Size Approval Voting

We propose a new class of voting rules, called Size Approval Voting. According to this rule, the e®ective weight of a vote from a given indi- vidual depends on how many other alternatives the very same individ- ual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved alternatives. Then, for a given pro¯le of individual votes, all those alternatives with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting is characterized by a set of natural properties