Approval voting and Shapley ranking

Approval voting allows voters to list any number of candidates. Their scores are obtained by summing the votes cast in their favor. Fractional voting instead follows the One-person-onevote principle by endowing voters with a single vote that they may freely distribute among candidates. In this paper, we show that fairness requires the distribution of votes to be uniform. Uniform fractional voting corresponds to Shapley ranking that was introduced to rank wines as the Shapley value of a cooperative game with transferable utility. Here we analyze the properties of these "ranking games" and provide an axiomatic foundation to Shapley ranking. We also analyze Shapley ranking as a social welfare function and compare it to approval ranking.