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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.

• 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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