Estimating Historical Election Results under Counterfactual Electoral Systems

• In Event: Alternative Voting Schemes

Abstract

Despite the salience and importance of electoral system reform, not just in the political science literature but also 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 present new methodological tools for estimating historical election results under counterfactual electoral systems. Specifically, I use data from elections that happened under a Single-Member District (SMD) plurality ruleset to develop the methodology required to estimate what would have happened if that election had occurred under a variety of different rulesets instead. In this stage of the project I focus on the case of Canada, because it has a long democratic history during which it has (nearly) always used an SMD plurality electoral system, but is also currently engaged in a highly salient public conversation about changing that electoral system to a more proportional ruleset. Ultimately, I aim to give a range of credible answers to questions like: what would happen if America abolished the Electoral College?

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 considerations. So I present two sets of models: one simple set that assumes strategic voting does not occur, and a more complex set that explicitly models strategic voting.

First I present methods for estimating historical elections under several different counterfactual electoral systems given the strong assumption that strategic voting does not occur. For some counterfactual electoral systems and in the absence of strategic voting, we can exactly calculate the number of seats obtained by each party. This includes many proportional allocation systems, for example party list proportional representation with the largest remainder method, as well as any system that combines existing districts into larger districts, for example translating a riding-based parliamentary system into a regional proportional system or an electoral college. For other systems, for example ranked choice voting or party list proportional representation with runoffs, more sophisticated methods are required to estimate choices that electors did not have to declare. I use spatial models and data from public surveys to simulate rankings and runoff stages under the assumption that votes are not a function of the electoral system.

Of course, this assumption is only a starting point; surely some electors would change their vote choice in response to a change in the electoral system. To account for this, I present early results from the extension of a formal model of strategic voting to cover electoral systems other than SMD plurality. Two major problems arise in creating this extension. First, a full methodology to estimate how strategic voting would differ between electoral systems requires a unified model of how strategic voting incentives differ from one electoral system to another when electors hold the same sincere preferences. Worse, in order to estimate expected strategic behaviour under counterfactual systems using data under SMD, we would first require a model of strategic voting under SMD that agrees with the empirical historical election results. To handle these problems, I present early work on a series of plausible models that could have produced a given empirical election outcome. Some simple properties of the electorate can be inferred with minimal assumptions: for example, given rational preferences an elector should never vote for their least-preferred party. Other parameters can be varied to produce multiple plausible ways of generating the election result, and by varying these parameters I present estimates of a range of outcomes that could have resulted from a change in the electoral system in that election.

The conversation about electoral system reform, in Canada as in many democracies, is based on claims about the outcomes of electoral system changes that have very little evidence. In order to better understand how future elections would change under varied electoral rulesets, a clear case to develop our theories on is historical election data. By constructing game theoretic predictions so that they agree with past empirical results, comparing them to a baseline of totally sincere voting, and presenting a range of possible results under strategic behaviours, we can develop more realistic predictions about how specific countries’ elections would change if they were to adopt a particular alternative electoral system.

Author

• Samuel Baltz, Massachusetts Institute of Technology