Heterogeneity in General Multinomial Choice Models

2001

In this paper I describe the mixed logit (MXL), a flexible discrete choice model based on random utility maximization, and discuss its applicability to the study of multiparty elections. 1 Mixed logit models have seen application in marketing and transportation research (Algers, Bergstriom, Dahlberg, and Dill'en 1999; Bhat 1998a, 1998b; Brownstone and Train 1999; Jain, Vilcassim, and Chintagunta 1994; Revelt and Train 1998; Train 1998), but have seen only limited application in political science (Glasgow 2001).

1999

We propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analogous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas.

Political Studies, 2005

Most models assume that voting behaviour can be summarised by a single additive equation. There are good reasons, however, for believing that some voters place more weight on some considerations than others or use different decision rules. In both cases, a single additive equation will produce misleading accounts of the causal processes. Modellers should therefore allow for such differences. In order to illustrate these propositions, I examine evidence from the 2001 British Election Study, which suggests that some voters place more weight on leaders than others. I end by calling for attention to shift from causal complexity to causal diversity.

2014

Electoral democracies are built on the idea of representation. The electorate selects politicians to represent their interests in the law-making process. Given that citizens hold meaningful preferences about political outcomes, this electoral linkage is supposed to ensure that implemented policies are in line with the public’s will. In political science, spatial voting theories model this connection between citizens’ opinions about policies and their electoral decisions. But what if ordinary voters are not equipped with policy views that easily permit them to select matching candidates: does this distort the simple model of representative democracy? I argue that the electoral linkage between voters and candidates is affected if voters do not reflect the assumptions made about their policy preferences in spatial voting theories. Spatial voting theory builds on a rational choice framework in which policy preferences are assumed to be well-defined, fixed and exogenous. For decades, beh...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This article develops a formal framework to aid political designers in the comparison of social choice functions. It generalizes earlier assumptions of "impartial culture" so that we may begin to investigate the effect of politically interesting variations on the probability that different social choice functions will satisfy given performance criteria. As an application of the framework, a detailed Monte Carlo study compares the ability of four different social choice functions to select a Condorcet winner when voter preference orders have been generated from a spatial representation of ideal points and alternatives. We also investigate the potential of alternative methods of selecting winners in presidential primary elections.

American Journal of Political Science, forthcoming, 2013

Empirical models of spatial voting allow legislators’ locations in an abstract policy or ideological space to be inferred from their roll call votes. These are typically random utility models of Euclidean spatial voting, where voters assign utility to each of two alternatives associated with each roll call. The specific functional forms of the utility functions are generally assumed rather than estimated. In this paper, we attempt to infer important features of these utility functions. We first consider a model in which legislators’ utility functions are assumed to be a mixture of the two most commonly assumed utility functions (the Gaussian function assumed by NOMINATE and the quadratic function assumed by IDEAL and many other estimators). Applying this estimator to large number of roll call data sets, we find that in nearly every case legislators’ utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result is substantively important to the formation and interpretation of law, because it suggests that extremists are ideologically rigid whereas moderates are more likely to consider influences that arise outside liberal–conservative conflict. Finally, we considered a third model extension examining the possibility that legislators have asymmetric utility functions. Our results tentatively suggest that, conditional on party, as legislators become more conservative their sensitivity to policy alternatives on the right increases.

SSRN Electronic Journal, 2000

Formal work on the electoral model often suggests that parties should locate at the electoral mean. Recent research has found no evidence of such convergence. In order to explain non-convergence, the stochastic electoral model is extended by including a competence and sociodemographic valance in a country where regional and national parties compete in the election. That is, the model allows voters to face different sets of parties in different regions. We introduce the notion of a convergence coefficient, c for regional and national parties and show that when c is high there is a significant centrifugal tendency acting on parties. An electoral survey of the 2004 election in Canada is used to construct a stochastic electoral model of the election with two regions: Québec and the rest of Canada. The survey allows us to estimate voter positions in the policy space. The variable choice set logit model is used to built a relationship between party position and vote share. We find that in the local Nash equilibrium for the election the two main parties with high competence valence, the Liberals and Conservatives, locate at the national electoral mean and the Bloc Québécois, with the highest competence valence, locates at the Québec electoral mean. The New Democratic Party has a low competence valence but remains at the national mean. The Greens, with lowest competence valence, locate away from the national mean to increase its vote share.

Most election forecasting research to date has been conducted in the context of single-round elections. However, more than 40 countries in the world employ a two-stage process, where actual voting data are available between the first and the second rounds to help politicians understand their position in relation to each other and to voter preferences and to help them predict the final outcome of the election. In this study we take advantage of the theoretical foundation on voter behavior from the political science literature and the recent methodological advances in choice modeling to develop a Nested Logit Factor Model of voter choice which we use to predict the final outcome of two stage elections and gain insights about the underlying political landscape. We apply the proposed model to data from the first stage and predict the final outcome of two stage elections based on the inferences made from the first stage results. We demonstrate how our proposed model can help politicians understand their competitive position immediately after the first round of actual voting and test its predictive accuracy in the runoff election across 11 different state governorship elections.

We consider six models of voter behavior that might govern the statistical process of vote-casting. From an empirical analysis of "election-like" data we conclude that a spatial model of voting, augmented by a specified error structure, describes this process much better than the other five models. An important benefit of identifying the properties of this process is that doing so permits one to evaluate voting methods in terms of their success in identifying the proper winners of elections, so that it is not necessary to rely entirely on comparisons of logical properties in evaluating voting methods.

2011

We analyze the interaction between electoral competition and voters' decision to vote. We show that when voters consider both the benefits and the costs of voting, politicians offer differentiated policies to motivate citizens to vote. In particular, politicians adapt their policies to the most sensitive voters—thus less sensitive voters abstain on the grounds of perceiving politicians as being too similar. In a multidimensional policy space, this implies that citizens who only care about a few issues do not vote.

Games, 2013

We study strategic voting in a setting where voters choose from three options and Condorcet cycles may occur. We introduce in the electorate heterogeneity in preference intensity by allowing voters to differ in the extent to which they value the three options. Three information conditions are tested: uninformed, in which voters know only their own preference ordering and the own benefits from each option; aggregate information, in which in addition they know the aggregate realized distribution of the preference orderings and full information, in which they also know how the relative importance attributed to the options are distributed within the electorate. As a general result, heterogeneity seems to decrease the level of strategic voting in our experiment compared to the homogenous preference case that we study in a companion paper. Both theoretically and empirically (with data collected in a laboratory experiment), the main comparative static results obtained for the homogenous case carry over to the present setting with preference heterogeneity. Moreover, information about the realized aggregate distribution of preferences seems to be the element that best explains observed differences in voting behavior. Additional information about the realized distribution of preference intensity does not yield significant further changes.

2007

The profound transformations in Chile’s party structure since 1989 has led several authors to examine the main cleavages shaping partisan divide and the impact of different factors on citizens’ party preferences. No study, however, has examined the influence of these factors on actual vote choice. We implement a Bayesian multinomial probit model to analyze voter choice in Chile’s 2005 election. We show that the authoritarian-democratic cleavage dominated voter choice, with socio-demographic variables playing a less important role. We also find that the presence of a second conservative candidate significantly affected citizens’ electoral behavior, increasing the support for the right and influencing the electoral outcome in a way that cannot be accounted for by analyses focused exclusively on citizens’ party identification.

SSRN Electronic Journal, 2009

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 socioeconomic 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).

Electoral Studies, 1998

Analysis of plurality voting where district magnitude is greater than one offers students of electoral behaviour unique opportunities. In this paper we use aggregate voting data from English local elections to explore a number of issues concerning the relationship between parties, candidates and voters. Our first task is to measure the level of unused votes and consider the impact of party competition and electoral marginality. Multimember districts also provide the potential for intra-party comparisons of candidates. Accordingly, we measure the range of votes between candidates from the same party and consider the impact of incumbency, gender and ballot position on differential rates of electoral support. Although the empirical focus of the paper is on English local government, its findings may well prove relevant to an understanding of the relationship between voters and parties in other electoral systems where a choice about the number of votes to use and the way in which to cast them is available.

Sociological Methodology

In this article, a modeling strategy is proposed that accounts for heterogeneity in nominal responses that is typically ignored when using common multinomial logit models. Heterogeneity can arise from unobserved variance heterogeneity, but it may also represent uncertainty in choosing from alternatives or, more generally, result from varying coefficients determined by effect modifiers. It is demonstrated that the bias in parameter estimation in multinomial logit models can be substantial if heterogeneity is present but ignored. The modeling strategy avoids biased estimates and allows researchers to investigate which variables determine uncertainty in choice behavior. Several applications demonstrate the usefulness of the model.