[Election-Methods] A Monotone, Clone Proof Lottery for which Sincere Rankings = Optimal Strategy (Correction)

[fsimmons at pcc.edu]

I'm sorry to say my original claim is not true.

Counterexample:

Sincere Rankings
4 A>B>C
3 B>A>C
2 C>B>A

If (in the third faction) B is sufficiently close to C in utility, it is to that faction's advantage to reverse the order of B and C.

On the other hand, as long as C has greater utility than B, and epsilon is sufficiently small, the probability distribution

(1/9 - epsilon, 1/9 - .75epsilon, 1/9 - .50episilon, ... , 1/9 + epsilon)

in place of my original suggestion will do the job.

In this example, epsilon < 2*(deltaR)/9 is sufficiently small, where deltaR is the percentage difference in utility between C and B.

Forest

> 
> Draw a ballot at random. Use the ranking on this ballot to rank 
> all of the other ballots from worst to best 
> according to their favorites. 
> 
> Elect the favorite indicated on the k_th ballot with probability 
> 2*k/(n+n^2) , where n is the number of 
> ballots.
>