Can you outsmart this logical fallacy? - Alex Gendler
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.
