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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?

  • In studies of similar questions, up to 80 percent of participants

  • chose the equivalent of the second statement:

  • that Lucy is a portrait artist who also plays poker.

  • After all, nothing we know about Lucy suggests an affinity for art,

  • but statistics and probability are useful in poker.

  • And yet, this is the wrong answer.

  • Look at the options again.

  • How do we know the first statement is more likely to be true?

  • Because it's a less specific version of the second statement.

  • Saying that Lucy is a portrait artist doesn't make any claims

  • about what else she might or might not do.

  • But even though it's far easier to imagine her playing poker than making art

  • based on the background information,

  • the second statement is only true if she does both of these things.

  • However counterintuitive it seems to imagine Lucy as an artist,

  • the second scenario adds another condition on top of that, making it less likely.

  • For any possible set of events, the likelihood of A occurring

  • will always be greater than the likelihood of A and B both occurring.

  • If we took a random sample of a million people who majored in math,

  • the subset who are portrait artists might be relatively small.

  • But it will necessarily be bigger

  • than the subset who are portrait artists and play poker.

  • Anyone who belongs to the second group will also belong to the first

  • but not vice versa.

  • The more conditions there are, the less likely an event becomes.

  • So why do statements with more conditions sometimes seem more believable?

  • This is a phenomenon known as the conjunction fallacy.

  • When we're asked to make quick decisions, we tend to look for shortcuts.

  • In this case, we look for what seems plausible

  • rather than what is statistically most probable.

  • On its own, Lucy being an artist doesn't match the expectations

  • formed by the preceding information.

  • The additional detail about her playing poker

  • gives us a narrative that resonates with our intuitions

  • it makes it seem more plausible.

  • And we choose the option that seems more representative of the overall picture,

  • regardless of its actual probability.

  • This effect has been observed across multiple studies,

  • including ones with participants who understood statistics well

  • from students betting on sequences of dice rolls,

  • to foreign policy experts predicting the likelihood of a diplomatic crisis.

  • The conjunction fallacy isn't just a problem in hypothetical situations.

  • Conspiracy theories and false news stories

  • often rely on a version of the conjunction fallacy to seem credible

  • the more resonant details are added to an outlandish story,

  • the more plausible it begins to seem.

  • But ultimately, the likelihood a story is true

  • can never be greater than the probability that its least likely component is true.

Meet Lucy.

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B1 TED-Ed lucy poker portrait fallacy artist

Can you outsmart this logical fallacy? - Alex Gendler

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    林宜悉 posted on 2020/04/15
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