Representation and district magnitude in plurality systems

Despite the widely accepted theoretical prediction that high district magnitudes should yield less proportional results in plurality systems, empirical evidence is surprisingly mixed. We argue that these mixed results are ultimately due to a lack of clarity about the counterfactual being considered. We use a simple model to show that an increase in district magnitude reduces expected proportionality in a plurality system only if it is accompanied by a reduction in the number of districts. This conditional prediction helps to explain the diversity of existing findings and is consistent with our own analysis of both U.S. congressional delegations and local councils in Britain.