Multiwinner Approval Rules as Apportionment Methods
This work connects theoretical frameworks in voting theory and apportionment, potentially aiding in the design of fairer electoral systems, but it is incremental as it builds on existing concepts.
The paper links multiwinner election rules to apportionment methods, showing that specific rules like Proportional Approval Voting correspond to established methods such as the D'Hondt method, and explores properties of these induced methods.
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.