Multiwinner approval voting: an apportionment approach

To ameliorate ideological or partisan cleavages in councils and legislatures, we propose modifications of approval voting in order to elect multiple winners, who may be either individuals or candidates of a political party. We focus on two divisor methods of apportionment, first proposed by Jefferson and Webster, that fall within a continuum of apportionment methods. Our applications of them depreciate the approval votes of voters who have had one or more approved candidates elected and give approximately proportional representation to political parties. We compare a simple sequential rule for allocating approval votes with a computationally more complex simultaneous (nonsequential) rule that, nonetheless, is feasible for many elections. We find that our Webster apportionments tend to be more representative than ours based on Jefferson—by giving more voters at least one representative of whom they approve. But our Jefferson apportionments, with equally spaced vote thresholds that duplicate those of cumulative voting in two-party elections, are more even-handed. By enabling voters to express support for more than one candidate or party, these apportionment methods will tend to encourage coalitions across party or factional lines, thereby diminishing gridlock and promoting consensus in voting bodies.