A distributed voting scheme to maximize preferences

We study the problem of designing a distributed voting scheme for electing a candidate that maximizes the preferences of a set of agents. We assume the preference of agent i for candidate j is a real number xi,j , and we do not make any assumptions on the mechanism generating these preferences. We show simple randomized voting schemes guaranteeing the election of a candidate whose expected total preference is nearly the highest among all candidates. The algorithms we consider are designed so that each agent has to disclose only a few bits of information from his preference table. Finally, in the important special case in which each agent is forced to vote for at most one candidate we show that our voting scheme is essentially optimal. Mathematics Subject Classification. 68W15, 91B12.