Analyzing Complete Approval Voting Data under Thurstonian Framework

賽斯通架構下完整核准式選擇資料之分析

10.6129/CJP.2010.5202.06

蔡蓉青(Rung-Ching Tsai)；Ringo Moon-Ho Ho

核准式選擇 ； 隨機效用模型 ； approval voting ； random utility model

中華心理學刊

52卷2期（2010 / 06 / 01）

205 - 219

英文

核准式選擇是一種常用的票選型態。在核准式選擇的票選型態中，選民要從選項中挑選出他（她）所核准的部分選項。例如在聘任委員會於面談後要決定是否錄用應徵者時，在第一階段很常見的作法就是使用核准其資格的核准式選擇。過去在面對核准式選擇這類的社會決策資料時，「全選」和「全不選」兩種選擇反應大都因為不影響票選結果，在資料分析時常常是將其摒除於分析或模型之外。然而「全選」和「全不選」兩種選擇其實是很普遍且常常被收集或觀察到的選擇反應，所以在了解核准式選擇行為背後的機制時，實有將其涵蓋在內的必要。在此論文中，我們嘗試延伸目前利用效用模型的架構來調查核准式選擇行為背後機制的作法，特別將「全選」和「全不選」兩種選擇反應也考慮進去，以期能更完整地了解選擇行為背後的機制以及票選行為之中的個別差異。最後會利用兩個實際應用的例子來說明提出的效用模型之用途及評估它在描述決策機制上的表現。

The method of approval voting is a commonly used voting procedure. In an approval voting task, each judge is usually asked to select a subset of the alternatives. For example, it is a common practice that the recruiting committee, after interviewing a set of job applicants, may apply approval voting to determine the qualification of the candidates at the first run of the hiring process. In analyzing social choices such as elections, the ”none” and ”all” responses are often discarded since they do not affect on the overall decision or conclusion. However, in understanding and modeling the approval voting mechanism or heuristics, it becomes preferable to include these two responses in the analysis as well. In this paper, we extend the current random utility approach to allow for the modeling of ”none” and ”all” responses and therefore provide a more complete account of the approval voting mechanism in the underlying choice process as well as the individual difference in their judgment. Empirical examples are given to illustrate the usefulness of our approval voting model formulation.

1. Agresti, A.(1996).An introduction to categorical data analysis.New York:Wiley.
2. Aitkin, M.,Anderson, D.,Hinde, J.(1981).Statistical modeling of data on teaching styles (with discussion).Journal of Royal Statistical Society,419-461.
3. Aitkin, M.,Rubin, D. B.(1985).Estimation and hypothesis testing in finite mixture models.Journal of Royal Statistical Society. Series B,47(1),67-75.
4. Akaike, H.(1970).Statistical predictor identification.Annals of the Institute Statistical Mathematics,22,203-217.
5. Brams, S. J.,Fishburn, P. C.(1983).Approval voting.Boston:Birkhauser.
6. Brams, S. J.,Nagel, J. H.(1991).Approval voting in practice.Public Choice,71,1-17.
7. deDoncker, E.,Ciobanu, M.,Genz, A.(1999).Parallel computation of multivariate normal probabilities.Computing Science and Statistics,31,89-93.
8. Everitt, B. S.(1988).A Monte Carlo investigation of the likelihood ratio test for number of classes in latent class analysis.Multivariate Behavioral Research,23,531-538.
9. Falmagne, J. C.,Regenwetter, M.(1996).A random utility model for approval voting.Journal of Mathematical Psychology,40,152-159.
10. Fishburn, P. C.,Little, J. D. C.(1988).An experiment in approval voting.Management Science,34,555-568.
11. Fligner, M. A.(ed.),Verducci, J. S.(ed.)(1992).Lecture notes in statistics: Vol. 80. Probability models and statistical analyses for ranking data.New York:Springer.
12. Hurvich, C. M.,Tsai, C.-L.(1989).Regression and time series model selection in small samples.Biometrika,76,297-307.
13. Kahneman, D.,Tversky, A.(1979).Prospect theory: An analysis of decision under risk.Econometrica,47,263-291.
14. Luce, R. D.(1992).Where does subjective-expected utility fail descriptively?.Journal of Risk and Uncertainty,5,5-27.
15. Maydeu-Olivares, A.,Böckenholt, U.(2005).Structural equation modeling of paired- comparison and ranking data.Psychological Methods,10,285-304.
16. Merrill, S.(1979).Approval voting: A 'best buy' method for multi-candidate elections?.Mathematics Magazine,52,98-102.
17. Regenwetter, M.,Grofman, B.(1998).Approval voting, borda winners, and condorcet winners: Evidence from seven elections.Management Science,44,520-533.
18. Regenwetter, M.,Ho, M.-H.,Tsetlin, I.(2007).Sophisticated approval voting, ignorance priors, and plurality heuristics: A behavioral social choice analysis in a Thurstonian framework.Psychological Review,114,994-1114.
19. Thurstone, L. L.(1927).A law of comparative judgment.Psychological Review,34,273-286.
20. Tsai, R.,Böckenholt, U.(2006).Modeling intransitive preferences: A random-effects approach.Journal of Mathematical Psychology,50,1-14.
21. Tsai, R.,Böckenholt, U.(2002).Two-level linear paired comparison models: Estimation and identifiability Issues.Mathematical Social Sciences,43,429-449.
22. Yang, C. C.,Yang, C. C.(2007).Separating latent classes by information criteria.Journal of Classification,24,183-203.