An Alternative Approach to Ml Estimation of Multinomial Choice Models

The principal assumption of a multinomial choice model is that there are a number of individuals whose properties are known; I also observe the choice of each individual, and the set of alternatives available to him. I can then construct a utility function that is associated with each of the outcomes, and estimate its parameters --- usually through the maximim likelihood method (although sometimes different methods, such as Bayesean estimation, are used). This methodology ignores additional information that is sometimes available in the problem context. Consider, for example, a problem of modeling a voter's choice in an election. On the input, one usually has data from a pre-election survey, where each respondent indicates his socio-economic characteristics, his policy preferences on a set of issues, and the political party (or candidate) he intends to vote for. In a "spatial' voting model it is assumed that the voter's utility toward a party is a function of the distances between the voter's preferences on each issue, and the party's stated positions on those issues (Poole and Rosenthal, 1984; Schofield and Sened, 2006). All previous research treated party positions as exogenous and arbitrary. However, from the problem context I know that each party cares about the share of vote that it receives. I know that the observed policy positions of each party is rational, conditional on the party's utility function, the set of alternative policy positions available to the party, and the party's knowledge of the voters' decision model. That information is ignored in the traditional multinomial choice models, since the set of alternatives available to each party is not observable. This short paper proposes a methodology to incorporate this additional information in the likelihood function. In the first section, I postulate the assumptions used in this approach, and define the modified likelihood function. In the second section, I use it to re-evaluate a voting model estimated in Schofield (2007)