Referendum Paradox for Party-List Proportional Representation

We consider two-tiers elections based on closed party-list proportional representation (PLPR), where party platforms involving multiple dichotomous issues are endogenously determined by their supporters’ preferences (via issue-wise simple majority voting). Assuming that voters compare platforms according to the criterion of the Hamming distance and provided a high enough number of voters and issues, we show that the outcome of PLPR may be Pareto dominated by the multiple referendum outcome defined as the issue-wise majority will in the whole electorate. We refer to this situation as the PLPR paradox. We characterize the set of party platforms for which the PLPR paradox is possible. We also investigate several restrictions upon voting situations that may be sufficient for avoiding the paradox.