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Construction of voting situations concordant with ranking patterns

Author

Listed:
  • Emilio De Santis

    (University of Rome La Sapienza)

  • Fabio Spizzichino

    (University of Rome La Sapienza)

Abstract

Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections’ outcomes, no matter how paradoxical it may appear. In this respect, we consider a set of candidates $$1, 2, \ldots , m $$ 1 , 2 , … , m and, for any subset A of $$\{1, 2, \ldots , m \}$$ { 1 , 2 , … , m } , we fix a ranking among the candidates belonging to A. We wonder whether it is possible to find a population of voters whose preferences, expressed according to the Condorcet’s proposal, give rise to that family of rankings. We will show that, whatever be such family, a population of voters can be constructed that realize all the rankings of it. Our conclusions are similar to those coming from D. Saari’s results. Our results are, however, constructive and allow for the study of quantitative aspects of the wanted voters’ populations.

Suggested Citation

  • Emilio De Santis & Fabio Spizzichino, 2023. "Construction of voting situations concordant with ranking patterns," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 129-156, June.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:1:d:10.1007_s10203-023-00393-2
    DOI: 10.1007/s10203-023-00393-2
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    References listed on IDEAS

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    1. Emilio De Santis & Yaakov Malinovsky & Fabio Spizzichino, 2021. "Stochastic Precedence and Minima Among Dependent Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 187-205, March.
    2. Gil Kalai, 2004. "Social Indeterminacy," Discussion Paper Series dp362, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Fabio L. Spizzichino, 2019. "Reliability, signature, and relative quality functions of systems under time‐homogeneous load‐sharing models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(2), pages 158-176, March.
    4. Christian Klamler, 2005. "Borda and Condorcet: Some Distance Results," Theory and Decision, Springer, vol. 59(2), pages 97-109, September.
    5. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, December.
    6. Van Newenhizen, Jill, 1992. "The Borda Method Is Most Likely to Respect the Condorcet Principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 69-83, January.
    7. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    8. Moshe Shaked & J. George Shanthikumar, 2015. "Multivariate conditional hazard rate functions – an overview," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(3), pages 285-296, May.
    9. Montes, Ignacio & Rademaker, Michael & Pérez-Fernández, Raúl & De Baets, Bernard, 2020. "A correspondence between voting procedures and stochastic orderings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 977-987.
    10. Gil Kalai, 2004. "Social Indeterminacy," Econometrica, Econometric Society, vol. 72(5), pages 1565-1581, September.
    11. Mala, Jozsef, 1999. "On [lambda]-majority voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 39-44, January.
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    More about this item

    Keywords

    Majority graphs; Ranking patterns; Paradoxes of voting theory; Load-sharing models;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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