> 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.