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Social choice, optimal inference and figure skating

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  • Stephen Gordon
  • Michel Truchon

Abstract

We approach the social choice problem as one of optimal statistical inference. If individual voters or judges observe the true order ona set of alternatives with error, then it is possible to use the set of individual rankings to make probability statements about the correct social order. Given the posterior distribution for orders and a suitably chosen loss function, an optimal order is one that minimises expected posterior loss. The paper develops a statistical model describing the behaviour of judges, and discusses Markov Chain Monte Carlo estimation. We also discuss criteria for choosing the appropriate loss functions. We apply our methods to a well-known problem: determining the correct ranking for figure skaters competing at the Olympic Games.
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  • Stephen Gordon & Michel Truchon, 2008. "Social choice, optimal inference and figure skating," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 265-284, February.
    • Handle: RePEc:spr:sochwe:v:30:y:2008:i:2:p:265-284
    DOI: 10.1007/s00355-007-0243-2
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    References listed on IDEAS

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    1. Tommi Meskanen & Hannu Nurmi, 2006. "Distance from Consensus: A Theme and Variations," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 117-132, Springer.
    2. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    3. Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.
    4. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    5. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
    6. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    7. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
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    Citations

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    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Michel Truchon, 2002. "Choix social et comités de sélection : le cas du patinage artistique," CIRANO Burgundy Reports 2002rb-02, CIRANO.
    3. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    4. Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    5. Eric Zitzewitz, 2014. "Does Transparency Reduce Favoritism and Corruption? Evidence From the Reform of Figure Skating Judging," Journal of Sports Economics, , vol. 15(1), pages 3-30, February.
    6. Boudreau, James & Ehrlich, Justin & Sanders, Shane & Winn, Adam, 2014. "Social choice violations in rank sum scoring: A formalization of conditions and corrective probability computations," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 20-29.
    7. James Boudreau & Justin Ehrlich & Mian Farrukh Raza & Shane Sanders, 2018. "The likelihood of social choice violations in rank sum scoring: algorithms and evidence from NCAA cross country running," Public Choice, Springer, vol. 174(3), pages 219-238, March.

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    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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