When Politics and Models Collide: Estimating Models of Multiparty Elections

TLDR

The spatial model of elections, which traditionally uses multinomial logit, fails to account for party substitutability and may not reflect voter decision‑making in multiparty contexts, suggesting conditional logit models that incorporate party positions could provide a more accurate representation. The study tests whether multinomial logit offers advantages over successive binomial logit applications and examines whether conditional logit and multinomial probit better capture party dynamics and relax the IIA assumption. The authors compare binomial logit, multinomial logit, conditional logit, and multinomial probit models using simulated data and survey data from multiparty elections to assess estimation accuracy. Multinomial logit provides little advantage over binomial logit, while conditional logit enables analysis of party movements; multinomial probit outperforms conditional logit for evaluating the impact of changing the choice set and can be feasibly estimated with more than three alternatives.

Abstract

Theory: The spatial model of elections can better be represented by using conditional logit models which consider the position of the parties in issue spaces than by multinomial logit models which only consider the position of voters in the issue space. The spatial model, and random utility models in general, suffer from a failure to adequately consider the substitutability of parties sharing similar or identical issue positions. Hypotheses: Multinomial logit is not necessarily better than successive applications of binomial logit. Conditional logit allows for considering more interesting political questions than does multinomial logit. The spatial model may not correspond to voter decision-making in multiple party settings. Multinomial probit allows for a relaxation of the IIA condition and this should improve estimates of the effect of adding or removing parties. Methods: Comparisons of binomial logit, multinomial logit, conditional logit, and multinomial probit on simulated data and survey data from multiparty elections. Results: Multinomial logit offers almost no benefits over binomial logit. Conditional logit is capable of examining movements by parties, whereas multinomial logit is not. Multinomial probit performs better than conditional logit when considering the effects of altering the set of choices available to voters. Estimation of multinomial probit with more than three choices is feasible