Endogenously Weighted Voting

We define Endogenously Weighted Plurality Voting (EWPV) as the voting rule that, each individual being allowed to cast exactly one vote, selects the individual(s) who obtain(s) the greatest number of indirect votes. Endogenously Weighted Approval Voting (EWAV) selects the individual(s) who obtain(s) the greatest number of indirect votes when each individual can cast as many votes as he wants. In both cases, each individual can vote for any other individual, i.e., the set of candidates is the set of voters. In this study, we give necessary and sufficient axioms for EWPV and EWAV. We also propose a simple model where EWAV is more efficient than the traditional Approval Voting.