Proportional Public Decisions

We consider a setting where a group of individuals make a number of independent decisions. The decisions should proportionally represent the views of the voters. We formulate new criteria of proportionality and analyse two rules, Proportional Approval Voting and the Metod of Equal Shares, inspired by the corresponding committee election rules. We prove that the two rules provide very strong proportionality guarantees when applied to the setting of public decisions. Our Contribution In this paper we propose new formal criteria of proportionality that capture the following intuition: an α fraction of voters shall be able to influence at least α fraction of decisions. Thus, our criteria require that a rule used for making decisions should respect minorities of voters to the extent