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The likelihood of dubious election outcomes

Author

Listed:
  • Donald G. Saari

    (Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA)

  • Maria M. Tataru

    (Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA)

Abstract

A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the "correct" one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes.

Suggested Citation

  • Donald G. Saari & Maria M. Tataru, 1999. "The likelihood of dubious election outcomes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 345-363.
    • Handle: RePEc:spr:joecth:v:13:y:1999:i:2:p:345-363
    Note: Received: April 11, 1997; revised version: November 12, 1997
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    Citations

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    Cited by:

    1. Eric Kamwa & Vincent Merlin, 2019. "The Likelihood of the Consistency of Collective Rankings Under Preferences Aggregation with Four Alternatives Using Scoring Rules: A General Formula and the Optimal Decision Rule," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1377-1395, April.
    2. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    3. Regenwetter, Michel & Grofman, Bernard & Marley, A. A. J., 2002. "On the model dependence of majority preference relations reconstructed from ballot or survey data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 451-466, July.
    4. Takahiro Suzuki & Masahide Horita, 2023. "A Society Can Always Decide How to Decide: A Proof," Group Decision and Negotiation, Springer, vol. 32(5), pages 987-1023, October.
    5. Mostapha Diss & Eric Kamwa, 2020. "Simulations in Models of Preference Aggregation," Post-Print hal-02424936, HAL.
    6. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    7. Kamwa, Eric & Merlin, Vincent, 2015. "Scoring rules over subsets of alternatives: Consistency and paradoxes," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 130-138.
    8. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    9. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which “Almost” Rule is Optimal?," Group Decision and Negotiation, Springer, vol. 27(1), pages 129-151, February.
    10. Eric Kamwa & Vincent Merlin, 2018. "The Likelihood of the Consistency of Collective Rankings under Preferences Aggregation with Four Alternatives using Scoring Rules: A General Formula and the Optimal Decision Rule," Working Papers hal-01757742, HAL.
    11. McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.
    12. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
    13. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo.
    14. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute of Labor Economics (IZA).
    15. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    16. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    17. Donald G. Saari, 2023. "Selecting a voting method: the case for the Borda count," Constitutional Political Economy, Springer, vol. 34(3), pages 357-366, September.
    18. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.
    19. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.

    More about this item

    Keywords

    Voting · Central limit theorem · Paradoxes.;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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