Multiwinner approval rules as apportionment 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 some, but not all, of them induce apportionment methods that are well-established in the literature and in the actual practice of representation, be it proportional or non-proportional. For instance, we show that proportional approval voting induces the D'Hondt method and that Monroe's rule induces the largest remainder method. Our approach also yields apportionment methods implementing degressive proportionality. Furthermore, we consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment methods satisfying these properties.