Can you outsmart this logical fallacy? - Alex Gendler
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- Опубліковано 24 лис 2019
- Explore the psychology of the cognitive bias known as the conjunction fallacy, where we assume specific conditions are more probable than general ones.
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Meet Lucy. She was a math major in college, and aced all her courses in probability and statistics. Which do you think is more likely: that Lucy is a portrait artist, or that Lucy is a portrait artist who also plays poker? How do we know which statement is more likely to be true? Alex Gendler explores our tendency to look for shortcuts and the phenomenon known as the conjunction fallacy.
Lesson by Alex Gendler, directed by Artrake Studio.
Animator's website: www.artrake.com
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Reminds me of the joke advice that you should take a zebra on a train with you, because statistically train crashes when there is a zebra on board are much more unlikely.
I heard a similar joke about a mathematician taking his own bomb to a plane. The probability of two bombs on the same plane must be much smaller than just one bomb, right?
“1 in 20 Americans will have their house burglarized during their lifetime
That means that 19 in 20 Americans are burglars”
@@karelspinka3031
Nah it shouldn't, and a mathematician who does that is a bad mathematician
The two events (the existence of the first bomb "with the mathematician" and the second "with a real bomber") are most likely not linked events, so the state of one of them mathematically does not affect the probability of the other
@@AhmedAshraf-pd7mu that's the joke
Ahmed Ashraf Did you not read the comment?
Ted-Ed : Can you-
Me : no, but i’ll watch it anyway so i can
Lol same
But i managed it bc reverse psychology
😂😂
i think thats most of us
Sure you can, why not?
My dad told me a joke that reminds me of this “All schools should adopt llamas, because statistically, a school shooting is less likely to happen if a llama is present.”
(Going along with the joke) but then wouldn’t school shootings become MORE likely to happen with llamas around? Lol
Vaughn Johnson Only one way to find out!!
All students should be mandated to carry guns because there was never a mass shooting in a school where the students all had guns.
Note; don't attack me i don't defend this position. I'm just translating the joke logic into a nut right winger argument. And by doing it showing how ridiculous it would sound to anyone gifted with a reasonable and rational brain.
Paulo Branco (Still following the joke) Why stop there? Let’s give everyone tanks. I bet you can’t name one single school shooting in which every single person in the school had a tank. Checkmate liberal
@@atlas6533 let’s do it!
I think what happens in most people heads is that when you say "Is she more probable to be a painter or to be a painter plus a poker player?" they really hear "Is she more probable to be a painter who does not play poker or a painter who does?" I'm not quite sure it really is a problem about probabilistic intuitions (though as less people play pocker it still may be), rather than a problem with framing and rhetoric in language, that is, a problem with miscommunication. What if you rather ask people if it's more probable that she's a painter who may or may not play poker, or that she's a painter who plays poker? I would say more people would answer the question correctly, when the question is correctly framed.
good opinion, but if framed like that, then the second choice answers (shes a painter who plays poker) is kinda pointless. because the first choice already contains the 2nd choice . logically its like ; shes a painter who may or may not play poker ( 1 / 2 ) and shes a painter who play poker ( 2 ). people naturally like playing safe, and who choose first answers will always right because it contains two option already.
@@LovegiDavid That's the whole point
@@LovegiDavid This reasoning shows that current conclusion about people's thinking is based on participants having misinformation.
It's because the video doesn't present the original study accurately, which had 8 options, not 2, and the instruction was to rank their likelihood, not choose the most likely one. In that case, there would be no implication of exclusion. Sometimes TED-Ed simplifies or rewords stuff so that they're no longer quite correct.
Even with that misinterpretation, the logical answer would still be the first one. Even if it talks about her specifically, she's still more likely to be just a painter who does not play poker.
I constantly overestimate my ability to outsmart anything.
right there with you. 🤣
The key is to doubt yourself and your intuitions more, then you develop better critical thinking through skepticism.
@@InfiniteProdu i've been doubting myself and my intuition for a long time, and all i've gotten besides decent logical thinking is an incredible lack of self esteem.
Isn't it called the Dunning-Krueger effect?
@@user-rl4tg2mr9n ??
Lesson learned, always include as many details as possible when lying.
Kevin Nelson actually quite the opposite
@@Slizzyz I disagree, giving less detail is definitely more suspicious. Sure, giving way too much detail might be a bit weird, it's still better as a lie than if you're being extremely simplistic about it.
Leon Petard learned that when he was late for his shift at Strickland Propane
It's very well known that people who are lying have a tendency to add unnecessary details to their stories.
Well specifically, I add true details, especially ones I can prove. When I clog of their memory of what I have claimed with things that are actually true; I’m more likely to be able to produce evidence when asked.
For example, let’s say I am a kid who didn’t do his homework. When my mom asks if I did my homework, and I say yes, she’ll likely ask to see it. I have nothing to show, so this doesn’t work.
But if she asks to see my homework and I discuss what we went over in class that day, when I produce a worksheet I did in class claiming it’s my homework, she’s more likely to believe me because I have evidence backing my claims, even if my claims are false.
In conclusion, when possible, include half-truth details.
As an art major, I had peers who made beautiful art and majored in math. Knitting, crocheting, and weaving can use a ton of math (go ahead and make a swatch, and use it to construct a full garment by yourself). One of my favorite studies a peer did was by shibori dyeing fabric in the form of fractals.
This describes me so well! I have a contemporary art degree but I studied maths for my electives. I mostly do film photography but I also make sculptures and textiles haha.
It really is surprising (ok, /upsetting/ sometimes) that some people still think that the arts and STEM are oppositional in some way. Meanwhile there are people composing music based off datasets of everything from cows' gut microbiomes to geological and meteorological phenomena.
I think something important here is how human communication works as well. When someone says that one person does one thing and the other one does the same thing and something else, is implying that the first one doesn't do the second thing. Is how we as humans communicate most of the time, it would be weird te clarify every time that the first person COULD also do the second thing. Either way, the example you bring here is interesting regardless what I just said.
Hi, one year later. I'm not sure if this was the same thing, but the version I heard was related to how children can be indirectly taught to prejudice against particular people through these gaps in human communication. I think it was like... So-and-so's family makes pizza, and such-and-such's family makes cookies. The children were asked if such-and-such's family could make pizza, and I think the answer was typically 'no'. This is usually done in the context of stereotyping and overgeneralizing statements.
Ted-Ed gave up on me trying to "solve" anything so they thought I might be able to "outsmart" something... sorry Ted-Ed, I can't do that either😅
We would never give up on you, Sebastian!
hi Sebastian Elytron
I answered it correctly for once :D
@Mansuba's Counseling User Umm....so?
@@TEDEd Your Logic problems are not logical, they are silly, literally several are manipulated like Lucy's, since although we know that mathematical study is equally likely to draw or paint or play cards, since not knowing their tastes the fact that Study math is useless to know your taste.
Also about whether A occurs more than AB seems quite silly, as I said it is very manipulated in that, since it is impossible to know until asking the person (or knowing the data of the thing to analyze) their tastes, therefore it is a bad example and one very badly managed, since if we are really logical there are 50% of both being true or false since they are only statements of someone who does not connect for example Lucy and is based on what he saw and thought.
This is the only ted-ed I've ever instantly understood and solved!
Same.
I actually got this one!
I mean there were only two options, statistically, you had a 50-50 chance.
Demosthenes you didn’t even read the comment... I suggest u do because what you said has no meaning.
Ryan McLaughlin He was joking.
Flashbacks to kahoot where i felt rushed to get more points and pick the complicated answer.
underrated, same!!
I feel like this is less of a fallacy and more of poor understanding of linguistics. When presented with the choices, of the person being an artist vs an artist and poker player, it is implied by the phrasing of the second option that the first excludes the second group. Given that we are working with the knowledge that the person is definitely an artist, the question morphs into "is it more likely that the person is or is not a poker player given their interest in these related subjects?"
Well, tbfair this kind of research requires the assumption that everyone understand the question correctly and has perfect language understanding, so they are very likely to make the question as clearly as possible
Yes, the philosophical equation breaks down when the relationship between two of the variables is more probable.
As in stupidly put,
Tammy likes novels
Is it more likely she will
Meditate or meditate and read a book?
It becomes clearer at least to me when put to an absurd extent.
As in, Tammy likes novels
Will she murder or murder and read a book?
One has to according to this fallacy decide plain murder is the most likely thing for newly incarcerated Tammy.
And finally to get to my twisted sense of humor, one has to consider cause and effect because the book was a manifesto.
Thank you, thank you I see the exit I'll lock the door behind me.
@@kaugh damn "Stupidly put" 😥
Thank You!!! I was looking for someone who thinks this way. I had read about the same fallacy in Book 'Thinking fast and slow' by Daniel Kahneman (Winner of Nobel prize). I was shocked while reading the book that he had not considered what you have written in your comment.
I think this is not just poor understanding of linguistics rather this is how people look at problems while making a decision (unless people are consciously directed by other person by stating that their looking at the problem is wrong).
It's because the video doesn't present the original study accurately, which had 8 options, not 2, and the instruction was to rank their likelihood, not choose the most likely one. In that case, there would be no implication of exclusion. Sometimes TED-Ed simplifies or rewords stuff so that they're no longer quite correct.
I didn't know this was a fallacy, I just thought it was common sense to choose the one with less specifics added onto it.
wow you're so smart
wow you're so smart
Same
wow you're so smart
I was also confused. Like, what am I missing? Of course it's the 1st option. How did 80% of people pick the other option?
This is the first time in my life that I was able to realise the right answer in a Ted video on my own, I'm gonna cherish this for I know it's statistically unlikely that it will ever happen again.
This is similar to when teachers tell you you picked the right answer on a test, but another answer was more right.
If you're interested in that kind of stuff, I recommend "Thinking fast and slow" by Daniel Kahneman
I’m on chapter 7 it’s pretty cool
Read it. I recommend reading it but not paying too much for it.
@@sebastiancai7431 he spoke about this in chapter 16 .
It's also in How To Think Like Sherlock Holmes by Maria Konnikava.
@@silentseashelllistener3818 ty. ill defintely check out that book.
I was so confused at the start when they said that people would choose the portrait painter who also plays poker. It didn't even cross my mind that people would think that simply because she studied statistics!
Yeah I thought she played poker just cuz it was fun haha
I thought that only being an artist was more likely however when one is introducing themselves one would say that they play poker also.
I picked the second option because people have more that just one hobby. I would like to major math, I am also an artist and a frequent player of cards.
Me too, but after thinking about it, maybe people asume that the first sentence implies that she doesn't know how to play poker, making the comparison completely different
@@kuniosaiki there are a million hobbies, the likelyhood of playing poker or painting is therefore 1/1000000. Doing both would have therefore a likeleyhood of 1/10^12
Kunio Saiki, just because I don’t say all of my hobbies, doesn’t mean I don’t have them.
Same applies the the character in the video:
Is she an artist (has to be an artist, but can have other hobbies)
Or,
Is she an artist and a poker player (She HAS to be an artist and a poker player, but she can have other hobbies)
2:20 Misinterpretation might occur, when the question is asked, one might think that it's more likely for Lucy to be an artist which plays poker rather than a one who does not play poker.
But the question is clear. It's artist regardless of poker playing vs artist who plays poker.
You have got a good point
If you tell ppl to pick from 2 alternatives they assume they are different, otherwise it wouldn’t be logical to present 2. So if you say 1- artist 2-artist+poker, the logical mind assumes 1 does not involve poker, and if this is the only information then it is logical to pick 2. If your argument is the odds involving further specificities are always less probable to find in a population, then the counter argument is that so are the odds of not having that specificity. In other words, generally artist+poker vs artist+strictlynotpoker could have the same odds because you are singling out specificities In both of them. And if your mind does not assume 1 does not play poker then you have a hard time understanding conversations with humans.
This is exactly the comment I wanted to make. Given the choice presented, it is assumed that in the first instance, she doesn't play poker. The argument in the video doesn't take it that way.
Thank you for this comment, I was scrolling to see if anyone mentioned this and I'm glad someone did.
The problem for me is that I interpret the question to be, "Is it more likely Lucy is a portrait artist who does NOT play poker, or that Lucy is a portrait artist who DOES play poker?" When asked a 'this or that' question, the answers are almost always mutually exclusive and rarely if ever self contained so we skip to looking at the difference and seeing which of the different parts is more likely. I know it is not technically worded that way, but it could be interpreted that way if one sees 'does not play poker' as implied.
Ask people if it is more likely that Lucy is a portrait artist who may or may not play poker or that she is a portrait artist who does play poker and I suspect many more people will get it correct.
TLDR: It's the wording not the math.
Completely agree, I’m still mad at the question and they keep saying it’s our fault. I’m like, you made the question a trick when I still believe Lucy is more likely to be a portrait artist who plays poker than one who doesn’t play poker 😤
True, but to interpret that way is to read it incorrectly; or to at least inject personal assumptions. Hence, a fallacy.
@@tahu300 it's only posed as a word problem so that non-mathematicians can grasp the concept behind it. It can be represented mathematically.
I mean… it’s your fault when u understand something wrongly
Its definitely not the phrasing of the question. It's asked pretty neutral and easy to understand. I get that it was probably a misunderstanding on your site because of your perception
First rule of portrait artist club: don’t talk about being a poker player
To outsmart this logical fallacy, one must shave with Occam's Razor.
Nice one bro
Came here to say this... my thought exactly.
Simplest answer is likely the truest and most correct, until a more complex answer is more right.
Yep.
You'd actually have to shave with Hanlon's razor... ;)
Ok, that one was pretty obvious. Finally I was able to understand one of your riddles/fallacies :D
You are good at this
I got it too but 80% of people got it wrong
Ik I was actually surprised at how many people got that wrong
@@nocent9071 Could it be a problem of how the question is asked, and how fast? like "What is heavier, a pound of feathers or a pound of Iron?" trips almost everyone i've seen up, and it's stupidly easy
Morten Tversted I think that’s most likely a big part of it, and that’s actually a good explanation for why even people who understood statistics well tended to answer similar questions wrong.
What if the statement were altered?
1. Lucy is a portrait artist who doesn’t play poker
2. Lucy is a portrait artist that plays poker
The condition is then exclusionary so it is no longer subject to a conjunction fallacy.
All you need is 50% of people like Lucy to be poker players and then the tables are turned.
A similar case is:
Which is more likely?
John is born in England
or
John is born in England and has 10 fingers
The more general guess is correct but if we add the exclusionary condition then it’s extremely obvious that it would be more likely for John to have 10 fingers as opposed to some other number.
I don’t think this “conjunction fallacy” is given justice here. The video really just says that people will mentally substitute a nested probability question for a True/False binary question unless the question is phrased in a way that is less ambiguous.
Exactly, I think they mix probability with rhetoric and ended up missing the point, what I see is how so many people chose automatically just to fulfill an "artificial" pattern (Math and Poker)
It is still more probable for John to be born in England as opposed to being born in England AND having 10 fingers. That's because although having ten fingers is obviously more probable than any other number of fingers, that's not what's being discussed here - hence, the fallacy strikes.
You have to understand that the probability of a person living in England must be higher than the probability of a person who ALSO has 10 fingers in addition, and this can be shown through sets and subsets.
Set 1 - people who live in England.
Set 2 - people who live in England and have 10 fingers
Now, set one includes *everyone* in England - that means whether you have 10 fingers or 100, you will be a part of this group. Set 2 *excludes* all these people who don't have 10 fingers from itself, making it *smaller than set 1 while also being a part of set 1* . Hence, set 1 is larger! And the probability of someone lying in set 1 is consequently larger than them lying in set 2, a subset of set 1
@@TheRealArya It's obvious he understands that. What you don't understand is that he's arguing that **rhetorically, not mathematically**, the question implies that in option A), John doesn't have 10 fingers. This is why this video fails to demonstrate what it was meant to. No one will draw a Boolean Truth Table when someone asks such a question, they'll imply that the additional condition in option B is negated in option A, and they'll restrict their choice to the additional condition only.
@@om-bs4xy "the question implies that in option A)" and that's the fallacy. You interpereted the question that way.
You did not follow the logical reasoning but incorrect reasoning. See also the bandwagon fallacy or false dichotomy. It's information presented in a way to make you think in a unreasoned way, not a logical one.
@@lincolnduke And the video is about the conjunction fallacy. A is more probable than A+B, since they aren't mutually exclusive premises.
What's more likely, I die tomorrow or I die and the sun rises? If I don't die, neither matters. If I die and the sun doesn't rise, then only A happens. If I die and the sun rises, A+B happens. For total chance of A, take every time I die and everytime I die and the sun rises. For total chance of A+B, you only look at when I die and the sun rises.
It's not "necessarily bigger", there is a non-zero chance that they're equal.
I feel smart because for once my reasoning was similar to what the videos was. 😂 (also you all don't have to kill the vibe lol ... Trust me I know I'm not special)
Me before the video: *Has a stroke*
Don't get too proud, though - look up the blind spot bias to understand why.
That just means you understand basic set theory. The set of all of type A will never be smaller than the set of type B if type B is defined as "type A with extra qualifiers"
@@roguishpaladin Do you mean the bias blind spot ?
I also solved it, but in a different way. I thought, "Ok... a math major is well acquainted with the law of large numbers, so she would not be foolish enough to play poker."
Humans like stories and the second option sounds like a better story even if statistically it is less probable.
Stories have better taste than statistics - that's is why we prefer them like dessert
@@MaxVideoLee Made in abyss?
Makes sense 😊
Ice cream is better than broccoli any day you get me my homie
Statistics are useful we talking about groups (of people in this case). When talking about one individual perdon they are just useless most of the time.
This is the first (and probably last time) I got a TedEd problem correct. I was thinking Portrait (alone) is more likely and was already preparing myself to get lectured on why I was wrong. Yay for being right for once.
That was way easier than I expected. I kept Occam's Razor in mind and went with the option that had the least number of assumptions.
Yes. By not watching this video.
Wut? Why?
Wait, when did you get here, sir? Ah, by the way, the new video is great.
You don't solve a riddle by walking away from it genius 🙄
Yes...by not giving the answer😂😂
visionary
Honestly, I think it's the wording of the question. They might interpret it as this: Pr(A∩B)≥Pr(A∩B')
Is B' supposed to be not-b?
@@orbitalvagabond7371 Yes
Agreed. I indeed interpreted as P(A&B') and not P(A)
@@yescountry8196 what are you talking about? The dude clearly stated what he meant. It can be very well argued the question asks if Lucy is an artist who doesn't play poker vs if she is an artist who does. Obviously there is a bias but the the video doesnt really talk about the misinterpretation op had
Young City Bandit it is based on the way we ask each other questions. If someone asks an either/or question, we automatically assume that the answers are mutually exclusive, simply because that is almost always the case and people do not always say exactly what they mean. This leads to our brains trying to automatically fix apparent mistakes in communication. It would have been possible to phrase the question more clearly.
I took a cognitive psychology course... i learned this.... and I still got tricked 😭
i've heard this before and it always irked me because common conversation rules mean that providing this question to people automatically primes them to think 'lucy is a painter' means that 'lucy is a painter who doesn't play poker'
This isn't some profound weakness in language or in human understanding of probability, it's a trick question that fools people because they're used to conversing with other humans, who would *never ask a question like this*.
A big reason I think people assume 'lucy is a painter' implies she doesn't play poker as opposed to the other situation is because it doesn't even make sense to ask this question *unless* you are implying the negative, because otherwise the question cancels down to 'does lucy play poker or does lucy maybe play poker' which is a completely inane question, when faced with ambiguity, a person will choose a more sensible *implied* question (does lucy play poker and paint vs does lucy paint but no poker?) instead of an inane question that doesn't even make sense (does lucy play poker or does lucy maybe play poker?)
Claiming that people are 'bad at statistics' because they choose to interpret ambiguity by taking the most reasonable response is manipulative, and explaining it in a patronising way as though people don't understand the actual mechanic at play is just rude. If you rephrase the question "is it more likely to pick a random ace of any suit or an ace of hearts" nobody will think twice about answering correctly because the question isn't intentionally misleading or ambiguous.
👍
when the question is asked this way, it's implied in the first option that she does not play poker.. so since both questions asks about being artist, it's then a matter of just whether you think she plays poker or not
The first option is still correct, regardless of how you interpreted the question. It's more likely that she doesn't play poker than that she does play poker, regardless of whether she paints or not. It makes sense that someone who majored in statistics would play poker, but it's more likely that she does something else entirely. Among the people who majored in statistics AND became painters, more don't play poker than those who do.
@@free_h2o142
We could just as easily say that more statisticians play poker than don't, since "artist" is a given our only variable is poker.
If our entire set to choose from is "artists who are statistics majors," it's more likely that they're a poker player than not, because the number of those that do play poker is probably greater than the number of those who don't.
xxxxxxxxxxxxxx yy y'y'y'
If we have to choose between y and y' then y' is more probable, all values x are irrelevant and the probability of "y" is 100%, the only variable is ' which has a 3/5 probability as opposed to not ' which has a 2/5 probability. It's logical to choose poker player for our answer.
@@ryanalving3785 I don't think that there are more painters with a background in statistics who play poker than those who don't play poker. Does that mean most of them play chess and Go too? It's still a minority group. For a group of 10,000 painters with a background in stats, less than 50% will play poker too. Saying otherwise is to suggest that most play poker, chess, and cards ... etc.
@@ryanalving3785 but artist is not a given. If it's unlikely that a statistics and probability major is an artist it's even less likely that she's an artist who also plays poker since that is a subset of artist.
@@HartyBiker
If we're given two potential options, both of which include that the person is an artist; artist is no longer a variable. The probability of "artist" is, for our purposes, 100%.
So we can treat it as a given.
I feel like the trickyness lies mostly in the way the question is asked. Had the question been: What is more likely to he true? And the answers would have been:
- Lucy is a portrait artist and does NOT play poker
Or
- Lucy is a portrait artist and plays poker
Then both answers would be equally specific. This is what most people think when they read the question, and in this case either answer is equally likely and specific.
Why do you need to add "does not play poker" to the first scenario? It's clear that she does not play poker in the first scenario otherwise she would be the second scenario.
@@abcdef8915 Did you even finish the video? "Lucy is an artist" does not say anything about whether she plays poker or not.
@@AlnelExtreme you're assuming she is an artist. The possibility exists that she is not an artist.
@@abcdef8915 What? Where did you get that from? In both choices, Lucy is a portrait artist. The difference is that the second choice states that she plays poker. The first choice doesn't care about anything beyond the fact that she's an artist. She might play poker, volleyball, chess, whatever... or not. It doesn't matter. As long as she's an artist, the first choice fits. If she plays poker, then both choices fit, though the second choice would look more correct, but they'd both be correct nonetheless.
@@abcdef8915 the thing is that we don't know and it doesn't matter. She only has to be an artist, she may or may not play
I primarily this fallacy when lying to my teacher about how I “did” homework and forget it at home..
what
I actually assumed B, not because of the statistics part, but because I assumed a portrait artist, one who spends vast amounts of time looking at faces, picking up on subtleties in them, would be good at reading people's emotions, thus would likely be very good at reading people when playing poker
Yeah, but a poker player who is an artist also counts as an artist. Even if all artists were poker players, they would still be the same amount
Same logical fallacy.
I think where people struggle is that Option A includes all scenarios, ([artist and poker] as well as [artist and not poker])
this is the same exact mistake they just explained though :(
your brain makes me sad, friend.
"No, I don't think I will."
There are more interesting things to life than cracking fallacies, right?
@@progressx2880
Yes, of course
It all depends on the person's preference
People assume the question is in fact "is it more likely Lucy is a portrait artist who plays poker, or a portrait artist *who does not play poker*. This is assumed becuase it would in casual conversation be more normal to ask a question assuming two inverse possibilities (rather than asking more specific information within the same question).
I dont think this seems like a very effective demonstration of the fallacy.
that "misunderstanding" is also driven by the visual representation, maybe to that extent I am not sure if I want to call it misinterpretation or miscommunication.
Wanted to solve this myself, Ted presumes to give me the answer straight away with no thinking time
Pause button 😁😝
@@stumoo4049 With only 3 seconds between question and answer, pause button only works if you expect and are prepared for the immediate spoiler. Especially if you think he might be about to provide more context to the question, additional assumptions to make, etc
This lesson also applies to the The Law of Parsimony or Occam's razor. Between competing theories, the one with fewest assumptions is likely to be correct merely due to probability alone and hence simpler theory has to be rulled out first, before asserting more complex one.
A theory with one assumption: "God does everything". :-)
@@DeclanMBrennan Another theory with one assumption:"The universe started in the Big Bang". Trying to prove that God does not exist is at the very least an insult against his followers , or you are telling me you are attacking the deity you do not even believe exist?
Damn the thought at the beginning truly says beauty is everywhere but we all see it in a different way 😁😄😄
The problem formulation itself may be at fault for the results.
The test subjects may be understanding the first option as _Lucy is a portrait artist _*_who doesn't play poker,_* the part in bold being taken implicitly by contrast with the second option.
With that interpretation, the question becomes "what is the likelihood that Lucy plays poker, given that she was a math major in college (etc) and is a portrait artist," in which case the option that she is more likely to play poker is plausible.
Bravo
The problem formulation is just fine. You have no reason to assume the extra condition you put in bold. Anyone that does this must lack some serious reading comprehension or basic logical thinking skills. If anything, this problem shows people often misinterpret statements and changing them to their liking
It does not say Lucy is a portrait artist. It only asks which is the most probable answer. Lucy is a portrait artist or Lucy is a portrait artist and poker player. Which you must admit can only be less likely than she being just a portrait artist.
@Kurt E. Clothier I meant plausible in the sense that it's an admissible answer.
Under the mistaken interpretation, we're comparing P(Poker | Background & Painter) and P(¬Poker | Background & Painter). Without knowing the actual probabilities, we can't say with certainty that one is greater or equal than the other, making both answers plausible.
Under the intended interpretation, we're comparing P(Poker & Painter | Background) and P(Painter | Background), in which case we know with certainty that the latter is greater or equal than the former, making only one of the answers plausible.
Arguing which of the two options in the mistaken interpretation is more likely is besides the point in this exercise.
@@alexismandelias I don't agree that the problem formulation is without problem, but I generally agree with the rest of what you wrote.
A good formulation needs to take into account possible misinterpretations and be constructed in such a way that minimizes that possibility, without leading any answers.
A possible alternate formulation would pose the first choice as "Lucy is a portrait artist who may or may not play poker."
Also, note the possibility that a savvy reader may be assuming the extra condition on the assumption that it was the intended meaning, but whoever wrote it failed to express it clearly. Especially since the intended interpretation can be dismissed as having too obvious of an answer and therefore would be uninteresting to ask in the first place.
It's wild that this video holds your hand through a very simple and clear explanation of the fallacy and some people are arguing with it. Like seriously if you're confused, that doesn't mean the video got it wrong. It means that these types of word problems can be confusing and that our human intuition can often point us in the wrong direction.
I think much of the reason people get this wrong is due to communication norms. In everyday speech, if one conjectured these two options for Lucy’s hobbies, it could be assumed that in the first option she does not play poker. But I suppose it is the point of the video that our everyday communication style lends itself to lots of fallacious reasoning.
She is the true *Big Brain Moment*
I find u every where.you are literally in every video I click
Just A Dio Who's A Hero For Fun
That username and pfp is perfect genuinely amazing.
Clicked without checking name of video...
Ted ed is just enough!!
Same
I chose B and learnt something new about the wrong choice of answer I made. I'm very happy to have made the mistake. It allowed me to rethink and reassess in the future. Thank you!
I'd argue that when asked the question most people think the first option means "protrait artist and DOESN'T play poker", hence they pick the other one.
Possibly, but it's still more likely. Poker is played by a relatively small group of people, even accounting for the any increased likelihood of somebody like Lucy's background, that's likely still the case.
Chris L yes, while in real life that is true, the probability that any one person plays poker is not given in the facts of the case, so it can’t be determined
@@julianrosenfeld7177 at most it would be equally like, but it's hard to assume every math major portrait artist plays poker
@@fica1137 no one is assuming all of them do, but from my experience I would be surprised if 50% or more do. It depends 100% on how you define "plays poker" though, which makes this question useless.
but WHYYY are people thinking that when it doesn't say that!!
I once solved the Einstein riddle from Ted Ed.
What riddle?!
@@somerandomguy___ exactly.
ua-cam.com/video/1rDVz_Fb6HQ/v-deo.html
Well? What was the answer?
Well, it wasn't abstract or anything. It just requires pencil, paper, and some good memory.
This was actually simple, so it’s one I figured out.
I always understood it as if either statement a or b are correct, choosing statement b (2 conditions) would mean statement a (1 condition) is also correct but there’s only one right answer, so logically you should pick a.
I really like these videos, keep them coming!
The way the question was asked it seemed to imply that one of the options where true which because of the background information could be seen as that the poker option is more likely of the two, might that explain why most people answered that way?
Philip Yea it’s phrased as if one will be true while the other won’t be
The question is "which one is more likely.?"
But because of habit, people think
"Which one is correct ?"
This is how I explaine it lol
Yes, that’s kind of what the video is explaining.
It sounds more convincing but it is statistically the wrong answer.
The point is that it seems the first option (artist) is actually excluding poker when you make it alternative to the second
asiangirlmoviewjp.link/I9iVm
"What's more likely, that Lucy is a portrait artist or that Lucy is a landscape artist?"
I think my brain accidentally created a really weird play on words.
how is that even a play on words lmao
@@GalvakzaMusic 🤣🤣🤣
The best video on this subject. Thank you!
this is super helpful for anyone trying to do well on the ACT because, especially on the reading section, they try to trick you in a similar way!!
Actually, most people will interpret statement 1 as "Lucy is an artist and doesn't play poker" because that's the eay the question would most likely be posed in the real world
Exactly, and then it's like asking "Do you think my bicycle has only a front wheel, or a front and a back wheel.", in which case the latter is more probable." The riddle in this video is more of a language riddle.
It's because the video doesn't present the original study accurately, which had 8 options, not 2, and the instruction was to rank their likelihood, not choose the most likely one. In that case, there would be no implication of exclusion. Later studies Sometimes TED-Ed simplifies or rewords stuff so that they're no longer quite correct.
@@TosiakiS doing the lords work :D.
_"Finally, a worthy opponent, our battle will be legendary."_
*~ Albert Einstein*
I thought tai lung said that😂
Naaah
@@AlphaTechN
Congratulations, you have discovered the joke
@@pranavlimaye lol This is gold Imma use this someday
See the problem with quotes found on the internet is that they are often not true - Abe Lincoln
a visual way to observe this, in my opinion, is through a venn diagram. they're asking if Lucy ending up in a certain circle (one for portrait artists) is more likely than finding her in the place where the two circle intersect or not.
This makes a lot of sense. overthinking the scenario will make you fall for this trap, conjunction fallacy. Learned something new today!
The awkward moment when you’re watching this video in your college dorm & you’re a math major but got this wrong 😅 btw I’m not a portrait painter
Also watched this in my college dorm. Failed Trigo and Calculus once but actually got it right. How the turn tables lol
I would imagine some number of people misinterpreted the question and assumed the first option was meant to be “an artist who doesn’t play poker”
I think that's the point, and why this fallacy is so widespread
Isnt that the basis of every fallacy?
"Which shop offers better value? Thousands more people shop in shop A than shop B"
The statement is irrelevent to the initial question but people will likely link the two. That's bandwagon fallacy.
Yes, but consider this: the presentation of those two options creates a new constraint. If the *only* possibilities are that she paints or that she paints and plays poker, we now have new certainty that she definitely paints. So the question now becomes "Is it more likely that she does or does not play poker?"
In the absence of any other information, we should presume that it's less likely for her to play poker than the default of not playing poker. The selection of the second option is then the result of speculating that, considering her background, it is more likely than not that she plays a game she's probably good at. It's still not exactly a solid guess, since we don't have data to indicate the relative likelihood of math majors playing poker, but it's not as silly of a fallacy as it might appear.
Just subbed, you have a wealth of good stuff on your channel. Thanks!
From Daniel Kahneman, this is more like a heuristic of representativeness instead anything.
Availability heuristics......
Simply when you give the two options, we tend to interpret the choice: artist who does or artist who doesn't. Because otherwise this question is too simple. And it's statistically more plausible a mistake of comprehension than a question too simple
I agree
If you interpret it as she does or does not play poker, then the question becomes unsolvable with the given information, and it's more likely that a question would be simple but solvable than unsolvable.
Examples like this are a handy way to show the relationship between Bayes theorem (in probability theory) and subsets (in set theory) and dependent conditions (in propositional logic.)
These are all different abstractions which we use for talking about similar real phenomena. And what's peculiar is how many people intuitively get the real phenomena wrong, until the abstraction is pointed out to them.
Finally, I found a video that explains this fallacy really well
I took it as an either-or question, so basically: Does she play poker or not.
Exactly.
Yes, it's not even a variable since in both cases she paints.
Incorrect, option A includes option B so they aren't mutually exclusive. That is, the probability for the event-"her being an artist" includes the probability of the event-"her being an artist AND her being a poker player."
Formally speaking, option B is a subset of A, hence it will be wrong to present A as the complement B.
@@TheRealLap This has nothing to do with probability, and all with how you are interpreting the question. If you interpret it the way you did then what you are saying is obviously true, but if you don't then it's just not applicable. And there is no right or wrong here, because human language is inherently ambiguous. ;)
@@NikolasHonnef The question ask for which is more likely(hence probability), option A includes option B meaning that the two options are NOT: A, she does not play poker; B, she does play poker.
Whilst you might freely interprete it what you want(e.g. she plays the harpsichord), don't use English is ambiguous as a defense when others point out your mistake.
Y(＾_＾)Y
Lucy is a genius
**Scarlett Johansson entered the chat**
God dammnit I knew u could be here smh
?
Rj Pena
Movie reference
@@bingbonghafu
Can you explain the details?
@@bingbonghafu OHH WAIT!!!
Yet another piece of content on the internet that will make me feel smart, just be reminded of my stupidity minutes later when I fail miserably at simple, mundane tasks.
*Exquisite.*
Which is more likely: That a human is born with hands, or that a human is born with hands and feet? Same logic applies where the first one is always more probable because its less specific. I dont like these types of riddles because its all in the wording of the question so instead of applying logic and reasoning we are focusing on semantics and slick speech to trick the audience into answering a different question than what is really being asked.
Yeah this video is a mess
Yeah, that's the problem if you failed to understand statistical probability and logic, you'll end up assuming things based on your intuition.
@@neuron2912 it is not about understanding statistical probability and logic though, it is about interpreting language. Interpreting language is tricky, especially as not everyone speaks a language perfectly and no language is perfect.
I wolud not say taht you cna't unedstrand Egnilsh if you can inertrpet tihs seetnnce.
@@snuffeldjuret
"it is not about understanding statistical probability and logic though"
- Really? But the title is about outsmarting logical fallacy so why would it not be about understanding statistical probability and logic?
"Interpreting language is tricky,"
- You are interpreting a logical fallacy, not the language. Just find a way to translate it to the language that you can interpret easily.
You are just making a lame excuse for not being able to outsmart the fallacy. If you cannot interpret the English language, then common sense and logic will tell you, that it is almost impossible to outsmart the logical fallacy when it is expressed in English. It simply means that it is not for you to solve or you have to allot some time to study the language first before you solve it. I am a Filipino and I know how to speak Filipino, English, Japanese, Chinese, and a little bit of Korean. If you will ask me to outsmart a logical fallacy that requires me to have an advanced fluency and understanding of the Korean language for me to understand and solve it, then I am not gonna solve it. As simple as that. I will just simply admit that I can't solve the trick for now because I still have to gain knowledge and understanding of the language. But if it is translated to the language that I am well-acquainted, then it is something that I can able to pull off. Language is not a barrier for you to understand whether you can outsmart a logical fallacy. How will you outsmart it? It depends on you. Don't make the video about the language interpretation. There's no particular audience required anyway.
@@neuron2912 lol, you like your own comments and then try to talk to me about what is lame and not, that is hilarious. The question was stated ambiguous enough, especially with the image at 0:22 , for you to not be so aggressive about it. Take a chill pill dude, or dudette.
It’s fun to watch a TED video about logical fallacies when you debate with them! 😁
So, I fell for this one, and I think it's for a reason other than what they mentioned. In our common language, when we present an either-or disjunction like, "Which is likelier, X _OR_ Y," we often interpret the sentence to mean that they are not compatible options. We often use "or" in common language to be an exclusive sort of thing. Thus, when I heard the question, my mind framed it as: "Which is likelier, that Lucy is a portrait artist _who does not play poker,_ OR that Lucy is a portrait artist who _also_ plays poker," and in _that_ case, it is not obvious which is more likely, but the information about mathematics and statistics would seem to suggest that the latter is more likely.
In my case, at least, as I suspect in the case of other people, the mistake I made was not in thinking that a subset scenario could be more likely because it contained more "resonant" information, but rather in thinking that, because of how the question was presented, that the two options must be mutually exclusive, because otherwise the question is a bit nonsensical. We do this all the time when we speak to one another. We do not always speak precisely, and yet we usually understand one another's meaning. We do this by automatically reforming our fellow people's statements into something that makes the most sense to us in context.
I agree. If you changed the phrasing of option A to "Lucy is an artist (and she might also be a poker player but we don't know that for certain)" I suspect far fewer people would pick option B. Not sure that counts as a logical fallacy. At least not in this specific example.
There is no difference between the way you think you were deceived and the way the video stated.
I’m so glad I chose the first option because I realized that it was the exact same just more general, it’s pretty rare for me to see the answer before it is displayed 😭
It's in the framing of the question. Most people assume that the absence of mentioning her poker playing in Answer 1 means "what is higher, the probability of her being a painter who doesn't play poker or the probability of her being a painter who does play poker?" in which case the second answer may very well be true if you think she is more likely than not to play poker. It's not a fallacy, just an ignorance to fully understanding what the question is asking.
1:52
"The more conditions there are, the less likely"
Um... Duh! That's how internet searches work! There are fewer results for monkey's riding unicorns while eating a banana and juggling phonebooths than there are results for just monkeys.
nice example tho
@@vaishnavi1321 lol Thanks! I just typed whatever came to mind.
@@catguy5425 pretty good example explaining this without using probability
Spot on. Brilliant parallel. I will now serve as mnemonic for the idea (till the idea settles down on its own).
I actually tried to google this, and was disappointed that there are zero results with all of the conditions met. :(
When you finally manage to emerge victory after a ted ed vid without thinking too long
It goes to show you how much education is important for deductive reasoning. And how much you forget that you learned. When hearing the answer I thought it was obvious and wondered why anyone would think otherwise. But then I remembered I had taken stats class in college which probably made my understand if this easier
Let's be honest, this does say nothing about people intelligence or logical reasoning.
People who chose first option were just lucky that at that precise moment their mind processed and formed the image of two separate conjunctions of both characteristics. 🤷
Michael Lewis’ book- The Undoing Project- delves deeply into how the scientists - Daniel Kahneman (author of Thinking Fast and Slow) and Amos Tversky- came up the Conjunction Fallacy and other interesting counterintuitive human errors.
This is like Occam's razor in disguise. Great video!
Technically correct: the best kind of correct.
This is just semantics... The way the question is framed it sounds like she automatically paints in both scenarios
It sounded like that was a given and the question was actually about whether or not she plays poker.
Yes, it's either that she paints, or that she paints and also plays poker: painting is a part in either scenario.
I think the semantics somehow plays into how people actually think as well. So it might be telling of how people, when presented in a similar situation without phrasing being the issue,: would think of the question as " is she an artist that doesn't play poker" or "an artist that plays poker" whereas in actuality the scenario is "is she just an artist" or "an artist that also plays poker".
@@eatshamahsan1783 It is, it's very much about how people interpret information, and this is why it's a fallacy. Afterwards we go "oh it's very silly". It's people's illogical way to read something, the question did not trick you.
@@lincolnduke interpret information and interpret question are two different things. We ask these kind of questions in mathematics education all the time, but we avoid such ambiguities. E.g. you have a bunch of colored numbers in a bowl, you draw one at random. What is most probable, you draw a "3" or you draw a "red 3"?
When the options were introduced, I understood them options as:
a) Lucy makes her money As a portrait artist
b) Lucy makes her money as a portrait artist and poker player.
In which I assumed B was more likely, because it uses her background and the amount she makes from her portraits is potentially irrelavent. Whereas A assumes portraits makeup the bulk of her livelihood.
Agreed, this is my interpretation of what could be going on here too - the more characteristics you mention the less central they may be assumed to be.
This, as well, is wrong.
It did not state these were the only things that lucy does for a living.
What if she’s also a math teacher?
What if it was just her hobby?
These two statements do not contradict the two given choices.
I can regard that this thinking of yours is a fallacy as well.
Falsely assuming that lucy’s livelihood is limited to these two when in fact, no such constrictions were stated.
A, still is the probable answer.
It’s like telling to a math major that he /she must be good/fast in mental arithmetic just because he/she is a math major...
A better argument would be is that option A, was mistreated as “Lucy is a portrait artist BUT NOT a poker player”.
This, is now different as it is assuming that lucy can’t be a subset of math majors which does not play poker. And depending, on what choice you make. No choice is the better one. Statistically speaking, you don’t know which spectrum has the largest population.
But with such a vague statement such as “Lucy is a portrait artist”, realize that option A does NOT negate the fact that lucy could also be a poker player.
There's a rule of foot: The more complicated a story, the more likely that story is a lie. The less complicated, the more likely it is true.
Another key tell is that the story keeps shifting to fit the narrative. Say I give my cousin three dollars to go buy milk. He comes back empty handed. I ask him what happened and he says the wind blew it away. At first I believe him because it's a simple and probable story at first glance. But then I find out there was no wind that day; it was sunny and completely calm. So I ask him where the wind came from and he says it was a rogue wind. I look up rogue winds and find out the probability of such a wind occurring in those conditions to be near zero, so I ask him again. He says a truck drove past him and that must have created the wind. Now I'm getting suspicious, because the street between the grocery store and our house is too narrow for trucks. He tells me it was a small truck and then starts yelling that the weather service must be wrong because it was windy that day, he witnessed it. So I ask the neighbors if they saw any trucks or if it was windy and they all agree they witnessed neither, so now my cousin has to include them in the conspiracy. The story keeps growing, adding details that are neither confirmed nor even plausible, but he keeps at it. Before you know it, he's implicating the whole NOAA, the truck companies, and our neighbors into a complex narrative designed to distract me from a far more banal and likelier scenario: that he spent the three dollars on himself.
What if your cousin said he lost it and must've fallen off somewhere on his way to the store while still having taken the money for himself?
A pretty simple story and a highly credible one but nonetheless false. What happens then?
@@Isaac.D.grizzly "How'd the money 'fall off', coz? It was supposed to be in your pocket."
@@garcalej Not good enough. Sure it's supposed to stay inside but it doesn't help considering there's been thousands if not millions of incidents wherein objects far bigger such as wallets, phones, keys, etc have fallen off from pockets. Moreover, if your cousin was on foot, the motion from his legs could've influenced the money falling out and since notes are practically weightless, he couldn't have possibly been notified of it falling on the ground.
@@Isaac.D.grizzly I have to say, I've never known paper money to simply "fall out" of a person's pants.
@@garcalej There's a research that states almost 2 in 3 have had lost their wallets at least once. Now how could something of such considerable size keep getting lost to a point that it's actually common?
Again, a practically weightless piece of paper would fall victim just as easily if not much easier.
Your rule of *thumb* is not foolproof and neither are countless other beliefs many live by. So maybe it's not the wisest thing to do but sure, to each their own I guess. Anyway, I'm off. 😁
Am i the only one who needs to pause and rewind Ted videos so as to understand the initial quotes?
I swear- I completely overlooked the overcomplciations and said the 1st was more likely, and was waiting for an explanation as how it was the 2nd one
I equated the first option to be "paints and does not play poker" vs "plays poker and paints" framing it in this manner makes it possible that the first one could be more likely then the second
This video glosses over the fact that reading the second statement (paints and poker) likely makes the first statement read more like “paints and no poker” than just “paints.” In this case, “paints and poker” is more likely than “paints and no poker”
Possible. And here assuming that the 1st one includes 'no poker' is a fallacy.
Possibly, but option b is still less likely for the same reason.
@武孫 He is not saying that the interpretation is correct; he said that that is how people interpret.
@武孫 The video offers one explanation (the conjunction fallacy) for why people get the question wrong. I'm just offering another explanation.
It's because the video doesn't present the original study accurately, which had 8 options, not 2, and the instruction was to rank their likelihood, not choose the most likely one. In that case, there would be no implication of exclusion. Later studies Sometimes TED-Ed simplifies or rewords stuff so that they're no longer quite correct.
I feel like the contention here is that the question sounds like an either or. I was just thinking what are the chances that she doesn’t play poker compared to the chances that she does.
It is an either/or. You declare which of the following is more likely.
Lucy paints
Lucy plays Poker *and* paints
The second is by definition a subset of the first - it narrows the field down just as much, and then some. Either the first set of circumstances is more likely, or the second set of circumstances is more likely.
I think you're trying to say the answers sound exclusive. I felt that way in the beginning as well.
Exactly, I interpreted the question as "is she only an artist or is she an artist and plays poker" in which case the second is not a subset of the first, they are separated groups
Garsh darn it, I fell for it! And this is considering I was taught about occams razor and picking the most parsimonious explanation. Yet, yes, a more nuanced person with different facets seems more believeable than one without! Such is life.
IF I WERE TO ASK YOU WHAT IS MORE LIKELY:
A)That Lucy is a portrait painter.
Or B)That Lucy is a portrait painter that breathes air.
WhiCh dO yOu tHinK iS mOrE LikeLy? (lol)
The question doesn't specify very well whether the options are mutually exclusive.
I think when people give questions with just two answers, its a signal in language that the options are mutually exclusive.
But after they ask the question in this video, they then explain how the option with more required conditions is less likely which implies that the options were not mutually exclusive.
I actually outsmarted this. Ever since I had the Introduction to Formal Logic and Set Theory course in my university I've been on fire logically XD.
The reason for logical Fallacy:- As per Gestalt Psychology, we tend to perceive closely associated objects to always come together.
this sounds like the logic behind what the principle of parsimony (Occam's razor) is based off. the explanation with the fewest assumptions is usually the best one, because of probability
I feel like some or maybe even many people may choose the wrong answer in the test discussed at the beginning not because they're using that fallacy, but because of their expectations of test construction and human communication. As in, they see "and also a poker player" and assume that that's relevant information the test author is trying to hint them with(or other interpretations to this effect), and that becomes their basis for choosing rather than the logical fallacy discussed.
Ted-Ed just pulled a gotem!
1:43 is inaccurate because the set and subset could be the same size. The statement should say "...necessarily be bigger (or equal to) than the subset..."
It's obvious. Bigger than often includes them being equal as well.
I think it's about Lucy being an artist and a poker player being more plausibly close to the truth than just Lucy being an artist. What we're actually getting at here is how it seems like Lucy would be more the type to just be a poker player, if anything, so if that's the case, Lucy being that as well as an artist would be at least more plausible than her just being an artist. If she was that and not an artist, it would at least be significantly more close to the truth...
I'm exactly the type who tries to distinguish plausibility and probability, and even I fell for this. Granted, I got one question wrong at the end of a workbook math test when I was little because I missed the part where the sentence said "not" (I noticed they started to highlight them after that), but I feel like it should be a bit more clear. Maybe see if that changes anything
This is a great example of *”don’t assume things.“*
actually, if you don't assume things, you won't be able to function.