Justice in Voting by Demand Revelation
In: Public choice, Band 29, Heft 2, S. 65-70
ISSN: 0048-5829
The demand-revealing method of making public choices, in its original form, has a feature that many people regard as unjust, ie, it gives too much voting power to the wealthy. This objection can be overcome by adopting the generalized demand-revealing method defined as follows. There are N voters Vi (i = 1,2, $..., N) & (for simplicity) just two options or candidates A & B. Voter Vi "puts up" an amount xi of money & T is defined as summation i of fi (xi), where fi is a continuous strictly increasing unbounded function such that fi (0) = 0. Option B is adopted if T greater than 0 & not if T less than 0. Then Vi pays nothing if T - fi (xi), denoted by Si, has the same sign as T, ie, if Vi did not affect the outcome. Otherwise he is charged an amount fi to the -1 power (absolute value of Si) where fi to the -1 power denotes the inverse function of fi. The ordinary method has fi(x) = x for all i & x. A complete proof that this procedure motivates honesty is given, & this also supplies a proof for the ordinary case, which had not been previously published in complete detail. 1 Figure. AA.