issue), or else because it still gave some states more influence that they were hesitant to give up. And the reason we haven't gotten rid of the electoral college system since then is likely because doing so would require a constitutional convention (which opens the entirety of the constitution to changes) and any changes need a 3/4th majority to pass, something which is unlikely to happen with how divided the country is (and it doesn't help that every time the electoral college and the popular vote have disagreed lately, it has been the republican party that benefits from the discrepancy)
@@zachrodan7543 I quite like the electoral college though, I think it is a smart system designed for something that is meant to not be ruled by simple majority, but through compromise and with federal limitation. You could try and apply what I did to the cities in each state. Maybe it won't span THAT many orders of magnitude, but I imagine some states have cities of a few thousand and other of millions of people. I don't know if you have the data divided like that though...
Welcome to the world of statistics, where all data is nuanced and the conclusions derived thereof can be so varied that there's always something for everyone to take hold of and run away with.
So much this. I have grown to hate having to tell anyone with near any opinion based off statistical analysis that has no idea how to interpret the conclusions that they would do better to shut their mouth before they embarrass themselves further. An idiot can push a conclusion based off some statistical analysis they ran and it could take a small team of PHDs to work out why their analysis is flawed or inconclusive...
Credit to you for putting the summary entirely at the front of the video, for the quick browsers. That is your civic duty at work. (I stayed to the end obviously I'm a stats nerd)
Omg... I know this is an old vid and this comment will never been seen, BUT.... knowing Benford's law, the title piqued my interest. 🤔 Decided to watch and a Biden 2024 campaign ad preluded Matt's video. If I was a conspiracy theorist I'd have gone nuts!! 😂
I get Biden ads. I get Republican ads. I get ads from religious organizations. I get ads from pseudoscientific products. They should know I don't like most of it and they still do it. At some point, they need to just pick people to show stuff to.
Let's be honest: most people invoking Benford's Law don't understand Benford's Law. They are using it because it is an argument that supports what they want to believe (ie confirmation bias), even if the argument itself is flawed. People do this all the time, including you if you are reading this comment. Very easy to spot when someone you disagree with does it, very hard to notice yourself doing it. We should all be a little bit more mentally disciplined about this kind of thing.
What are your thoughts on this? Chicago .....hmmmm! Democrat-run city, in a Democrat-run State, with election workers appointed by Democrat management....hmmmm. Oh, and isn't that one of the cities where Republican scrutineers were banned from being close enough to monitor the counting process, on Dominion vote counter machines (owned by Dianne Feinstein's husband's company) running Hammer and Score-card software controlled by the Democrat Deep State. Hmmmm, I think that might explain the graphical distortions in not following Benford's Law and the lop sided random distribution of POTUS Trump's vote count across the Chicago precincts. Just say'n, that is probably a statistically significant reason to commence a complete audit of the Illinois voting process. Not to mention the rest of the country.
@@jamescarney6894 My thoughts are that this is exactly what I was talking about. You don't want to believe that Donald Trump lost the election, so you bend over backwards trying to prove that 2+2=5. The only way you could believe in this insane conspiracy theory is motivated reasoning.
@Mr. Natural Completely agree! But if my Technical Communications minor taught me anything, you should capture your audience from the start. Plus, this particular video isn't presenting anything that a layperson couldn't readily understand. It would be a nice intro to a stats class, IMHO.
For a while I always thought it was crazy how powers of 2 always seemed to start with a 1 when the number of digits goes up. Thought it was pretty cool that you would get “pseudo powers of two” since the lead digit often went 1,2,4. Then one day I realized that it literally HAS to start with a 1 every single time 🤦♂️
Yeah, but the fact that 2^10 is so close to a round base ten number 1000 is a nice coincidence, isn't it? The pattern basically starts at 256, 512, 1024, 2048... And then not so nice.
Oh, I understand now. This means, "The decimal representation of the smallest integer power of two for a given number of digits always starts with a 1." That took me a while.
Don't forget gerrymandering: the lawmayers have been intentionally rigging those districts for years to come in even MORE consistently percentage-wise over and over again...
Gerrymandering applies to *districts*, though, not to *precincts*. Precincts are small administrative regions within which in-person votes are cast and tabulated; districts are much larger regions that are represented by a given elected official. One precinct's land area may in fact encompass parts of multiple districts! Precincts aren't gerrymandered; districts are. And while I feel that gerrymandering is a serious problem that we should address, it's not a dynamic that would affect the distribution of leading digits among precinct-level vote totals.
Our reporters got an exclusive interview with Benford's Law. It told us it's happy that people have gotten so interested in it over the past week, but asked us all could we please learn the conditions under which it does and doesn't apply?
For anyone who is still wondering why Benford’s law holds, think about plotting data on a Log scale instead of a linear scale. On a log scale 30% of the horizontal space is taken up by values that start with one, 17% by twos, and so on. It turns out that in the real world data is often random with an exponential distribution and not a linear distribution, so the data looks evenly distributed on a log scale, not a traditional straight scale. Hence Benford’s law.
Steve Mould explanation is pretty clear. To go from 10 to 20, you need to multiply by 2. 20 to 30, it's 1.5, 80 to 90, 1.125. You need more momentum to go from a number that starts with 1 to a number that starts with 2, than from 8 to 9.
The first part of your comment (the analogy with the log scale) is correct and very interesting. But the conclusion about "exponential" and linear distributions is incorrect. In fact, Benford's law applies to uniform distributions (over many orders of magnitude, as Matt mentioned).
So did i; it makes me reflect on how much of a better place we’d be in if everyone took the other side’s concerns seriously and addressed them instead of trying to discredit them.
Been seeing benford's law in discussions about the voter irregularities, and this helped clear things up. I already figured it was mainly a tool that could point to fraud, as you brought up, but now I better understand how it could be better used.
There should be a professional sport where you're given a dataset and each side need to prove opposite points via cherry-picking/scaling the graphs, etc. Not that it would be that interesting, but it would be a less destructive way of occupying that kind of people than letting them work for politicians.
It's actually a really important life lesson, to learn how to manipulate data to get any result you want. Because that's how you learn to be very careful when someone else presents you data. Especially if that person is trying to sell a trillions-dollar product (such as a US presidential election). Kinda like why everyone should learn a little magic. It teaches you not to trust your eyes. And learn how to write a bad (but effective) argument. It trains your alarm bells needed when watching media (which will be ringing constantly). Of course the downside is that you'll be training everyone to be utter conmen if they want to.
@@hrgrhrhhr me too.... I think in general it would lead to a more enlightened population who are more aware of how statistics can be manipulated.... along with how the phrasing of a question can change how people answer it
I’m not arguing that Biden won, but i do find it strange that millions of people just decided not to vote this year. And millions more decided to vote in 2020 than the normal trend.
Matt, this was a fantastic video and incredibly impartial and fair, with a great message on the end. Everyone should advocate for their best possible argument and we should all cool our heads and look at these problems in the way that you have. You've set a fantastic example for "both sides" and they all need to chill out and get to work verifying that everything checks out. Its when we don't have people like you doing this stuff do people lose trust. Thanks Matt, this video should be shared around--not because it undermines an argument for the Trump side, but instead because its a cool headed rational explanation and example that its ok to advocate for your position because by only people listening to each other and thinking will we get to the truth of the matter.
Indeed. Hence the assumption baked into binary floating-point numbers, that the first bit of the mantissa is always 1 (or else you have 0, which is indicated by a special exponent value); so you get a free space for the sign, since you do not need to store this first bit.
@@kalebbruwer In floating point, you have to throw away one possible value for the exponent, because you can't represent zero otherwise. But you can use this special exponent to indicate other things than zero, such as short integers or more than one kind of "not a number".
@@bluerizlagirl In floating point, the sign and exponent are stored before the mantissa. I was talking about integers where you throw away leading zeroes. I know that's not a thing with computers, but I wasn't talking about computers.
@@kalebbruwer Floating point is basically the same principle as resistor colour codes. And even "zero ohm" links (in a resistor-like package, for machine handling) have a special marking with one black band.
@@richardm8155 I mean one of the big issues is the fact Fox called arizona way too early. Especially in a state most people would have considered solid red up until this point. The complaints may be valid, idk, but I don't really watch Fox much though.
The thing I loved the most about this is how it explained why in a logarithmic idle game the 1s values stayed the same so much longer as things increased.
Not to get political, but what the hell is a number?
They're some kind of Arabic invention.
@@chazk7530 um actually the number zero is an arabic invention you would now this if you didn't have some stupid L I B E R A L education /s
@@chazk7530 oh I was thinking it was some type of antibiotic
It's racist.
@@SquidwardTentacles225 number sounds more like an anesthetic.
If you write the numbers in binary, apparently almost all the numbers start with a 1
But the law is for base 10, not base 2, dear!
Only 0 in binary doesn’t start with a 1. This is irrelevant for the decimal world
More specifically 100% of numbers start with 1 in binary
@@KhoaNguyen-fs6to benfords law works for all bases.
@@matthewhubka6350
No. There's still zero.
Also I suppose you could right any number with a leading trail of zeros.
I love how you pointed out the importance of context in interpreting data! It's so often overlooked.
Honestly that was the most interesting part about this video
This. So many times i interact with people who don't account for context and just say,"the number don't lie". Of course numbers don't lie, but people can and you have to know the context behind the numbers
@@maxe159 "Senor Joe, the numbers don't lie, and they spell disaster for you at Sacrifice!"
- Scott Steiner
@范德萨阿斯顿发大水发大水发阿斯顿发大水发大水发范德萨我和你吻别我爱你他妈的翔宇我和你吻别元的钱破开该 it's certainly a good question to ask but it's also important to mention specifics. His logic seemed sound to me and if you just say "he could be wrong" without pointing to anything specific, it doesn't hold any weight.
I'd say rather than overlooked, it's often swept under the rug to push an agenda.
Fellow data geek here, this was a TEXTBOOK example of how an analyst approaches their work. Bravo, well done!
'Some More News'. He makes the best
Biden-Roasts.
@@slevinchannel7589 you made it political 😐
@@wizzotizzo No,
i didnt. I literally just said something about Biden-Coverage.
See for yourself: the channel i named literally covers BOTH THE GOOD AND THE BAD.
Yes, i said Both as in 'how unbiased news should work'.
@@slevinchannel7589 you made it political 😐
@@conception3509 you're watching a video on this topic gtfo
Im sure the comments will be all perfectly reasonable and coherent discussion on the complete video.
Phrhbfnxlxir bkdkzuxtzvwn bald man doodoo
Lmao sans from undertale number talk
Especially right now everyone got their anger out at the capitol!
Hahaha!
im joe balden, and i approve this message
The way I see it, these things are like metal detectors. They're great at finding points of interest, but you have to start digging to see if it's a coin or a bottlecap.
Perfect analogy
@JRPGFan20000 I was gonna go with unexploded bombs, but sure, I guess a gun kind of works too. XD
I think this is a fair assessment. I don’t see why people are against recounting the election
Yes. It's a red flag detector. A red flag comes up and further investigation must be done.
@JRPGFan20000 or two pretty best friends
Let's look at the comments section to see what the experts think
The Dunning-Kruger Effect is a hell of a thing. All the gullible conspiracy theorists who haven't taken a math class in a decade or more are suddenly mathematicians, just like how they're also epidemiologists and economists who clearly know "so much more" than people with degrees in those fields.
😂
@@kane2742 .... Laws don't apply to the left. 😂
You think this guy is an expert? If he were a true unbiased mathematician then he would be arguing that Trumps distribution should follow the same pattern if his theory on the precincts was correct.
@@jajajajajaja867 being unbiased doesn't mean that he agrees with your narrative lol
These kinds of misunderstandings are, I think, a subset of a larger problem of people getting 'evidence' confused with 'indicators.' One is often the other, but not necessarily so. The indicator should cause you to look closer, but if you look closer and find no evidence you shouldn't continue to tout the indicator.
Tbf in this case I think the people touting this were just dishonest from the start.
Evidence does not equal proof
@@hedgehog3180 depends. I personally think they were just desperate. I thought from the beginning that it would be close if trump won by any margin in 2020, but fewer in my view felt the same in 2016 leading to many not accepting that election for vert much rhe same reason trumpers didn't want to accept 2020.
It's like many had selective amnesia when it comes to rhe outcomes they wanted.
Yeah. Even The Colorado Supreme Court thinks it was a blowout. No need to interfere this time. [eyeroll]
@@edgunther8136"The absence of evidence is not the evidence of absence."
Getting some insight behind the votes from a mathematician is refreshing.
Even better then it comes from a Standup Mathematician!
@Stephen Thacker how so? I live in Michigan and a lot of us are flabbergasted.
@Stephen Thacker supply a mathematical proof then
@Stephen Thacker I need proof plz
@Stephen Thacker can you explain further please?
Thanks for mentioning my name and my work starting at 3:56 :) I did an analysis of the Maricopa County election results and got pretty much the same patterns. Here's an interesting tidbit... At 2:00 you talk about the populations of the 3,141 counties and Benford's Law. At 13:25 you talk about the digits in pi, .... and, of, course, the first four digits of pi are 3141 :) You went full circle or 2πr.
WOAH it’s the man himself
...autograph?
only a mathematician would notice this... nice one, man.
You've clearly done some seriously good maths work but, honestly, those jokes. Call me irrational, but I love it when a tangent turns into a punch-line.
@@ElevatedKustoms link?
County precinct groups are too uniform. Benford described the nature of numbers on a larger scale, so if you cherry pick a city block, or man-made precinct and chart the the leading digits, it will fail as bad any of the full state chart by county assessments of in the swing states for Biden counts. Or, blue state, Trump counts. The selective adherence to the law is suspect.
They need to start bringing out maths experts on election coverage, its not like they don't have huge amounts of time.
Mathematicians don't have time for stupid elections
@@poorman-trending nah, more like most people watching the news won’t care abt a mathematician and just arguing over nothing somehow brings in better ratings and views
@@poorman-trending Exactly, and I would guess a mathematician wants nothing to do with politicians for this reason--or maybe they would because they want to show them what the truth actually is?
@@maxwellsequation4887 Perhaps they should, we need them voting.
@@maxwellsequation4887 Pretty sure they do. It just the general public is less likely to listen to a mathematician than a celeb or political figure, thus lower rating for news organization.
I really like that you compared side by side the digit pairs of pi with the last two digits of Biden votes. A very clever way to impartially show the expected variation at that sample size. Without that comparison, people surely would be looking for patterns in the noise, which as we know is a dangerous thing.
If PI is carried to millions of decimal places there are many of what would seem to be improbable strings of numbers such as "1234567890" or "1122334455667788" or "666666666666", but it always breaks out of these patterns.
@InSomnia DrEvil wym again
@@swinde yup, have 1 million monkeys randomly pressing keys on a type-writer for infinity and you get a quote from shakespear at some point
@@arronaltI always thought that the saying referred to the Tale of Two Cities just because of that scene from the Simpsons. "It was the best of times, it was the...blurst of times?? You stupid monkey!"
@@fortcolors9887 He's meaning 'again' as in the original accusation...
This is why statistics is a degree and profession, and not a topic.
That's true for so many current issues.
@Rye Bread lmao that was great
I'll just leave my disagreement here. Plenty of stuff you can discuss without a degree. Just because you might get it wrong doesn't mean you shouldn't discuss it
I believe that Mark Twain had an adage, “You have lies, damn lies and statistics.” Based on this it appears you can use several different number sets to argue whichever point you are trying to prove. I have found that looking at the process to outcome is ultimately the only way to actually prove a thing. But as he said, these are only used to determine if something needs to be investigated. It appears that, in the case of Chicago, that a closer look is needed.
Statistics is definitely a topic though?
Just took a math stat midterm and one of the trick questions hinged on verifying that the data were random! Very relevant to this video.
Maybe you should revise, because data being random is only relevant when we’re sampling the population so we can make sure it is close to the population, but in this case of election we are looking at the entire population, meaning every single vote. We don’t sample the votes for the election, we count them.
@@anandrai492 yeah, but if the question is "how well does chicago's districts of roughly 100 to 1000 fit Benford's law" the answer is gonna be "not well". Gotta check your data before you try to fit them to something and draw conclusions.
(And the question on the exam was about predicting an election based on a survey and finding a rejection region such that alpha, the chance of a type 1 error, is less than some value bla bla - which only worked in the question if you make sure the survey was random and only then can you apply the CLT and estimate it with a Normal)
@@bzboii I took stats and got a B
@@bzboii or you can just focus on something else besides the raw count like second order or summation. www.researchgate.net/publication/319526944_Benford's_Law_The_Second-Order_and_Summation_Tests
Surprisingly educational video for what I thought was going to be mindless political clickbait.
This guy's agenda is nothing political: he's peddling his fantastic book!
He's British lol
@@tangyspy *Australian
@@tangyspy does his nationality affect my statement? I'm making a reference to how he mentions agendas in the video, and how this appears to be a protracted ad for his book 😂
Sure, that also means that, knowing the initial digits, no one has been able to distinguish it from a normal number. The non-randomness would have to be "further down".
Its a good book!
1:58 Let's not get distracted that there are 1000π counties in the US
That’s wack
Mmmmmm, a thousand counties with pie.
@@GoatPopsicle Gotta catch em all.
I hate how close to reality this statement is.
1kπ
As someone who lives in America, I find this video very interesting! Thank you for creating!
Where did the 15,000,000 votes in 2024 go?
Lmao just take the L, its already below 4 million votes with votes still being counted (which should've been done the day after).
Less popular candidate gets less votes, not everything needs to be a controversy 😅
Shhhh… you are not supposed to notice patterns, you are supposed to swallow what media tells you and call the Orange Man bad!
@@edar8881 Printers go brrr.
The 15 mil deceased voters who voted for Biden didn't endorse Kamala
More people need to understand how statistics can mislead you, and how misleading people can make statistics lie to you
@@paperburn Ironically Bill Gates favourite book is on that subject.
@@diesel92kj1 "92% of all statistics are made up on the spot!"
It's a standard government/business/PR tactic: present the statistics' results but never reveal how those statistics were derived. As a simple example look at washing-machine detergent adverts (or any other adverts based on provable results rather than aesthetics): they all claim they're the best, but what is 'the best', & under what conditions?
You can also move the goalposts by adjusting the size of the sample: '9 out of 10 cats prefer it' sounds great, until you realise that only 10 cats were used to test the food (& they were prolly preselected from certain specialised parameters anyway) :)
@@snafu2350 Interesting concept...I didn't know cats used washing machine detergent! LOL (I have to laugh at my own jokes otherwise there would be complete silence. It's a well known fact that 9 out of 10 comedians laugh at their own jokes... Is it just me or is thing going round and round in circles?)
@@snafu2350 It's something I enjoy about UK adverts - they do have some legal requirements about explaining where the result of the survey comes from, sometimes you even see text like "out of 87 people surveyed" when a shampoo is talking about being preferred. Radio ads are even better as you get someone trying to quickly rattle through all the legal disclaimers etc at the end, but they have to do it slow enough that you can still understand them. Still not a perfect system, and you wish the audience were better educated about sampling error etc, but it's nice to still see it
The takeaway: if you discover an anomoly, you actually have to investigate the source of said anomoly before you can accurately say you know its cause.
Studying the anomalies, rather than the commonalities, might produce some interesting insights.
We know some athletes are enormously better than average. We can ask what role does economic status play into their performance?
I like both W J and Jeff original comments !
The problem is that all places where anomalies are accused, seem to lock up and hide the data to substantiate their “certification.” Sort of like Pfizer asking for, what, 95 years or something before disclosing the study data on the vaccine? Quite equally, and scaringly similar when you think about it.. but you probably aren’t concerned or see the analogy ;)
If I understand what you're saying, I agree. For example, the anomaly in the Trump vote tallies compared to the Biden tallies may, I suspect, be explained in several ways, but most of them having to do with the programming of the voting machines, or how the results are calculated after they're input.
What algorithms could be used to modify (just assuming hypothetically, not claiming they were) the election results? Would they take into consideration the possibility that some of the data coming in are invalid? How would they handle for example, a massive input illegitimate votes for one candidate over the other? Would it try to compensate by manipulating the data for both candidates to resemble expected outcomes, according to what forensic analysts might expect? The idea being to hide the cheating enough to make it look legit.
I'd like to see an analysis like this this one across a larger sample, or better yet, across two larger samples, one of states that reported no "irregularities" compared with a second, of the collection of states that reported substantial irregularities. That would be interesting...
Exactly, another great example of this is his "Perfect Bridge Game" video where he explains away the anomaly of a 1 in 2.2 x10^27 event occurring not just once, but several times.
"AND ELECT ION DATA"
To be honest, if there were someone named "Ion Data" running for any position, I'd be very tempted to elect them based on the name alone.
This reminds me of that time an acquaintance called Justin Case blocked me from Facebook because I wouldn't stop unnecessarily tagging him in my comments.
Elect Ions are a bit of a charged subject.
ION DATA 2024
Science is right and the media isn’t, also humans suck
I would elect ion data if it weren't for all the negative energy around, everywhere in their campaign, up, down....strange....I'll get my coat...
I, for one, welcome our new, presumably robotic, overlord.
"The moral of the story is that everyone has their own agenda they want to push on you.......check out my book Humble Pi!"
Awesome
I mean, at least his agenda is clear, and not harmful to the discussion
That’s why he didn’t do an analysis of Milwaukee.
@@melanieb8746 Whats up with Milwaukee?
What's wrong with advertising his own product in his own video? Is it really worse then all the VPN ads?
I'm going to use this pinned comment to reply to the most-common questions/complaints. It'll be updated infrequently but I am trying to read everyone comments.
- WHY DID YOU ANALYSE DATA FROM CHICAGO NOT A SWING STATE?
Good question. It is because the first Benford-Biden theory I was sent was based on the Chicago precinct vote totals (there's a link way down in the video description). So I analysed the same data they did. I did not choose the Chicago dataset: people claiming election fraud did. You are very welcome to analyse data from elsewhere and show us your working.
- WHY DOES TRUMPS PLOT MATCH BENFORD'S LAW?
It does and it doesn't. I was going to say in the video that Trump's plot is also a bad fit for Benford: there are way too many 1s and then fewer digits from 3 up. That spike of 1s is because Trump got an overwhelming number of vote totals between 10 and 19 and so at a glance it looks like a good fit. I cut that bit though as the video was going to be as long as the election.
- SOME PEOPLE ARE CRITICAL OF THAT PAPER YOU QUOTED
In terms of legitimate criticism, you are probably thinking of Walter Mebane and I have linked to their papers in the video description. But they specifically disagreed with how 'Benford's Law and the Detection of Election Fraud' (2011) treats the 'second digit' check while still agreeing that "It is widely understood that the first digits of precinct vote counts are not useful for trying to diagnose election frauds."
- A STRING OF DISJOINT WORDS AND EMOJIS
I'm not sure how to constructively engage with that, but I'm glad you watched the video and wanted to get involved with the comments. I thought I did a pretty good job of being all-math-no-politics in the video but appreciate people are very passionate about these things. Other commenters: I encourage you to engage constructively wherever possible and 'down thumb' anything untoward.
- IS THAT TRAILBREAKER ON YOUR SHELF?
Yes it is. It is exactly what meets the eye.
That was an enlightening video, Matt. Love from Brazil.
You made math not boring. Congrats.
@@Robbya10 trump's votes had a less robust distribution than Bidens in Chicago though
@@Robbya10 no lol he just got like no votes in Chicago
I think it would have been more interesting to compare 2020 Biden in Chicago to 2016 Hillary in Chicago than 2020 Biden to 2020 Trump if you are going to use just one city instead of national data. Else, we are comparing apples to oranges. Good explanation otherwise on the precinct size rationale.
2024 here . Where did 20,000,000 of them go?
Where did you get the 20 mil from? Harris got 75 mil votes, compared to 81 in 2020, trump 77 mil, his margin is barely mediocre. Mate you don't even understand how elections are called, the election was called before even half the votea in California were counted in. Oh you clown 😅
20 million Trump hating democrats stayed home to let him win? Really???????
Maybe they never existed......
They were never real.
They stayed home
@@Trash_owo millions of Trump hating liberals didnt stay home to let him win. Their names should be on voter roles. So you're saying those millions of liberals were sick of the liberal crap too.?
But wait this doesn’t fit my biases
It also doesn't fit the facts.
@@pitapocketortwo buddy, you can’t get more factual than this mathematics youtube channel.
In that case reality must be wrong.
@@pitapocketortwo no, he means biases
@Joshua Jason Karl i do lol and this guy agrees with the other educated sources
There's an implicit narrative here that worth making explicit. When it comes to data analytics, the proper question to ask is: why do I have the data that I do? If you simply take your data and analyze it without considering how that data was generated (both collection methodology as well as the phenomenon you wish to understand), you will probably completely misrepresent the actual reality and fail to really understand why you had that data. I suspect this happens *a lot* in practice, especially when companies do data analytics for a myriad of reasons and often have less than stellar data collection methods, let alone failing to consider the real-world process responsible for the data and what, therefore, they should expect to see.
Justin, In Chicago's Graph, Trump's Benford curve shows significantly lower 3's and 4's. That looks like Democrats are THROWING away trump votes in the 300 and 400 and 500 count precincts THUS forcing the 1's in Trumps to be abnormally high.
Second, for Biden, those Blue Democrats are PADDING (adding illegal votes) in the 100's, 200"s precinct counts and making them into 300's, 400's and 500's and 600's. There are no examples in elections that show standard bell curve except Blue Democratic cities which have decades of high-level corruption outside of vote counts. Those cities are complete ghettos with decades of declining population.
@@foundingfathers4462 You didn't watch the video, did you?
@@ThisIsMego nope
@@foundingfathers4462 Ghettos with declining populations? Never been to a big city have you now? News flash! Some people hate Trump! In cities with over a couple hundred thousand people, it’s a different world than most red counties. I suggest you go to a big city with your Trump flag and conspiracy theories and see how many times you get cursed out.
@@ThisIsMego From the ignorant analysis in his comment, I don't think he'd understand the video even if he did watch it. A nice example of the Dunning-Kruger effect.
Benford's is an acid test, it can be used as an indicator of places to look, it doesn't mean they are not explainable. For forensic accountants alot of the time the evidence is circumstancial and indirect.
this
Good way of putting it.
yea so if you see something unusual it should indicate to investigate, it is not proof in itself.
he literally says this a number of times in the video
The numbers can NOT lie as they are not human.
Compared to Bidens normal distribution, Trumps vote counts are best described by a Poisson distribution, which is a pretty sophistacated roundabout way of saying, that Trump just ain't popular in Chigago.
Lets take a look at crime statistics in Chicago while we are at it. Oh. Oh my.
@@CarpetFTW cope lol
@@CarpetFTW What's the argument you're trying to make? Cmon, spit it out, don't just dogwhistle.
@@stellanightsk He's just pointing out the fact that statistically, Chicago has high crime. There wasn't an argument, there was a joke.
And if we look at election results from years prior, we'll see a trend emerging. Republicans just ain't popular in Chicago.
As a retired stats prof (hopefully not Dannycode's), I wanted to thank you for clearly explaining your process and the underlying theories. I'm always (yes, still) looking for interesting examples of phenomena. to use.
As a retired Professor, what did you think of the the presenter in this video using the second digit distribution to justify the Benford result in question for Biden, but then using the Benford result for to justify the second digit distribution in question for Trump.
@@fomori2 most underrated comment so far. I'm an accountant, and elections are perfect use for it. I use it as a litmus test for finding irregularities in bulk data.
Here’s proper use of Benford’s Law for elections.
ua-cam.com/video/1ald3w9FBmA/v-deo.html
@@fomori2 what?
@@JamesWolfpacker Did you learn nothing? Stop spreading misleading information as if you're not literally commenting on a video debunking the snake oil you're selling. Shoo now.
The one bit about the random data anomaly due to some employee's breakfast made me laugh out loud. Great video.
Trying to rip off an auditing company sounds like a great idea
@@Stargazer1312 Sounds like a good challenge for some.
Thank You for a non biased look at this without going political.
@@mangonel One might say facts don’t care about your feelings
Also roll tide
@@mangonel sure doesn't feel that way when you are in a class discussing bayesian statistics...
Roll Tide Baby!!!!!
@@mangonel I am going to be an annoying pedant here and say that this is technically correct (the best kind of correct), but in reality people collect the data, choose how to analyze it, select the scale on graphs etc. so there is plenty of room for biases to sneak in
@@mangonel stats sure as hell isn't.
Who's back after 2024 election
I’d like to see Matt upload a video explaining where all the missing votes went. I like this channel and his books, but the dude comes off as a total hack now.
He calls everyone 'they'.
@@accidentalfinder4916 Only to the ignorant...
this video age like milk 😂
I'm about to see if it's bs or not
"While I have you here" - I'm still here Matt, trapped. Please, release me.
😂
The cutest comment I've ever seen
This a solid, apparently impartial exploration of the topic. Would be nice if the media had as much respect for its audience as you do yours.
@Gideon U Settle down, "free thinker"
> Would be nice if the media had as much respect for its audience as you do yours.
Realistically, the general media is not going to go into a topic at the mathematical depth a math-focused UA-cam channel is going to. That's simply because the audiences are different.
@@henryptung If they're incapable of or otherwise unwilling to address certain topics they should stop speaking as an authority thereof.
Unfortunately for the media, "respect for its audience" doesn't really bring in the click-bait revenue like oversimplified sensationalism does.
@@Maus5000 lol trusts talking heads.
I'm a retired forensic accountant. I'd be happy to explain forensic accounting to anyone who wants to know about it. I should warn you that there's a great deal of statistics involved and attention to detail is mandatory. As a general rule, the only people interested my explanations are other accountants. After a few minutes everyone else discovers that the topic is less fascinating than they thought.
Do some YT videos ;)
I’d be interested. Took accounting in college from a forensic accountant.
Hey man i was wondering what is a good place to study this on my own, this election got me really interested
I'm starting out in data and I would frankly love to chat about forensic accounting! I've done some reconciliation and QA and analysis, but none of it really involves intense stats and I'd like to do more than just make pivot tables in excel haha
Hey man, I'm actually interested in forensic accounting
I do love how you pointed out the unusualness of the data on both sides, presenting it as strange, then showing how it’s not.
If you had just done this for one side or the other, and left the undisclosed one up to viewer interpretation, it would have been biased, and not an “impartial step back”
Guy makes complex statistical analysis look like algebra for beginners
Because it really is.
@@davidz2690 Twit off ya spoon
@@57thorns if it is than it’s not impressive at all that you can do it
it's not complex analysis
This is not complex math in any way( complexity wise nor complex numbers lol)
I getting tired of seeing the us election banner ad from UA-cam
How do you turn it off?
Ditto. I wish there was an 'I get it; don't show this anymore' button
@@ajmoe YOU CAN'T. THEY NEED TO KEEP BRAINWASHING WEAK MINDS.
I don't see it. Did they stopped doing that or they are doing it now only for US?
@@elenabob4953 I've never seen it, must be US exclusive.
I love how objectively this video is made. No jumping to conclusions, no accusations, no unfounded claims, just mathematics :) and the fact you didn't just answer the question, but started digging deeper into things like the so-called Trump Tower, it really shows why you make such a good teacher!
If only other people think objectively like this
@Johnny Five check Maricopa county, that one has the same problem
@Johnny Five well you can do it yourself, it's really simple, download the data, put it into excel and take a look at it.
@@roycebutler8590
Is it possible the precinct populations there are equally as clumped into an order of magnitude as Chicago's is?
@@leongkinwai9709 I'd be shocked, it's a very red county, and it still wouldn't make sense because that's not really how benfords law works
the only thing i really learned was use a random number gen for filing false tax returns :)
Let's check if these data are random!
Statistician: I'll use chi squared test.
Matt Parker: I'll use it as an excuse to put pi in my video.
😂
“These data are”, “this datum is”
@@nelsblair2667 thanks, I have corrected.
69th like
chi_squared gives you one number to test for significance. Matt's idea (a great one) is to give us a picture of what random data actually looks like. I am very impressed. From mere observation, it looks to have the correct mean and s.d. _ a beautiful illustration.
Fantastic video. Textbook example that a light touch is often better than a heavy hand when engaging with such topics. Many youtubers seem to cripple their own perfectly valid points with unnecessary subjective filler.
This is what I've been trying to say about all discourse in America these days. Thank you for putting it into words
Here is a far better video on Benford's Law.
See STEP #1 for the video on Benford's Law
www.foundingfathers.org/Papers/Politics/BenfordsLaw_n_ElectionFraud.aspx
@@foundingfathers4462 singingbanana, nice
yeah, that's a good video, from a great mathematician (also happens to be a friend of Matt Parker)
not sure, why it would be far better though, says pretty much the same thing from what I remember. In particular it also says that the data has to span multiple orders of magnitude, which is why you wouldn't be able to use it in this case
what do you mean "unnecessary subjective filler"?
@@silversilk8438 anything that could make the video sound like it has an agenda or anything that sounds condescending. It’s an easy way to get people to refuse to accept your points. Even if they’re otherwise accurate.
How to make a Matt Parker video: explain an interesting math topic and find a way to throw pi in it
It would be irrational not to
funny thing, in the book "Humble Pi", pi only really appears in the title
I'm wondering why he didn't use tau instead.
In videos where it isn't featured, it still is, just as iπ
Gotta make it very clear to tauers he's in the pi camp
I feel so unburdened by what might have been.
12:15 "There was a spike at 82 because one employee was claiming their breakfast on their way to work every day, which they weren't allowed to do. You can only claim breakfast when you're on the road for work purposes."
*Employee: commuting is for work purposes.*
Someone needs to start their day at the home office then move to a main location on the company dime. (well $0.82) but you get the idea.
@@medleyshift1325 That muffin and drink cost more than $.82, the frequency of the .82 is what called attention to it.
@@JohnDobak it's a play on dime sorry for not being more clear.
Love this. You can tell any story you want with data . Digging in an seeing more than 1 aspect of the data is where you start to be able to call out anomalies and ultimately see a holistic view . Well done !
I'm just glad to have made it into one of Matt's videos. I'm one of the data points on the chart!
Glad you could spot yourself as a datapoint. Like a bar-chart version of Where's Waldo?.
If I zoom in really close I think I can see you.
“Hey, I can see my vote from up here!“
@@standupmaths Who the eff is Waldo?
@@standupmaths Sad that only people from Chicago can feel the love here, though I kind of understand why other cities and counties are out of the question.
I'm gonna need this video close at hand this year
Sadly, I think the game this year is going to be selecting people to be election observers from the Republican party who are going to be making claims in bad faith to distort the process. I wonder if the Democrats should try to invite UN observers in, though I don't know what can cut through the Republican's echo chamber. All the while places like Fox, OANN and NewsMax are seeding disinformation, a number of the voters aren't going to listen. With 2020, all the claims were easily debunked and coming from dubious places. I hope I'm wrong, but this year my bet would be there are going to be lots of supposed issues reported in count rooms etc - and lots more waste for the American taxpayer...
@@neilbiggs1353 So claims are only false when y ou r enemy is making them. Actions are only crimes when y ou r political enemy is committing (or even just being accused of committing) them. Beliefs are false if y ou r political enemy believes them. And people are not victims unless they agree with y ou r ideology. Do y ou know what a cu lt is?
@@guillermoelnino I know what a cult is - it's when a group of people buy in to everything a pedagogue says without critical analysis. You know, like when they keep trying to claim an election was stolen when the evidence says otherwise, when the lawyers pushing the claims are being sanctioned, disbarred and convicted, when they are paying massive defamation suits... This isn't difficult if you have any ability to parse information...
@@neilbiggs1353 ok cultist
@@guillermoelnino I love the intersection of ironic or moronic that you represent! Calling people cultists when you are clearly indoctrinated by one of the most incompetent liars in US political history. You'd think the blatant lies that he has been shown to have made in the New York cases would get through, but there are none so blind as people like you that will not see!
I saw a documentary on netflix about Benford's law. I was screaming at my screen when they kept on claiming it was kinda "magical" and no one knew how and why it worked.
lol but I guess it's true in a philosophical sense nobody knows why 1+1=2
@@nmarbletoe8210 maths is a game and those are what the rules say, so. The astonishing thing is the ways in which we can use maths to interpret the world
@@nmarbletoe8210 well, it's an axiomatic truth, the tools to prove it with logic aren't hard, just redundant
@@nmarbletoe8210 tachyos.org/godel/1+1=2.html this is literally the formal proof for why 1+1=2
N Marbletoe There is actually a mathematical explanation on why 1+1=2. But you need to go deep and use set theory for an explanation. 1+1=2 is a mathematical statement that can be proven. Even the existence of zero is actually proven under ZFC.
Regardless of this data, the one's who don't want to verify and look into anomalies have something to hide.
You are referring to Trump's tax returns?
Right! Which is why I don't trust these "scientists" with their round earth theories. They're tired of me asking them to verify the data according to my needs, say it's a waste of money. I know they're got something to hide.
@@garsm2290 The IRS does that automatically, even more so for those with large finances. The fact that Trump was never charged EVER means his tax history and payments were all lawful. Despite it not being public what anyone owes or has paid in taxes, the IRS and the government does and concerning Trump's business of property and building development much of is in New York, you can't simply not report and you can't just tell the city your building doesn't exist so you don't have to pay that years property tax. I guess a bunch of naive college kids who own nothing and assume mostly everything about much of what they think is true wouldn't really understand this yet or bother to think it out.
@@nlsantiesteban Noel, come on. Your claims of the earth not being round is hardly comparable to either holding or not holding the most powerful office in the world for the next four years.
@@nlsantiesteban you mean the round earth that was investigated and debunked by people asking questions and then getting people to prove it?
As long as people investigate and aim for transparency that's fine by me. No single data point is going to be sufficient.
Scotus has ruled in favor Benford's Law several times including Enron case and it was way more tame then the 4+ deviations we are seeing in some the big cities in swing states
Hacker, you *did* watch this video, right...?
@@Kaoskadosk hope u know Trump's result may have actually been tampered with and that's y I wasn't random anymore... Please do a critical thinking of this, who cheats himself out of an election on a slim chance of winning in court?
@@cozmik_kay i agree, but the examples in the video are bad because no one is contesting Chicago's results.
@@lostalone9320 Yeah, except in this case it's regarding election data, which as this video points out, is pretty pointless to apply Benford's law to.
Guys stop commenting about wanting to see the comments then we won’t get to see the comments we really would like to
Tom Scott: "you can't trust me"
Matt Parker: *writes that down*
Weird Idea: they "plotted" it xD
TS: "But you can like me"
- Source: Madeup
I have a lot of respect for the fact that you didn't just stop at "the trump one looks suspicious!" and actually explained why both claims are faulty.
That kind of honesty, regardless of where you stand politically, is something we need WAY more of in today's world.
I think that's what Trump is looking for. A validation of EVERY SINGLE LEGALLY cast vote. The only thing I will believe is if they contact every voter to verify their votes.
@@PayNoTax-GetNoVote while that would be great, wouldn’t you say that’s impractical? Should we do that for people who voted in 2016? What if people change their answers over the phone because some guy is haranguingthem? What if people, knowing that race was so close, change their initial vote?
Jesus, get real. He lost, hopefully the investigations complete and assure everyone that, yes, that’s true. Assuming he didn’t lose without evidence is conspiracy thinking
@@iMasterchris Also, the way some people are talking now, if some random 'phones my house and asks about my voting, I'd put the phone down and draw the curtains
Thank you for actually explaining the answer to a question a lot of people have. Much more useful than the little warnings social media companies have that "Election fraud is rare according to the AP" or whatever.
Big tech thinks you are too stupid to handle it
@@fromdarktolight6353 TBH most Trump supporters are too stupid to learn anything
Shut up
"Here's a rubber stamp from our political donors, don't ask questions please."
@@antiantiderivative Ah yes, you’re one of those “open-minded” and “tolerant” lefties.
My sister got me Humble Pi for Christmas, and I had no idea it was you until I got to the end of this video!
Your sister is awesome
Lessons learned from this video:
Use Benford's law to detect weird data results and then research why the results are the way they are to find out if anything is wrong.
Context people, context matters
Agreed. Statistical models are not definitive last court of appeals. It is as you said, research why they are that way and this Law is still a good rule of thumb. What is good for the gander should be good for the goose, my question in this presentation is but why would Trump's numbers follow Benford's all things being equal it should behave like Biden's too.
BLM= Benfords Law Matters too
@@lpcruz5661 this question is literally answered in the video. Watch the video before commenting. Otherwise, you come across as simply willfully ignorant for asking questions that have already been addressed.
@@LoveJoyPeace4612 I have indeed watched it till the end. I believe my comment is fair. He explains why Biden' does not. Then you can explain to me why Trump follows Benford's? Did he include p-values? He quoted a 2011 paper, well there are recent researches on Benford Law, see this journals.plos.org/plosone/article?id=10.1371/journal.pone.0151235
@@lpcruz5661 Trump's results don't follow Benford's Law either. There's far too many ones and far too few middle numbers. As he showed, that's because half his actual numbers were below 60, and I bet most of those were between 10 and 19.
When I saw Biden's Benford distribution being used on twitter arguments and was googling expert opinions, I was expecting more depressing political articles but instead I discovered this delightful mathematics youtube channel
I feel quite lucky to have stumbled here
@@420atheism just like the people that mentioned the law in the first place
BIDEN WINS.....BIDEN IS THE 46th PRESIDENT.
@@420atheism It's almost as if you haven't watched the video!
Matt is amazing and the math puns (and Parker Square memes) are really funny.
@@420atheism As a fellow stoner i can only recommend you to take a smoking break for a month and think about your life decisions. Because i think some are not the best
I did one statistics and probability course in my third semester of engineering. All I have ever been doing now is watching statistic videos.
I hate this subject. But I love it. Help.
Lol so true about stats
Most annoying math to do but the most beautiful math to see
Mood
You and me both!
All my Stats professor ever talked about was gambling!
Same, but biology
I applaud you for making a video about politics... about maths.
What I've learned from this video: don't have the same breakfast every day
And always roll a die when choosing.
@@nicothoe as a Gamemaster, dice aren't that good at being random either
@@ijemand5672 Why aren't they random enough?
What I haven't learned from this video, because I knew it already: Numbers in tax returns and accounts are not random.
@@ijemand5672 dice are very good at being random.. a 6 sided dice has a uniform distribution to all of its faces, it's pretty good at being random unless its loaded
"You only get Benford's Law in SOME situations."
So it's Benford's poorly enforced law?
Benford's understaffed police station
Benford's suggestion.
Lets build a wall around it
benford's US police force
In Minnesota they'd defunded enforcement of statistical laws, and now there are outliers running wild.
As an wise accountant once said:
"I only trust statistics I made up myself"
made up or made?
@@ajinasawor "made up" or shuffling your data around until it suits you.
@@Playerdelta08 an accountants job is just making stuff up.
I trust numbers, but the conclusion of those numbers is something that can differ. Take climate change, 415ppm co2 in the air is 0.04% of the atmosphere. It SOUNDS small, but is it really small? No, it covers perfectly in the holes of water vapor, and is actually quite a huge number relatively. A small number, that has a great impact.
It wasn't an accountant who said that, but a propaganda minister. A German. Some Joseph Goebbels, look him up or watch Der Untergang. And he said: write in the papers that Winston Churchill said this.
Biden's Law is when 15 million votes appear then disappear.
Abracadabra! 🎩🐇
13:20 Matt: i decided to compare it to the first 2069 digits
Me: there must be a spike at 69 in random numbers chosen by people
...or it's the same as the number of precincts in the Chicago data set.
@@Khaim.m For this case it is. But removing one case from the set doesn't invalidate Kalpit's hypothesis. I'd be surprised if there's NOT a spike there in human chosen numbers. I'd expect to see a few others in there as well.
@@arfyness Might you know any places where I can find an accurate survey of random numbers? I think analyzing it might be fun before I see what others have to say about it.
@@Khaim.m Or Chicago chose to have 2069 districts because it ends in 69.
@@Khaim.m They could have had 2070 precincts instead. But nooooooo, they had to pick a prime number...
Awesome analysis showing how "science-based" arguments aren't always what they seem.
Yea usually, people that scream science as proof of their claim don't actually understand how the scientific method really works. It has become quite rampant with the politicization of science.
Kind of like global warming right?
Only if people don't understand the science.
@@takinasteamer Except basically it is accepted throughout the scientific community as fact... Which is not what the OP meant!
"Here's a chart that agrees with me"
"Is that really what that chart says?"
"No, but people don't usually double check."
As a Republican and a Trump voter, I thank you for your video. That really helped me understand the concept. I wanted to check and see if any of the arguments stood up on the other side, and they do. Looking at both sides is so important. Thanks a lot. Love your video.
I don't know English, but I'm wondering, judging by the video, the elections were fair or not? (there are simply no subtitles and I don't understand, but I'm very interested)
LOL - Everyone knows the Dem's cheated>
You can't win the house and legislature and lose the presidency. It's impossible. Who would vote for both sides ?
@@adelarsen9776 do you even live in the Û.S.?
@@adelarsen9776 the house is proportional which means it should fairly closely follow the desires of the people, in this election it did, with the dems leading. The senate is by state, and there are more red states than blue ones, so we should expect too see a slight red lean, and we do. The presidency is by the electoral collage, which leans red compared to actual votes. This is because of a bias towards small states and most small states are red. This is why there has only been one republican president to win the popular vote in the past 5 elections
@@adelarsen9776 Many people (including both Democrats and Republicans) didn't like Biden... but didn't like Trump more. Part of those million of votes weren't for Biden, they were against Trump.
Who has gone back to this after 15M votes for dems dissapeared?
Except it wasn't 15 million. It's less than 7 million. Please stop spreading information that is inaccurate. All that being said they absolutely stole the 2020 election and they tried to do it this time too and this is coming from somebody who didn't vote Republican ever in his life until a few weeks ago.
@@Jason-TheChad-Muska_circa1995why believe something like that? There's no evidence for it
Where did you get the 15 mil from? Harris got 75 mil votes, compared to 81 in 2020, trump 77 mil, his margin is barely mediocre. Trumps popular vote was less than 50%. Mate you don't even understand how elections are called, the election was called before even half th votea in California were counted in. Oh you clown 😅
nothing like sorting youtube comments by recent to lose your faith in humanity
I feel called out
One of the most real comments on youtube.
Thankfully, most of them are just “interesting video, thanks!”
Would be worse though if those comments were found at the top instead.
It seems to go in spells - you get batches of people who watched and understood, then you get ignorant goons posting sequential word vomit as they get triggered by something being debunked, a few complete morons who beg for the ineffectual law to tested on other states (to prove what exactly has never been revealed...), then some people who would be sued if they tried repeating their baseless claims on TV...
I tried using Benford's Law in my country election a few years ago, grouping by cities (instead of our precincts, which are called "electoral zones"). Cities across the country span several orders of magnitude in population, so it checks that box. Every candidate followed benford's law pretty closely, from what I remember.
Of course with this method you have the problem of only looking at the global results of the election, so potentially a localized fraudulent data could be hiding amid all the other genuine data that was generated across the country.
Thank you for letting us know. There aren’t many people analyzing data. Mostly talking theory.
I even remember articles seeing the same nonsense 2016 when Hillary lost but I don't remember people debunking it and insulting and attaching people for not being a statistician. It's amazing that people can died in Iran because of this and people stay silent but when the guy you support has to deal with a legal process it's an outrage.
if only such an approach were even relevant here in the U.S.
unfortunately, as the start of the trump presidency indicated (along with 6 other presidential elections since 1980), the popular vote doesn't determine the presidency. because we still rely on a system from when the nation was formed, and which was probably only needed to begin with as a result of half of the country wanting to count 3/5th of their slave population in their political power without actually giving the slaves any say in the matter. As for why we didn't switch to the popular vote after getting rid of slavery, and in doing so also getting rid of the need for the weighted voting system that is the electoral college, I have no clue. probably either because when the amendments at the time were passed banning slavery and extending equal rights, people weren't even considering that the electoral college would become a problem (and every subsequent time the constitution has been amended has been at a point people weren't even considering it to be an issue), or else because it still gave some states more influence that they were hesitant to give up. And the reason we haven't gotten rid of the electoral college system since then is likely because doing so would require a constitutional convention (which opens the entirety of the constitution to changes) and any changes need a 3/4th majority to pass, something which is unlikely to happen with how divided the country is (and it doesn't help that every time the electoral college and the popular vote have disagreed lately, it has been the republican party that benefits from the discrepancy)
Are you a election manager?
@@zachrodan7543 I quite like the electoral college though, I think it is a smart system designed for something that is meant to not be ruled by simple majority, but through compromise and with federal limitation.
You could try and apply what I did to the cities in each state. Maybe it won't span THAT many orders of magnitude, but I imagine some states have cities of a few thousand and other of millions of people. I don't know if you have the data divided like that though...
Commenting to help this quality video get on more people’s feeds
It worked. Gracias!
It worked
Commenting on your comment, to make the algorithm show it to more people.
@@Cory_Springer reply to your reply, in order to- sh$t my quesadillas are burning
Much appreciated
We all know why.
Welcome to the world of statistics, where all data is nuanced and the conclusions derived thereof can be so varied that there's always something for everyone to take hold of and run away with.
Lets assume the votes are correct, but how they reflect into the college voting system is a bit off.
Nailed it...
Not really.
Statistics is just one piece of the puzzle. Look at all the other foul pieces and you have your truth.
There are lies, damned lies and then there are covid19 statistics.
So much this. I have grown to hate having to tell anyone with near any opinion based off statistical analysis that has no idea how to interpret the conclusions that they would do better to shut their mouth before they embarrass themselves further. An idiot can push a conclusion based off some statistical analysis they ran and it could take a small team of PHDs to work out why their analysis is flawed or inconclusive...
Thank you for being an entertaining educator, the world needs more of the same.
Credit to you for putting the summary entirely at the front of the video, for the quick browsers. That is your civic duty at work. (I stayed to the end obviously I'm a stats nerd)
I am going so far to say that the whole video is similar structured to scientific texts...
@@S41t4r4 that is true. Say what you are going to say, say it, and say what you said.
@@stevensutton4677 Dems the rules of public speaking (and essay writing)
Omg... I know this is an old vid and this comment will never been seen, BUT.... knowing Benford's law, the title piqued my interest. 🤔
Decided to watch and a Biden 2024 campaign ad preluded Matt's video. If I was a conspiracy theorist I'd have gone nuts!! 😂
I get Biden ads. I get Republican ads. I get ads from religious organizations. I get ads from pseudoscientific products. They should know I don't like most of it and they still do it. At some point, they need to just pick people to show stuff to.
Lol "problematic at best" is going to be my new motto
It's the subtitle of my life.
@@delphicdescant i'm getting it printed on a tshirt
Tinder bio
If you want an official motto for a family crest:
"Difficilis ad Optimus"
Sadly though even those words now have become politicised
Let's be honest: most people invoking Benford's Law don't understand Benford's Law. They are using it because it is an argument that supports what they want to believe (ie confirmation bias), even if the argument itself is flawed.
People do this all the time, including you if you are reading this comment. Very easy to spot when someone you disagree with does it, very hard to notice yourself doing it. We should all be a little bit more mentally disciplined about this kind of thing.
What are your thoughts on this? Chicago .....hmmmm! Democrat-run city, in a Democrat-run State, with election workers appointed by Democrat management....hmmmm. Oh, and isn't that one of the cities where Republican scrutineers were banned from being close enough to monitor the counting process, on Dominion vote counter machines (owned by Dianne Feinstein's husband's company) running Hammer and Score-card software controlled by the Democrat Deep State. Hmmmm, I think that might explain the graphical distortions in not following Benford's Law and the lop sided random distribution of POTUS Trump's vote count across the Chicago precincts. Just say'n, that is probably a statistically significant reason to commence a complete audit of the Illinois voting process. Not to mention the rest of the country.
@@jamescarney6894 My thoughts are that this is exactly what I was talking about. You don't want to believe that Donald Trump lost the election, so you bend over backwards trying to prove that 2+2=5. The only way you could believe in this insane conspiracy theory is motivated reasoning.
i disagree
but tbh joe is yo mama and if you know that, then that means i wouldn't have too say joe for you to even relate it too "joe", yo mama.
@darknightoftroy "2000 Mules", I guess you are one of them.
If my stats classes were this interesting, I wouldn't have hated stats. ;)
If this comment wasn’t so stale, it wouldn’t be stale.
@Mr. Natural Completely agree! But if my Technical Communications minor taught me anything, you should capture your audience from the start. Plus, this particular video isn't presenting anything that a layperson couldn't readily understand. It would be a nice intro to a stats class, IMHO.
@Mr. Natural I think we are just going to have to agree to agree, sir. :)
the derivitives and anti derivitives of "ln" and stuff... ik what you mean, i got a 1 in my ap stats test :(
My son has a Master Degree in Stats
For a while I always thought it was crazy how powers of 2 always seemed to start with a 1 when the number of digits goes up. Thought it was pretty cool that you would get “pseudo powers of two” since the lead digit often went 1,2,4. Then one day I realized that it literally HAS to start with a 1 every single time 🤦♂️
Yeah, but the fact that 2^10 is so close to a round base ten number 1000 is a nice coincidence, isn't it? The pattern basically starts at 256, 512, 1024, 2048... And then not so nice.
Oh, I understand now. This means, "The decimal representation of the smallest integer power of two for a given number of digits always starts with a 1." That took me a while.
@@AbsoluteHuman 4096 and 8192 are fine, but it gets REAL nasty after that
Don't forget gerrymandering: the lawmayers have been intentionally rigging those districts for years to come in even MORE consistently percentage-wise over and over again...
How do districts matter in statewide races?
@@mrb152 where electoral votes come in
@@ryliewhite3888 No, the electoral votes come from a group of people from both parties
@@ryliewhite3888 But, technically you are right if there are no faithless electors
Gerrymandering applies to *districts*, though, not to *precincts*. Precincts are small administrative regions within which in-person votes are cast and tabulated; districts are much larger regions that are represented by a given elected official. One precinct's land area may in fact encompass parts of multiple districts!
Precincts aren't gerrymandered; districts are. And while I feel that gerrymandering is a serious problem that we should address, it's not a dynamic that would affect the distribution of leading digits among precinct-level vote totals.
2:11 nobody asks “how is benford’s law?” 😔
:(
Our reporters got an exclusive interview with Benford's Law. It told us it's happy that people have gotten so interested in it over the past week, but asked us all could we please learn the conditions under which it does and doesn't apply?
+
For anyone who is still wondering why Benford’s law holds, think about plotting data on a Log scale instead of a linear scale.
On a log scale 30% of the horizontal space is taken up by values that start with one, 17% by twos, and so on.
It turns out that in the real world data is often random with an exponential distribution and not a linear distribution, so the data looks evenly distributed on a log scale, not a traditional straight scale. Hence Benford’s law.
Steve Mould explanation is pretty clear. To go from 10 to 20, you need to multiply by 2. 20 to 30, it's 1.5, 80 to 90, 1.125. You need more momentum to go from a number that starts with 1 to a number that starts with 2, than from 8 to 9.
Great explanation
The first part of your comment (the analogy with the log scale) is correct and very interesting. But the conclusion about "exponential" and linear distributions is incorrect. In fact, Benford's law applies to uniform distributions (over many orders of magnitude, as Matt mentioned).
@@kilimanjarocruz660 and which mathematical operation converts magnitude differences to additive differences?
How can I use it to defeat Batman?
I'll admit it, I came here as a skeptic....but you convinced me. Well done video.
So did i; it makes me reflect on how much of a better place we’d be in if everyone took the other side’s concerns seriously and addressed them instead of trying to discredit them.
Been seeing benford's law in discussions about the voter irregularities, and this helped clear things up. I already figured it was mainly a tool that could point to fraud, as you brought up, but now I better understand how it could be better used.
+
There should be a professional sport where you're given a dataset and each side need to prove opposite points via cherry-picking/scaling the graphs, etc.
Not that it would be that interesting, but it would be a less destructive way of occupying that kind of people than letting them work for politicians.
Can I quote you?
It's actually a really important life lesson, to learn how to manipulate data to get any result you want.
Because that's how you learn to be very careful when someone else presents you data. Especially if that person is trying to sell a trillions-dollar product (such as a US presidential election).
Kinda like why everyone should learn a little magic. It teaches you not to trust your eyes.
And learn how to write a bad (but effective) argument. It trains your alarm bells needed when watching media (which will be ringing constantly).
Of course the downside is that you'll be training everyone to be utter conmen if they want to.
Honestly I would watch that, it sounds kind of interesting
@@hrgrhrhhr me too.... I think in general it would lead to a more enlightened population who are more aware of how statistics can be manipulated.... along with how the phrasing of a question can change how people answer it
There is that sport. It's called political commentary. CNN, MSNBC, and FOXnews are the major teams.
I like how the "Trump Tower" encroaches on Pi's distribution.
Trump needs to get a slice of pi
the trump tower distribution was very much MP.
pi pi ??/
Heh
Pi is humble, what can I say
I’m not arguing that Biden won, but i do find it strange that millions of people just decided not to vote this year. And millions more decided to vote in 2020 than the normal trend.
Registration was apparently way up.
Covid. Nothing else to do. Duh.
Hey dipshit. All the votes haven't been counted yet
@@universenerddlol 20M votes aren’t going to abracadabra out of thin air bro
@@Hydrolysis_Moment what are you referring to? Kamala has 10 million less votes than Biden and votes haven't even finished counting yet
This was a great explanation of when & why Benford’s does (or does not) apply. Enjoyed that a lot! Well done!
Matt, this was a fantastic video and incredibly impartial and fair, with a great message on the end. Everyone should advocate for their best possible argument and we should all cool our heads and look at these problems in the way that you have.
You've set a fantastic example for "both sides" and they all need to chill out and get to work verifying that everything checks out. Its when we don't have people like you doing this stuff do people lose trust. Thanks Matt, this video should be shared around--not because it undermines an argument for the Trump side, but instead because its a cool headed rational explanation and example that its ok to advocate for your position because by only people listening to each other and thinking will we get to the truth of the matter.
Benford's law gets real spicy in binary!
Indeed. Hence the assumption baked into binary floating-point numbers, that the first bit of the mantissa is always 1 (or else you have 0, which is indicated by a special exponent value); so you get a free space for the sign, since you do not need to store this first bit.
Yeah, since every number except 0 starts with a 1. But It could actually still be useful if you look at the 2nd and 3rd digits
@@kalebbruwer In floating point, you have to throw away one possible value for the exponent, because you can't represent zero otherwise. But you can use this special exponent to indicate other things than zero, such as short integers or more than one kind of "not a number".
@@bluerizlagirl In floating point, the sign and exponent are stored before the mantissa. I was talking about integers where you throw away leading zeroes. I know that's not a thing with computers, but I wasn't talking about computers.
@@kalebbruwer Floating point is basically the same principle as resistor colour codes. And even "zero ohm" links (in a resistor-like package, for machine handling) have a special marking with one black band.
Damnit I did it. I looked down. Never look down.
As a normal person, I was thinking about this exact question.
"Do your own research." For the majority of voters in American elections, that usually consists of asking if a candidate is Republican or Democrat.
Worse: their research consists of what Fox or CNN yells at them to believe.
the usa has unbelievably crappy media
no wonder the rest of the world reports their stuff for them
@@smoog it's ironic because now the republicans no longer like Fox anymore.
@@captainriker9088 Yeah just because they aren't spewing EXACTLY what the Republicans want to hear any more 😂
@@richardm8155 I mean one of the big issues is the fact Fox called arizona way too early. Especially in a state most people would have considered solid red up until this point. The complaints may be valid, idk, but I don't really watch Fox much though.
Benfords law doesn't prove false values.. it's more of a starting point to find out of place data that could later on be false values.
heavy statistic anomalies are very rare.
It's always worth it to take the time to check these 1 out of a 100 cases a second time.
In other words it's a hint or tip, like intuition. It helps decide where to focus limited resources in investigating something.
@@gblargg yeah.. exactly. It will never prove anything by itself. It would only be used to give cause for an investigation.
It's also important not to use inappropriate laws in the first place (= useful laws in inappropriate situations), or else you'll chase everything.
@@googleuser9383 Heavy statistical anomalies are actually extremely common when a statistical method is inappropriately applied.
Uff, just looking at the downvotes I get the impression that some people really don't like math
some people don't like critical thinking or education at all, unfortunately.
Why Illinois? Why not do the data for Georgia or Pennsylvania instead?
Lol, they have that data for SCOTUS
he didnt pick Chicago at "random" lets just say that
Why the data for Georgia or Pennsylvania?
Why not North Carolina or Oklahoma?
@Bane Yes, the test should be done on a contested state/city, not one that Biden would win regardless.
illinois need a audit tbh
Over 7k dislikes.... Certain people mad this didn't agree with their conspiracy theories.
Except the exact same jump was seen in the Georgia runoff.
@@MumboJumboZXC cope
@@MumboJumboZXC Cope harder.
@@MumboJumboZXC yo can I have some of that copeium
@@MumboJumboZXC cope harder, snowflake
The thing I loved the most about this is how it explained why in a logarithmic idle game the 1s values stayed the same so much longer as things increased.
Will this video teach people to double check their data and sources prior to spewing nonsense into the internet?
I can only dream.