[EM] Condorcet Jury Theorem

[Greg Nisbet]

my premise, poorly articulated, but my premise nonetheless is that an
"adaptive" voting method that takes into account voters' previous behavior
may be able to outperform OMOV in the long run on average.

P=NP is only meant to evoke the relevant properties of objective truth i.e.
that it is true or false and that people don't know for certain what it is.
It is also meant to illustrate how people are NOT Condorcet jurors
themselves. We are NOT objective truth with some noise thrown in. In fact,
even in the P=NP problem, we would only distrust putting it to a public vote
because we have so much additional information about the problem. In
retrospect, using it as an example was a mistake. A system of the ilk I am
proposing doesn't know anything about the "content" of the issues, simply
what different people believe.

Nevertheless, I believe that we can simulate a Condorcet jury by weighting
people differently based on past behavior. This would make the resulting
voting methods adaptive rather than memory-less. The current methods that I
believe have been proposed thus far are all memory-less. The result of the
n+1st election can't depend on the nth election, indeed the results of any
elections are independent of the order in which they are conducted.

However, I would argue that this ignores important information that we have
in real life. We know something about the structure of non-randomness in
people's opinions and can account for it. Assuming people are honest, I
believe it is possible for an adaptive voting method to outperform methods
that enforce OMOV for the very limited goal I set forward in my first post…
to attempt to determine the truth of propositions, not to make any type of
normative decision.


"I'm pretty sure that "P = NP?" is a question for which the average person
of the public's chance of getting the answer right is much lower than 50%.
So we don't ask the public (and if we had to, the jury theorem says we
should ask just a single person instead of averaging opinions).
Similar arguments have been made against democracy in general, even back to
the ancient Greek times, to the effect that statecraft is a skill and the
public isn't skilled. The jury theorem still works: you don't need to assume
people being wrong in non-random ways for the theorem to tell you it's not a
good idea to predict P = NP by vote."

You absolutely do need people to be wrong in non-random ways. If p<.5 for
people, but we were still Condorcet Jurors, you would ask as many people as
possible and then negate the answer. That clearly doesn't work; therefore,
we are not Condorcet Jurors. I'm not claiming that jury theorem doesn't work
or is inapplicable, far from it. I'm claiming that if we have more
information on voters and their past behavior, we should be able to devise
an algorithm that will outperform OMOV.*

*assuming honest voters. I don't want to have to worry about strategic
voters yet.
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