[EM] Condorcet Jury Theorem

[Kristofer Munsterhjelm]

Greg Nisbet wrote:
> http://en.wikipedia.org/wiki/Condorcet's_jury_theorem
> 
> Let's pretend for the moment that we are attempting to determine the
> truth of propositions rather than deciding on policy (this matters,
> since policy decisions can't be objectively right or wrong and alters
> what the "credibility" function would be, as I will describe later)
> 
> now the condorcet jury theorem has a bunch of assumptions, but two of
> them are relevant for the question I wish to pose to the community
> today
> 
> 1) objective truth exists. A jury's decision is either correct or
> incorrect and by the condorcet jury theorem this probability
> approaches one as teh jury size approaches infinity.
> 
> 2) the condorcet jury theorem assumes that all the jury members vote
> completely independently of each other.
> 
> now for the purposes of democracy (1) doesn't hold true as stated.
> there's no such thing as a "correct" policy decision. I suppose we
> could modify our notion of correct to mean "correct according to the
> correct utility function" but that ultimately doesn't get us anywhere
> ... so I'll just pretend that we're voting on propositions rather than
> policy decisions.
> 
> now (2) obviously does not hold in real life. voter's guesses are not
> independent of each other. That's why we don't expect to be able to
> guess difficult math problems like "P = NP" or the like by proposing
> them to the general population and seeing what most people vote on.
> Ignorance has patterns to it... people are wrong in non-random ways.

Eh, I don't see how that follows. The Condorcet jury theorem says that, 
given your assumptions (objective truth and independence), then if the 
prospective jury members each have a greater than 50% chance to reach 
the right decision on a yes/no vote, adding more members to the jury 
will improve the probability that they get it right, while if they have 
less than 50% chance, adding more members to the jury will lower that 
probability.

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.