Strategic voting under proportional representation

Previous investigations of strategic voting equilibria in mass electorates have looked only at elections held under plurality-rule electoral laws. This paper investigates such equilibria in multimember districts operating under Various largest-remainders methods of proportional representation (PR). In principle, strategic voting imposes a limit on the number of viable lists under PR, just as it imposes a limit on the number of viable candidates under plurality rule, as noted long ago. The results proved here provide some formal underpinning for this idea and yield specific hypotheses, for each electoral system, concerning the maximum number of lists/candidates consistent with equilibrium levels of strategic voting. Our results also clarify the conditions under which these theoretical upper bounds on the number of lists/candidates are binding in practice. We use Colombian and Japanese electoral data to test the model's predictions.