Multiwinner Approval Rules as Apportionment Methods

TL;DR

This paper connects approval-based multiwinner election rules with apportionment methods, revealing how certain voting rules correspond to well-known proportional representation techniques.

Contribution

It demonstrates that multiwinner approval rules can be interpreted as apportionment methods, establishing a formal link between voting rules and apportionment procedures.

Findings

Proportional Approval Voting induces the D'Hondt method.

Monroe's rule induces the largest reminder method.

Certain multiwinner rules induce apportionment methods with desirable properties.

Abstract

We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that they induce apportionment methods that are well-established in the literature on proportional representation. For instance, we show that Proportional Approval Voting induces the D'Hondt method and that Monroe's rule induces the largest reminder method. We also consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment methods satisfying these properties.