Approval voting and Shapley ranking

Approval voting allows electors to list any number of candidates and their final scores are obtained by summing the votes cast in their favor. Equal-and-even cumulative voting instead follows the One-person-one-vote principle by endowing each elector with a single vote that may be distributed evenly among several candidates. It corresponds to satisfaction approval voting, introduced by Brams and Kilgour (in: Fara et al (eds) Voting power and procedures. Essays in honor of Dan Fesenthal and Moshé Machover, Springer, Heidelberg, 2014) as an extension of approval voting to a multiwinner election. It also corresponds to the concept of Shapley ranking, introduced by Ginsburgh and Zang (J Wine Econ 7:169–180, 2012) as the Shapley value of a cooperative game with transferable utility. In the present paper, we provide an axiomatic foundation for Shapley ranking and analyze the properties of the resulting social welfare function.