Using Monte Carlo Simulation for Classifying Electoral Systems

Abstract Many political scientists view electoral systems as falling on a continuum between pure proportional representation and single-member district voting. The closer an electoral system is to single-member district voting, the more strongly it tends to favor larger parties in the translation of votes into seats, thereby incentivizing voters to concentrate their support on larger parties. Although the continuum perspective is widespread, there is still no reliable measure that allows real-world electoral systems to be classified continuously with sufficient precision. This paper proposes a simulation-based approach that combines Monte Carlo methods with the Gallagher index to rank electoral systems along the continuum. Using a standardized procedure, 10,000 random vote distributions are generated for each UN member state. Based on these distributions, seats are allocated according to the respective electoral system, and the Gallagher index is calculated for each simulated vote distribution. Averaging the index values yields the simulative disproportionality index (DPIsim), which indicates where an electoral system is located on the proportional–majoritarian continuum. In contrast to empirical election results, simulated election outcomes are not affected by variation in strategic voting behavior or party system configurations and thus allow for more consistent comparisons across electoral systems.