The cost of proportional representations in electoral system design

We present an impossibility result concerning the design of dual vote electoral systems that meet three key conditions: proportional party representation, proportional local representation, and local accountability. By identifying the necessary number of compensatory seats to meet these three conditions in dual vote systems, we show that the number is not bounded in general; thus, it can be very costly to achieve the three conditions. When a cap is applied to the total seats, combined with a district-decentralization, semi-compensatory dual vote systems that distribute the limited compensatory seats to enhance proportionality become vulnerable to strategic manipulations. Specifically, when political parties seek to maximize their legislative representation, they might employ the strategy of creating 'decoy' party lists.