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.
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