In article <_PcS5.firstname.lastname@example.org>, Chip Eastham <email@example.com> wrote:
>"Dan Goodman" <dog@fcbobDOTdemon.co.uk> wrote in message >news://firstname.lastname@example.org...
>> p.s. the Isaac Asimov story isn't that much like my random democracy idea, >> because the vote is effectively made by Multivac, I haven't read the story >> but I'm sure this is the idea. The whole point of the random democracy >idea >> is to get rid of the fiction of a "best" government that "most represents" >> the views of the populace, as this is an unattainable ideal (cf. Arrow's >> paper "A Difficulty in the Concept of Social Welfare" in the Journal of >> Political Economy volume 58 issue 4), and to replace it with a government >> that is statistically unbiased.
>I thought the sci-fi analogy was pretty close, though in some of Asimov's >stories it did seem that Multivacs was able to predict human actions before >they occurred, though not necessarily with 100% accuracy.
>One wonders if the ancient Greeks would have fought as hard for >"statistically unbiased" government as they did for the "fiction" of one >that "most represents" those governed.
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.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 email@example.com Phone: (765)494-6054 FAX: (765)494-0558