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Re: Math and the electoral college's virtue
Posted:
Nov 20, 2000 4:38 PM
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> What does "statistically unbiased" mean here? In statistics,
> an unbiased estimator is one whose expectation is the value
> of the parameter; in testing, an unbiased test is one for
> which the probability of rejection under any alternative is
> at least as great as under the null hypothesis.
>
> If one adds randomization, the proof of the Arrow Paradox
> becomes extremely short; the problem is that the utility
> function has an arbitrary scale parameter.
What I meant by it was that in a "random democracy", nobody's vote is more
important than anyone else's, which isn't true in general for nonrandom
democracies. In the recent American elections for example, a vote for Nader
(at least in terms of deciding who the president is, it has other purposes)
is essentially a wasted vote. The random democracy system has a few things
going for it, for instance strategic voting wouldn't happen, because there
really would be no point voting for anyone except who you really want to get
in. Of course it has disadvantages too, it's much more susceptible to
corruption for instance.
How would you adapt Arrow's proof to deal with randomization? I'm not
entirely sure what this would mean.
Dan Goodman
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