Skip to main content

Advertisement

Log in

Probabilistic models of profiles for voting by evaluation

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

Considering voting rules based on evaluation inputs rather than preference rankings modifies the paradigm of probabilistic studies of voting procedures. This article proposes several simulation models for generating evaluation-based voting inputs. These models can cope with dependent and non identical marginal distributions of the evaluations received by the candidates. A last part is devoted to fitting these models to real data sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

No data availability statement is applicable here.

Notes

  1. Data are available in the supplementary material. The association is the Eclaireuses and Eclaireurs Unionistes de France and the general assembly stood in January 2022 in Bordeaux, France. Data are from private communication.

References

  • Alvo M, Philip L (2014) Statistical methods for ranking data, vol 1341. Springer, New York

    Book  Google Scholar 

  • Armstrong DA, Bakker R, Carroll R, Hare C, Poole KT, Rosenthal H (2021) Analyzing spatial models of choice and judgment, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  • Aubin J-B, Gannaz I, Leoni S, Rolland A (2022) Deepest voting: a new way of electing. Math Soc Sci 116:1–16

    Article  Google Scholar 

  • Balinski M, Laraki R (2007) A theory of measuring, electing and ranking. Proc Natl Acad Sci 104(21):8720–8725

    Article  Google Scholar 

  • Barbiero A, Ferrari PA (2017) An R package for the simulation of correlated discrete variables. Commun Stat Simul Comput 46(7):5123–5140

    Article  Google Scholar 

  • Berend D, Sapir L (2007) Monotonicity in Condorcet’s jury theorem with dependent voters. Soc Choice Welf 28:507–528

    Article  Google Scholar 

  • Berg S (1994) Evaluation of some weighted majority decision rules under dependent voting. Math Soc Sci 28(2):71–83

    Article  Google Scholar 

  • Bouveret S, Blanch R, Baujard A, Durand F, Igersheim H, Lang J, Laruelle A, Laslier J-F, Lebon I, Merlin V (2018) Voter autrement 2017—online experiment. Zenodo. DOI: https://doi.org/10.5281/zenodo.1199545

  • Brams SJ, Fishburn PC (2007) Approval voting, 2nd edn. Springer, New York

    Google Scholar 

  • Chollete L, Peña V, Klass M (2023) The price of independence in a model with unknown dependence. Math Soc Sci 123:51–58

    Article  Google Scholar 

  • Cooper DA (2007) The potential of cumulative voting to yield fair representation. J Theor Polit 19(3):277–295

    Article  Google Scholar 

  • Cooper D, Zillante A (2012) A comparison of cumulative voting and generalized plurality voting. Public Choice 150:363–383

    Article  Google Scholar 

  • Crain BR (1979) Estimating the parameters of a truncated normal distribution. Appl Math Comput 5(2):149–156

    Google Scholar 

  • Critchlow DE, Fligner MA, Verducci JS (1991) Probability models on rankings. J. Math. Psychol. 35(3):294–318

    Article  Google Scholar 

  • Cuberos A, Masiello E, Maume-Deschamps V (2020) Copulas checker-type approximations: application to quantiles estimation of sums of dependent random variables. Commun Stat Theory Methods 49(12):3044–3062

    Article  Google Scholar 

  • de Leeuw J, Mair P (2009) Multidimensional scaling using majorization: SMACOF in R. J Stat Softw 31(3):1–30

    Article  Google Scholar 

  • Diss M, Kamwa E (2020) Simulations in models of preference aggregation. Œconomia 10(2):279–308

    Google Scholar 

  • Downs A (1957) An economic theory of political action in a democracy. J Polit Econ 65(2):135–150

    Article  Google Scholar 

  • Dubin JA, Gerber ER (1992) Patterns of voting on ballot propositions: a mixture model of voter types. Technical report, California Institute of Technology

  • Durand F (2015) Towards less manipulable voting systems. Theses, Université Pierre et Marie Curie-Paris VI, September 2015

  • Durrleman V, Nikeghbali A, Roncalli T (2000) Which copula is the right one? SSRN Electron J (08). https://doi.org/10.2139/ssrn.1032545

  • Favardin P, Lepelley D (2006) Some further results on the manipulability of social choice rules. Soc Choice Welf 26(3):485–509

    Article  Google Scholar 

  • Gehrlein WV (2006) Condorcet’s paradox. Theory and decision library C. Springer, Berlin

    Google Scholar 

  • Genest C, Favre A-C (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4):347–368

    Article  Google Scholar 

  • Gormley IC, Murphy TB (2008) Exploring voting blocs within the Irish electorate: a mixture modeling approach. J Am Stat Assoc 103(483):1014–1027

    Article  Google Scholar 

  • Green-Armytage J, Tideman N, Cosman R (2016) Statistical evaluation of voting rules. Soc Choice Welf 46(1):183–212

    Article  Google Scholar 

  • Guiver J, Snelson E (2009) Bayesian inference for Plackett–Luce ranking models. In: Proceedings of the 26th annual international conference on machine learning, Montreal, Canada, pp 377–384

  • Joe H (2001) Multivariate extreme value distributions and coverage of ranking probabilities. J Math Psychol 45(1):180–188

    Article  Google Scholar 

  • Ladha KK (1995) Information pooling through majority-rule voting: Condorcet’s jury theorem with correlated votes. J Econ Behav Organ 26(3):353–372

    Article  Google Scholar 

  • Lantz B (2013) The large sample size fallacy. Scand J Caring Sci 27(2):487–492

    Article  Google Scholar 

  • Lin J (2016) On the Dirichlet distribution. Technical report, Department of Mathematics and Statistics, Queens University

  • Lin M, Lucas HC, Shmueli G (2013) Research commentary: too big to fail: large samples and the p-value problem. Inf Syst Res 24(4):906–917

    Article  Google Scholar 

  • Luce RD (1959) Individual choice behavior: a theoretical analysis. Wiley, New York

    Google Scholar 

  • McFadden D (1978) Modeling the choice of residential location. In: Spatial interaction theory and planning models, Karlqvist A, Lundqvist T, Snickers P and Weibull J (Eds), North Holland, pp 75–96

  • Milewski GB (2004) Using Bayesian methods to evaluate Thurstone’s simple structure concept. Fordham University, New York

    Google Scholar 

  • Murphy TB, Martin D (2003) Mixtures of distance-based models for ranking data. Comput Stat Data Anal 41(3–4):645–655

    Article  Google Scholar 

  • Negriu A, Piatecki C (2012) On the performance of voting systems in spatial voting simulations. J Econ Interact Coord 7(1):63–77

    Article  Google Scholar 

  • Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York

    Google Scholar 

  • Ng KW, Tian G-L, Tang M-L (2011) Dirichlet and related distributions: theory, methods and applications. Wiley, New York

    Book  Google Scholar 

  • Panagiotelis A, Czado C, Joe H (2012) Pair copula constructions for multivariate discrete data. J Am Stat Assoc 107(499):1063–72

    Article  Google Scholar 

  • Plassmann F, Tideman N (2014) How frequently do different voting rules encounter voting paradoxes in three-candidate elections? Soc Choice Welf 42(1):31–75

    Article  Google Scholar 

  • Poole KT, Sowell FB, Spear SE (1992) Evaluating dimensionality in spatial voting models. Math Comput Model 16(8–9):85–101

    Article  Google Scholar 

  • Rolland A, Grimault N (2023) voteSim: generate simulated data for voting rules using evaluations. R package version 0.1.0. https://CRAN.R-project.org/package=voteSim

  • Smith WD (2000) Range voting. DOI: https://doi.org/10.1.1.32.915

  • Szufa S, Faliszewski P, Skowron P, Slinko AM, Talmon N (2020) Drawing a map of elections in the space of statistical cultures. Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems. https://api.semanticscholar.org/CorpusID:218606924

  • Thurstone LL (1927) A law of comparative judgment. Psychol Rev 34(4):273

    Article  Google Scholar 

  • Tideman N, Plassmann F (2012a) Developing the empirical side of computational social choice. In: Annals of mathematics and artificial intelligence, vol 68 (1–3):31–64

  • Tideman N, Plassmann F (2012b) Modeling the outcomes of vote-casting in actual elections. In: Felsenthal DS, Machover M (eds) Electoral systems: paradoxes, assumptions, and procedures. Springer, New York, pp 217–251

  • Tideman N, Plassmann F (2014) Which voting rule is most likely to choose the “best’’ candidate? Public Choice 158(3/4):331–357

    Article  Google Scholar 

  • Tripathi RC, Gupta RC, Gurland J (1994) Estimation of parameters in the beta binomial model. Ann Inst Stat Math 46(2):317–331

    Article  Google Scholar 

  • Wilhelm S, G MB (2023) tmvtnorm: Truncated multivariate normal and student T distribution. R package version 1.6. https://CRAN.R-project.org/package=tmvtnorm

  • Yu PL (2000) Bayesian analysis of order-statistics models for ranking data. Psychometrika 65:281–299

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the reviewers for their seminal and helpful remarks on earlier versions of this article.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antoine Rolland.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rolland, A., Aubin, JB., Gannaz, I. et al. Probabilistic models of profiles for voting by evaluation. Soc Choice Welf 63, 377–400 (2024). https://doi.org/10.1007/s00355-024-01535-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-024-01535-0

Navigation