Working paper

Title: Proportional Representation and Vote Splitting in Mixed Electoral Systems. 

Author: Biung-Ghi Ju, Hocheol SHIN and Hucheol Jeon (Seoul National University)

Abstract:
In mixed electoral systems, parties may attempt to increase their proportional representation (PR) seats through vote splitting (with their allies or satellite-parties). We compare standard and new PR (seat allocation) rules in terms of their manipulability via vote splitting and their PR efficiency (seat ratios should be as close to vote shares as possible). Our results exhibit trade-offs between non-manipulability and PR efficiency. We show that the two requirements are not compatible. In the family of semi-mixed-member proportional (semi-MMP) rules including mixed-member majority rule (MMM), mixed-member proportional rule (MMP), and a spectrum of their hybrids, we show that improving PR efficiency necessitates sacrificing non-manipulability, and vice versa. Among PR efficient rules, constrained equal losses rule uniquely minimizes disproportionality, and constrained equal gains rule minimizes the vote splitting gain using satellite parties. Given any “well-behaved” rule, vote splitting (the satellite-party strategy) is weakly dominant over no splitting; and in the weakly dominant strategy equilibrium, any semi-MMP yields the same allocation of PR seats as MMM violating PR efficiency. Hence, to achieve PR efficiency, some measures preventing vote splitting strategy should be introduced.