Division of the Humanities and Social Sciences California Institute of Technology Pasadena, California 91125 When Politics and Models Collide: Estimating Models of Multi-party Elections

Theory: The spatial model of elections can better be represented by using conditional logit than by multinomial logit. The spatial model, and random utility models in general, suffer from a failure to adequately consider the sub­ stitutability of candidates sharing similar or identical issue positions. Hypotheses: Multinomial logit is not much 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-candidate settings. Multi­ nomial 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 a three-party election. Results: Multinomial logit offers almost no benefits over binomial logit. Con­ ditional logit is capable of examining movements by parties , whereas multi­ nomial logit is not . Multinomial probit performs better than conditional logit when considering the effects of altering the set of choices available to voters. *Earlier versions of this research were presented at the Annual Meetings of the American Political Science Association, Chicago, IL., September 1995 and at the Annual Political Methodology Summer Conference, Indianapolis, July, 1995. We thank John Aldrich, Nathaniel Beck, Mitch Sanders, Jonathan Katz, Simon Jackman, John Jackson, Dean Lacy, Jan L"eighley, Will Moore, Mitch Sanders and Guy W hitten for their comments on earlier versions of this research, and Methodology Conference participants· for their input. We also thank participants of the Southern California Political Economy Group for their discussion of this research on November 17, 1995 at the University of California-Irvine. Alvarez thanks the John M. Olin Foundation for support of his research. Nagler thanks the NSF for grant SBR9413939. Comments may be directed to the authors at: DHSS 228-77, California Institute of Technology, Pasadena, Ca 91125, Internet: [email protected]; and Department of Political Science, University of California, Riverside, Ca 92521-0118, Internet: [email protected], respectively. 1 The Theory and the Practice of Issue Voting Mod­