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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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    References listed on IDEAS

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    1. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, pages 13-46.
    2. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, pages 1333-1340.
    3. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
    4. Rath, Kali P, 1995. "Representation of Finite Action Large Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 23-35.
    5. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
    6. Khan, M. Ali & Sun, Yeneng, 1995. "Extremal structures and symmetric equilibria with countable actions," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 239-248.
    7. Carmona, Guilherme & Podczeck, Konrad, 2009. "On the existence of pure-strategy equilibria in large games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1300-1319, May.
    8. Rath, Kali P., 1996. "Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 305-324.
    9. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
    10. Carmona, Guilherme, 2008. "Large games with countable characteristics," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 344-347, February.
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    Citations

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    Cited by:

    1. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, pages 289-316.
    2. Kamwa, Eric & Merlin, Vincent, 2015. "Scoring rules over subsets of alternatives: Consistency and paradoxes," Journal of Mathematical Economics, Elsevier, pages 130-138.
    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. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    5. repec:eee:matsoc:v:87:y:2017:i:c:p:1-10 is not listed on IDEAS
    6. 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.

    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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