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.

我们考虑基于封闭式政党名单比例代表制（PLPR）的两级选举，其中涉及多个二分问题的政党平台是由其支持者的偏好（通过问题方式的简单多数投票）内生决定的。假设选民根据汉明距离的标准比较平台，并提供足够多的选民和议题，我们表明PLPR的结果可能是帕累托所主导的，这是由多次公投决定的，即在议题上多数派将全体选民。我们将这种情况称为PLPR悖论。我们描述了PLPR悖论可能发生的聚会平台的特征。我们还研究了对投票情况的几种限制，这些限制可能足以避免出现这种矛盾。