Portal de Periódicos da CAPES

Hierarchical Bayesian Prediction Methods in Election Politics: Introduction and Major Test

2013; Taylor & Francis; Volume: 12; Issue: 4 Linguagem: Inglês

10.1080/15377857.2013.837311

1537-7865

David J. Curry, James J. Cochran, Rajesh Radhakrishnan, Jon Pinnell,

Sports Analytics and Performance

Abstract The authors build a collection of latent construct models, one per voter, in a representative sample of the voting age population. A given voter's model is an algebraic expression of how that person integrates information about candidates and issues to arrive at a vote decision. Modeling individual decisions—called agent-based modeling—avoids aggregation fallacies and yields diagnostic insights unavailable from traditional pre-election polling methods. This article summarizes tests of the predictive accuracy of the method using data from 10 battleground states in the 2004 U.S. presidential election. Results are presented for the popular vote, the Electoral College vote, and within person. (Each person's predicted vote is compared to that person's actual vote obtained from a post-election survey.) Model accuracy is assessed relative to a standard voting intention model and to a meta-poll approach that combines multiple traditional polls over time, within state. The model's predictive accuracy compares favorably with other models tested, increasing confidence in its insights about voting behavior. A companion article expands on these diagnostics and reviews applications of the approach to campaign strategy and planning. KEYWORDS: agent-based modelingcampaign strategydiscrete-choice analysiselection diagnosticselection forecastingelection metricselection politicshierarchical Bayes modeling Acknowledgments The authors deeply appreciate William F. Christensen's contributions to our prediction validation efforts. Notes Source: Time, October 25, 2004. *All results are significant at p < .0001 or higher. a The November 1, 2004, meta-poll provides the best forecasts of the six meta-polls available. b The effective sample size of a meta-poll is a function of the number of polls available within a state up to that time, the size of each available poll, and each poll's relative age. c Totals for percentages are weighted totals using the total votes cast in each state as weights. (Using each state's electoral votes as weights yields the same values within 1 in 10,000.). d The raw mean squared error (MSE) has been multiplied by 1,000 for readability. a An electoral vote forecast is marked correct if it forecasts at least ½ × 146 = 73 votes for President Bush. A probability of winning forecast is marked correct if it exceeds 0.5 for President Bush. b mean squared error (MSE) for probability of winning has been multiplied by 1,000 for readability. Twenty-one polls had Senator Clinton trailing in New Hampshire (www.pollster.com/ 08-NH-Dem-Pres-Primary.php). The following polling/news organizations had her behind by 10 or more points: Reuters/CSPAN (Zogby) in 2 polls, USA Today (Gallup), ARG in 2 polls, Rasmussen in 3 polls, and CNN/WMUR (University of New Hampshire). Actual results are from CNN.com's Election Center. Other researchers, foremost Louviere et al. (Citation2000), offer elaborate discussions that explain the broad applicability of random utility theory and its many variants. For readers new to this area, these discussions are worthwhile. They are not summarized here. Although the example portrays the values as observable, in practice they are latent and as such would directly determine parameter estimates in a pooled model that aggregates data over individuals. Thus, in practice the situation is worse than portrayed in Table 1 because the analyst would not “see” the mistake. Note further that the fundamental incompatibility between the individual and aggregate “utility functions” is scale independent (Arrow Citation1963.). “Because automatic processes are not accessible to consciousness, people often have surprisingly little introspective insight into why automatic choices or judgments were made. A face is perceived as “attractive” or a verbal remark as “sarcastic” automatically and effortlessly. It is only later that the controlled system may reflect on the judgment and attempt to substantiate it logically, and when it does, it often does so spuriously (e.g., Wilson, Lindsey, and Schooler Citation2000).”. Standard statistical criteria, such as orthogonality, refer to properties of XTX, where X is the design matrix. Advanced criteria include level balance, minimum overlap between choice sets, and utility balance (Zwerina, Huber, and Kuhfeld Citation2005; Kessels et al. Citation2006; Kessels et al. Citation2008). We illustrate the power of MCMC methods to accurately estimate individual-level parameters in the Appendix. We use the term state to refer to all entities that feed electoral votes to the Electoral College, that is, states, the District of Columbia, and Congressional districts of states (Maine and Nebraska) that use the Congressional district method. Readers not familiar with the complexities of the U.S. Electoral College are referred to Christensen and Florence (Citation2008) or Kaplan and Barnett (Citation2003). Most polls published in the popular press are conducted by telephone using variations of random digit dialing plus conventional stratification and respondent qualification techniques (Taylor Citation2003; Berren and Bohara 2001). As the next section makes clear, the experimental design elements of our methods cannot be easily accomplished by telephone. Data from this pretest served as the basis for a master's degree thesis in the Department of Quantitative Analysis at the University of Cincinnati. For example, with five candidates in a single mock election, there are 248,832C5 = 7.9494e +024 ways of filling the election slate. To put this number in perspective, there are 31,536,000 seconds in a year. The fastest PCs today would require about 2.5e +012 years to simply enumerate all possible slates, a time longer than best estimates of the age of the universe, for example, 14e +09. Commercial pollsters use various stratification and other research design features unique to their organization and may use “statistical reweightings” of raw data during the analysis stage. Results are from the website CNN.com Election Results. In all likelihood none of our panelists participated in other polls prior to the 2004 election, a conclusion based on the vanishingly small likelihood of actually being invited to participate in another poll plus their commitment to the panel used in this research. A total of 1220 panelists participated in the pre-election phase. We removed panelists considering voting for a third-party candidate, yielding an analysis sample of size 1054. Post-election 888 panelists participated, but 38 indicated they did not vote, 2 voted for Ralph Nader, and 1 voted for an unnamed candidate, leaving 847 voters for the model versus actual comparisons. We define the perceived clarity of a candidate's position on a given issue as the reciprocal of Shannon's information measure for a random variable with n outcomes (positions) where the probability of the ith outcome is p i; i.e., I is maximized when the n positions are equiprobable; the case where the voting public is least sure of the candidate's position. The inverse of I, therefore, reflects clarity of position. These forms are (1) the single best profile to satisfy the most voters (Camm et al. Citation2006), (2) the best k profiles to satisfy the most voters (Wang, Camm, and Curry Citation2009), and (3) the single best profile when the utility estimates at the voter level are error prone (Wang and Curry Citation2010). The large number of “find your matching candidate” websites for the 2008 election is a testimonial to the importance of issues. However, these crude approaches neither pose nor assess trade-offs. Further, they use the same scoring rule on every participant rather than estimate the latent rule a person may use. As such, these approaches miss the nuances of differential weighting and differential value assessments. To operationalize a multivariate mixture model, each voter is viewed as being selected at random from the ensemble of sub-populations, which is a multinomial process with a Dirichlet density as the conjugate prior. See Rossi et al. Citation2005, p. 79. Additional informationNotes on contributorsDavid J. Curry David J. Curry is a professor of Marketing at the Lindner College of Business, at the University of Cincinnati. He received his PhD from the University of California, Berkeley, specializing in marketing, mathematical psychology, and psychometrics. His research currently focuses on alternative algebras for discrete-choice modeling and MCMC estimation techniques. James J. Cochran James J. Cochran is Bank of Ruston, Barnes, Thompson, & Thurman Endowed Research Professor and professor of Quantitative Analysis at Louisiana Tech University. He received his PhD from the University of Cincinnati, specializing in statistics and operations research. His research currently focuses on frequentist and Bayesian approaches to constrained optimization over sample data, finitization of probability distributions, optimization in nontraditional applications, and humanitarian applications. He is a Fellow of the American Statistical Association. Rajesh Radhakrishnan Rajesh Radhakrishnan is a load modeling and data analysis expert at Integral Analytics, Inc. in Cincinnati, OH. He holds master's degrees in Electrical Engineering and Quantitative Analysis from the University of Cincinnati. His interests lie in the areas of optimization, simulation, operations research, statistical analysis and programming. Jon Pinnell Jon Pinnell is the founder of the eponymously named consultancy focused on buyer decision making, consumer choice, and statistical methods. He has presented workshops in over 20 different countries. He received the Lysacker Award and was previously President of MarketVision Research. He has a master's degree from the University of Texas.