Consideration sets, intentions and the inclusion of "don't know" in a two-stage model for voter choice

TL;DR: In this paper, the authors present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage and explicitly accounts for the three types of missing data encountered in polling.

About: This article is published in International Journal of Forecasting.The article was published on 2004-05-01 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Multinomial probit & Missing data.

Summary

1 INTRODUCTION

• Modeling and forecasting voter choice is a key topic in the political science literature.
• Given the use of the models for such an important topic, it should not come as a surprise that there is abundant literature on the design and implementation of models for voter choice.
• The key problem for the inclusion of non-voters, that is, those who do not know and those who do not want to say into a forecasting model is of course the fact that there is no answer to the question concerning the voting intention for these individuals.
• Hence, it is of interest to include questions on consideration sets in the questionnaire, also since these may receive less “do not know” or “do not want to say” responses.
• In Section 5 the authors report on the empirical results and they provide a discussion of the main conclusions that can be drawn from these results.

2.1 Preliminaries

• The authors denote the stated vote intention prior to the election by the variable di, which can take J + 3 different values.
• If di = J + 1 the individual does not intend to vote, while di = J +2 indicates that the individual does not know yet and di = J +3 indicates that the individual does not want to say his or her vote intention.
• Individuals are assumed not to consider all parties in their decision process, but to choose one party from a particular subset of the parties at a particular point in time.
• Hence, for each individual there are Q = 2J potential consideration sets.
• Note that an individual may have an empty consideration set, which implies that he or she does not consider any party at all.

2.2 Two-stage Model

• The goal of this paper is to construct a choice model for the vote intention of the individuals stated prior to the elections and to use this model to predict the actual vote of the individuals at the election.
• In the second stage the authors model the actual choice among the parties in the consideration set of this individual.
• The parameter therefore models the effect of state-dependence.
• Additionally, the authors assume that an individual may always decide not to vote at all and hence they impose that ci;J+1 = 1 for all i.
• For identification purposes the authors impose that J+1 equals zero.

3.1 Estimation

• To estimate the model parameters in their two-stage model, the authors consider the likelihood function for the stated considerations and party choices of the individuals, c = fci; i = 1; : : : ;.
• The likelihood function involves the product of the probability that the consideration set of individual i is c i and the probability that the party choice is di given ci for all individuals, and thus for a given individual the product of a multivariate and a multinomial probit probability.
• The authors assume a flat prior distribution for the model parameters and use the Gibbs sampling approach of Geman and Geman (1984) to obtain posterior results.
• The unobserved utilitiesD ij and C i are sampled alongside the model parameters (data augmentation), see Tanner and Wong (1987).
• For details on a Gibbs sampling approach in multivariate and multinomial probit models, the authors refer to Albert and Chib (1993), McCulloch and Rossi (1994), Chib and Greenberg (1998), and McCulloch, Polson and Rossi (2000).

3.2 Forecasting

• The goal of this paper is to model the vote intention of individuals prior to the election and to use the estimated model to predict the actual voting behavior of the individuals in the upcoming election.
• These predictive probabilities can easily be computed using the Gibbs output.
• If the vote intention is unknown, the authors use their model and parameter estimates to predict the vote.
• In forecasting, the authors do not reweight the sample.
• In that case the choice simply corresponds to the largest utility.

4.1 Political Context

• The political context in this paper concerns the Dutch 1994 parliament elections.
• Shifts in the preference distribution can have substantial political consequences.
• To form the government a coalition of two or more parties has to represent 50% or more of the voters.
• Currently the four important political parties are CDA (Christian ), D’66 , PvdA (Social ), and VVD .
• The government of The Netherlands has formed a coalition between two or three of these four parties for the past several decades.

4.2 Data

• The authors data were collected by the market research agency Inter/View in April and June 1994 (elections were held in June 1994).
• The authors combine the other parties into one “Other party”(j = 5) category.
• As explanatory variables, individual-specific socio-economic and demographic variables are contained in the k-dimensional vector xi.
• The authors believe this stated voting behavior to be the best yardstick available for validation in the absence of the option of retrieving the real votes.

4.3 Descriptive Statistics of the Data

• Table 1 summarizes the actual votes in 1989, the intentions in 1994, the consideration set 1994, the actual votes in 1994, as well as a cross-tabulation of the vote intention variable with the explanatory variables.
• The VVD appear to be home owners with high incomes.
• This category could consider politics to be something quite distinct from their own interests.
• Finally, the “do not want to say” category does not have a particularly clear profile.
• Only for 2289 (49.5%) of the individuals, the vote intention is the same as their actual vote, which may be considered as a rather low number.

5 RESULTS AND COMPARISONS

• Next to the two-stage model presented above, the authors estimate three simplified versions of it.
• Note that this model does not predict the “no vote” option.
• Table 5 shows the posterior mean and standard deviation of the covariance matrix of the multivariate probit model for the consideration set formation.
• And, if the authors finally add the consideration set stage as in model D, the prediction becomes even better.
• Similarly, VVD appears to be competing less with PvdA and D’66 in model D1 relative to C.

6 CONCLUSIONS AND LIMITATIONS

• The prediction of outcomes of elections for political parties and candidates receives much interest in democracies across the world, an interest that is reflected intensive media coverage.
• Rather than imputing those missing responses based on available procedures, the authors have postulated a plausible behavioral mechanism for them that enables forecasts of votes of subjects in each of those categories.
• Loosely speaking, this sampler switches the two steps in the Metropolis-Hasting sampler of Metropolis et al. (1953).
• To derive the full conditional posterior distributions, the authors consider three cases.
• Sampling of and Æ Model (A.4) can be seen as a multivariate regression model with regression parameters and Æ.

Figures

Table 1: Descriptive statistics

Table 6: Prediction results of total election for the four models and fit statistics

Figure 1: Marginal predictive posterior densities of total election results

Table 7: Covariance matrix of the predictions

Table 2: Cross-tabulation of intended and actual vote

Table 4: Posterior results MNP-part of the 2-stage model

Table 5: Posterior results for in MVP-part of the 2-stage model

Table 3: Posterior results MVP-part of the 2-stage model

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Consideration sets, intentions and the inclusion of “don’t know” in a two-stage model for voter choice" ?

The authors present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage. Thus, the authors consider the missing data generating mechanism to be non-ignorable and build a model based on utility maximization to describe the voting intentions of these respondents. The authors illustrate the merits of the model as they have information on a sample of about 5000 individuals from the Netherlands for who they know how they voted last time ( if at all ), which parties they would consider for the upcoming election, and what their voting intention is. The authors find that the inclusion of the consideration set stage in the model enables the user to make more precise inferences on the competitive structure in the political domain and to get better out-of-sample forecasts. 

Q2. What are the future works mentioned in the paper "Consideration sets, intentions and the inclusion of “don’t know” in a two-stage model for voter choice" ?

The authors find that the predictive capacity of the model is further improved by the inclusion of a state-dependence variable accounting for previous voting behavior as an explanatory variable. The development of models to accommodate such effects is an important topic for future research. The authors leave these issues for future research. However, the authors can not split this set into all the parties it consists of, because the response parameters would be unidentified due too few observations. 

Q3. What are the variables that are included in the k-dimensional vector xi?

As explanatory variables, individual-specific socio-economic and demographic variables are contained in the k-dimensional vector xi. 

Q4. What is the term I[d 1 i = j]?

The term I[d 1 i = j] is a dummy variable that equals 1 if the actual vote of the individual in the previous election is party j and zero elsewhere. 

Q5. What is the effect of the consideration set stage on the prediction of election outcomes?

The authors find that the addition of the consideration set stage improves predictive accuracy and strongly decreases the posterior variance of the predictions. 

Q6. What are the limitations of the model?

One limitation is that the “other party” option includes very heterogenous parties, whereas their model assumes that the explanatory variables affect the choice for all parties within this set in the same way. 

Q7. What is the significance of the consideration set stage in the prediction of elections?

The prediction of outcomes of elections for political parties and candidates receives much interest in democracies across the world, an interest that is reflected intensive media coverage. 

Q8. What is the purpose of the consideration set stage in the model?

the inclusion of the consideration set stage in the model enables the user to make more precise inferences on the competitive structure in the political domain and to get better out-of-sample forecasts.