Triadic consensus: A randomized algorithm for voting in a crowd

Abstract

Typical voting rules do not work well in settings with many candidates. If there are even several hundred candidates, then a simple task such as evaluating and choosing a top candidate becomes impractical. Motivated by the hope of developing group consensus mechanisms over the internet, where the numbers of candidates could easily number in the thousands, we study an urn-based voting rule where each participant acts as a voter and a candidate. We prove that when participants lie in a one-dimensional space, this voting protocol finds (1 - ∈/ √n) a approximation of the Condorcet winner with high probability while only requiring an expected O(1/∈2 log2 n/∈2) comparisons on average per voter. Moreover, this voting protocol is shown to have a quasi-truthful Nash equilibrium: namely, a Nash equilibrium exists which may not be truthful, but produces a winner with the same probability distribution as that of the truthful strategy. © 2012 Springer-Verlag.