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Imagine a police line-up
where ten witnesses
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are asked to identify a bank robber
they glimpsed fleeing the crime scene.
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If six of them pick out the same person,
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there's a good chance
that's the real culprit,
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and if all ten make the same choice,
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you might think the case is rock solid,
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but you'd be wrong.
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For most of us,
this sounds pretty strange.
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After all, much of our society
relies on majority vote and consensus,
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whether its politics,
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business,
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or entertainment.
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So it's natural to think
that more consensus is a good thing.
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And up until a certain point,
it usually is.
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But sometimes, the closer you start to get
to total agreement,
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the less reliable the result becomes.
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This is called the paradox of unanimity.
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The key to understanding
this apparent paradox
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is in considering the overall level
of uncertainty
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involved in the type of situation
you're dealing with.
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If we asked witnesses to identify
the apple in this line up, for example,
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we shouldn't be surprised
by a unanimous verdict.
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But in cases where we have
reason to expect some natural variance,
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we should also expect varied distribution.
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If you toss a coin one hundred times,
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you would expect to get heads
somewhere around 50% of the time.
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But if your results started
to approach 100% heads,
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you'd suspect that something was wrong,
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not with your individual flips,
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but with the coin itself.
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Of course, suspect identifications aren't
as random as coin tosses,
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but they're not as clear cut
as telling apples from bananas, either.
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In fact, a 1994 study found
that up to 48% of witnesses
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tend to pick the wrong
person out of a line-up,
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even when many
are confident in their choice.
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Memory based on short glimpses
can be unreliable,
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and we often overestimate
our own accuracy.
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Knowing all this,
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a unanimous identification starts to seem
less like certain guilt,
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and more like a systemic error,
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or bias in the line-up.
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And systemic errors don't just appear
in matters of human judgement.
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From 1993-2008,
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the same female DNA was found
in multiple crime scenes around Europe,
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incriminating an elusive killer
dubbed The Phantom of Heilbronn.
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But the DNA evidence was so consistent
precisely because it was wrong.
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It turned out that the cotton swabs
used to collect the DNA samples
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had all been accidentally contaminated
by a woman working in the swab factory.
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In other cases, systematic errors arise
through deliberate fraud,
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like the presidential referendum held
by Saddam Hussein in 2002,
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which claimed a turnout of 100% of voters
with all 100% supposedly voting in favor
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of another seven-year term.
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When you look at it this way,
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the paradox of unanimity isn't actually
all that paradoxical.
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Unanimous agreement
is still theoretically ideal,
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especially in cases when you'd expect very
low odds of variability and uncertainty,
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but in practice,
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achieving it in situations where
perfect agreement is highly unlikely
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should tell us that there's probably
some hidden factor affecting the system.
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Although we may strive for harmony
and consensus,
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in many situations, error and disagreement
should be naturally expected.
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And if a perfect result seems too good
to be true,
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it probably is.