When politics and models collide: Estimating models of multiparty elections

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 decisionmaking 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.