确保比例性：多议席选区中补偿席位增加的逻辑模型
Ensuring proportionality: a logical model for compensatory seats added to multi-member constituencies
- University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对多议席选区两级选举制度，通过逻辑推导得出补偿席位数的闭合公式，并用CLEA数据集验证，为葡萄牙等国提供具体补偿席位建议。
AI中文摘要：
在具有多议席选区的两级选举制度中，需要多少补偿席位才能确保（完全）比例性？这个问题通过严格、概率性和经验性地估计席位与选票之间的差异来回答。1919年，波利亚（Pólya）指出，杰斐逊/东特（Jefferson/D'Hondt）方法有利于大党。这种席位盈余在各选区累积。在一些国家（如葡萄牙、波兰、西班牙和土耳其），这种累积直接导致最终议会中可量化的比例失调。在其他地方，补偿席位抵消了这种累积的席位盈余。采用逻辑优先的方法，在给定区域和国家分配方法、相关政党数量$n$以及最大政党规模$p$的情况下，推导出所需补偿席位数的闭合公式。如果有$c$个选区，逻辑推导表明，基于多议席选区中地方东特分配的两级制度，需要大约$\frac{c}{2}(n-\frac{1}{p})$个补偿席位来确保比例性。换言之，即每个选区半个补偿席位乘以一个随政党数量和最大政党规模增加而增加的数。所推导公式的有效性通过使用广泛的近期CLEA数据集进行经验分析。许多量并不太依赖于议会总规模，这意味着可以通过人为改变议院规模来减少方差。葡萄牙、波兰、西班牙和土耳其都采用单级东特制度，分析表明，如果它们要在该制度中增加补偿席位，合理的数量分别为40、75、75和120，前提是制度中其他属性不变。
英文摘要：
How many compensatory seats are needed to ensure (full) proportionality in two-tier electoral systems with multi-member constituencies? This question is answered by estimating the discrepancy between seats and votes rigorously, probabilistically and empirically. In 1919, Pólya showed that the Jefferson/D'Hondt method favours large parties. This seat surplus accumulates across constituencies. In some countries (e.g., Portugal, Poland, Spain and Turkey), this accumulation directly leads to quantifiable disproportionality in the final parliament. Elsewhere compensatory seats counteract this accumulated seat surplus. Using a logic-first approach, closed formulas for the required number of compensatory seats are derived given regional and national apportionment methods, the number of relevant parties $n$ and the size of the largest party $p$. If there are $c$ constituencies, it is derived logically that a two-tier system built on local D'Hondt apportionment in multi-member constituencies needs around $\frac{c}{2}(n-\frac{1}{p})$ compensatory seats to ensure proportionality. In words, that is half a compensatory seat per constituency times a number that increases with the number of parties and the size of the largest party. The validity of the derived formulas is analysed empirically using the extensive recent CLEA dataset. Many quantities do not depend much on the total parliament sizes, which means that the variance can be reduced by artificially varying the house sizes. Portugal, Poland, Spain and Turkey all employ a one-tier D'Hondt system and the analysis shows that if they were to add compensatory seats to the system, reasonable numbers would be 40, 75, 75 and 120, assuming that no other properties of the systems change.
