Estimating Historical Election Results Under Counterfactual Electoral Systems

Samuel Baltz (University of Michigan)

Abstract: Despite the salience and importance of electoral system reform, both in the political science literature and in the contemporary politics of many democracies, little direct attention has been paid to the following question: how might the results of a specific election have been different if it had been conducted under another electoral system? Using long-term historical data, game theory, and computational modeling, I develop new methodological tools for estimating historical election results under counterfactual electoral systems. Specifically, I use data from elections that used a Single-Member District plurality ruleset to estimate what would have happened if those elections had occurred under a variety of different rulesets instead. The core challenge of this counterfactual question is that electors' vote choices can be a function of the electoral system; the main mechanism through which this occurs is strategic voting. So I present two sets of models: one simpler set assuming that strategic voting does not occur, and a more complex set that explicitly models strategic voting. For some counterfactual electoral systems (like proportional representation without runoffs), we can exactly calculate the number of seats obtained by each party under the assumption that there is no strategic voting; for others (like ranked choice voting), I combine election results with survey data to simulate rankings and runoffs. Then I relax the too-strong assumption that votes are not a function of the electoral system, and I explicitly model strategic choices. I present several new ideas for simulating an electorate with realistic preferences that could have produced the observed election result, and then tweak the electoral system to obtain a distribution of plausible results under a counterfactual ruleset. By constructing game theoretic scenarios which could agree with the empirically observed results, comparing them to a baseline of sincere voting, and presenting a range of possible results that include strategic behaviours, I present specific conjectures about how countries' election results might change if they were to adopt some alternative electoral system.

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