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The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution

Author

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  • Zvi Drezner

    (California State University-Fullerton)

  • Mozart B. C. Menezes

    (Kedge Business School-Bordeaux)

Abstract

We investigate the quality of Condorcet solutions when compared to a central decision maker solution in the context of a facility location model in the plane. We perform an extensive set of experiments and conclude that if each population member votes according to his/her own self interest, then the Weber objective at the Condorcet solution point is very close to the optimal Weber objective value. Reducing the set of voters has little impact on the quality of the Condorcet solution. Being short of a good candidate has some impact but the final decision is still a good one. The distance metric seems to be of little relevance as well. As long as candidates are diverse, the Condorcet solution results in a good decision when compared to the decision by a benevolent dictator.

Suggested Citation

  • Zvi Drezner & Mozart B. C. Menezes, 2016. "The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution," Annals of Operations Research, Springer, vol. 246(1), pages 205-226, November.
    • Handle: RePEc:spr:annopr:v:246:y:2016:i:1:d:10.1007_s10479-015-1906-5
    DOI: 10.1007/s10479-015-1906-5
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    References listed on IDEAS

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    1. Z. Drezner & G. O. Wesolowsky, 1981. "Optimum Location Probabilities in the l p Distance Weber Problem," Transportation Science, INFORMS, vol. 15(2), pages 85-97, May.
    2. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    3. Hansen, Pierre & Thisse, Jacques-Francois, 1981. "Outcomes of voting and planning : Condorcet, Weber and Rawls locations," Journal of Public Economics, Elsevier, vol. 16(1), pages 1-15, August.
    4. Pierre Hansen & Martine Labbé, 1988. "Algorithms for Voting and Competitive Location on a Network," Transportation Science, INFORMS, vol. 22(4), pages 278-288, November.
    5. Z. Drezner & G. O. Wesolowsky, 1978. "A Trajectory Method for the Optimization of the Multi-Facility Location Problem With lp Distances," Management Science, INFORMS, vol. 24(14), pages 1507-1514, October.
    6. David L. Huff, 1966. "A Programmed Solution for Approximating an Optimum Retail Location," Land Economics, University of Wisconsin Press, vol. 42(3), pages 293-303.
    7. E. Weiszfeld & Frank Plastria, 2009. "On the point for which the sum of the distances to n given points is minimum," Annals of Operations Research, Springer, vol. 167(1), pages 7-41, March.
    8. P. Hansen & J.-F. Thisse & R. E. Wendell, 1986. "Equivalence of Solutions to Network Location Problems," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 672-678, November.
    9. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    10. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    11. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    12. Drezner, Zvi, 1982. "Competitive location strategies for two facilities," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 485-493, November.
    13. Noltemeier, H. & Spoerhase, J. & Wirth, H.-C., 2007. "Multiple voting location and single voting location on trees," European Journal of Operational Research, Elsevier, vol. 181(2), pages 654-667, September.
    14. Wendell, Richard E & Thorson, Stuart J, 1974. "Some Generalizations of Social Decisions under Majority Rule," Econometrica, Econometric Society, vol. 42(5), pages 893-912, September.
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    Cited by:

    1. Eiselt, H.A. & Marianov, Vladimir, 2020. "Maximizing political vote in multiple districts," Socio-Economic Planning Sciences, Elsevier, vol. 72(C).

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