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← Can you outsmart this logical fallacy? - Alex Gendler

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Showing Revision 4 created 11/21/2019 by lauren mcalpine .

  1. Meet Lucy.
  2. She was a math major in college,
  3. and aced all her courses in probability
    and statistics.
  4. Which do you think is more likely: that
    Lucy is a portrait artist,
  5. or that Lucy is a portrait artist
    who also plays poker?
  6. In studies of similar questions, up to 80
    percent of participants

  7. chose the equivalent
    of the second statement:
  8. that Lucy is a portrait artist
    who also plays poker.
  9. After all, nothing we know about Lucy
    suggests an affinity for art,
  10. but statistics and probability
    are useful in poker.
  11. And yet, this is the wrong answer.
  12. Look at the options again.

  13. How do we know the first statement
    is more likely to be true?
  14. Because it’s a less specific version
    of the second statement.
  15. Saying that Lucy is a portrait artist
    doesn’t make any claims
  16. about what else she might or might not do.
  17. But even though it’s far easier to imagine
    her playing poker than making art
  18. based on the background information,
  19. the second statement is only true if she
    does both of these things.
  20. However counterintuitive it seems
    to imagine Lucy as an artist,
  21. the second scenario adds another condition
    on top of that, making it less likely.
  22. For any possible set of events, the
    likelihood of A occurring

  23. will always be greater than the likelihood
    of A and B both occurring.
  24. If we took a random sample of a million
    people who majored in math,
  25. the subset who are portrait artists might
    be relatively small.
  26. But it will necessarily be bigger
  27. than the subset who are portrait artists
    and play poker.
  28. Anyone who belongs to the second group
    will also belong to the first–
  29. but not vice versa.
  30. The more conditions there are,
    the less likely an event becomes.
  31. So why do statements with more conditions
    sometimes seem more believable?

  32. This is a phenomenon known as
    the conjunction fallacy.
  33. When we’re asked to make quick decisions,
    we tend to look for shortcuts.
  34. In this case, we look for what seems
  35. rather than what is statistically
    most probable.
  36. On its own, Lucy being an artist doesn’t
    match the expectations
  37. formed by the preceding information.
  38. The additional detail about
    her playing poker
  39. gives us a narrative that resonates
    with our intuitions—
  40. it makes it seem more plausible.
  41. And we choose the option that seems more
    representative of the overall picture,
  42. regardless of its actual probability.
  43. This effect has been observed
    across multiple studies,
  44. including ones with participants
    who understood statistics well–
  45. from students betting on
    sequences of dice rolls,
  46. to foreign policy experts predicting
    the likelihood of a diplomatic crisis.
  47. The conjunction fallacy isn’t just a
    problem in hypothetical situations.

  48. Conspiracy theories and false news stories
  49. often rely on a version of the conjunction
    fallacy to seem credible–
  50. the more resonant details are added
    to an outlandish story,
  51. the more plausible it begins to seem.
  52. But ultimately, the likelihood
    a story is true
  53. can never be greater than the probability
    that its least likely component is true.