The fairest voting system is one where no one needs to vote! Ok, not quite.
This essay shows that if voters have to choose between several alternative options (where each option is assigned a score) and if each player has a preference (defined on the same scale as the scores) then under a reasonable definition of satisfaction it turns out that the best alternative is that whose score is closest to the average of all player preferences. Therefore, knowing the voters' preferences is sufficient and no voter actually needs to vote at all.
Moreover, I also show that if any one voter is insincere in his or her preferences, in an attempt to affect the results of the voting process, then the most that he or she can effect is a change of 1/N in the average preference, where N is the total number of voters.
Of course, in practice, no one knows how to assign scores to voting alternatives so these results are of academic interest only. They could, however, be applied to simulations of voter behavior, and in games.
Originally written on June 1, 2007.
I'm sharing this work under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license. See the LICENSE file for more information.