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Borda winner in facility location problems on sphere

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Abstract

We characterize a Borda winner in facility location problems on a sphere. We show that in desirable (undesirable) facility location problems, the center of population (the antipode of the center of population) is the unique Borda winner if the voters’ average coordinate is not equal to the center of the sphere, and that any location is a Borda winner otherwise.

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Notes

  1. Aboufadel and Austin (2006) defined the center of population as a balancing location at which the total gravitational force on population is directed toward the center of the sphere and explicitly derived the unique center of population.

  2. See, for example, Wendell and Thorson (1974) and Hansen and Thisse (1981) for the optimal result from the Benthamite criterion, and Kawamori and Yamaguchi (2010) for the optimal result from the Rawlsian criterion.

  3. It is known that the explicit characterization of optimal locations is generally impossible. See Zhang (2003) for an algorithm for a minisum location and Das et al. (2001) for an algorithm for a minimax location.

  4. Note that since \(\rho ^i\left( x\right) =\pi -\rho ^i\left( -x\right) \), a location is a maxisum (maximin) location if and only if the antipode of the location is a minisum (minimax) location.

References

  • Aboufadel E, Austin D (2006) A new method for computing the mean center of population of the United States. The Professional Geographer 58:65–69

    Article  Google Scholar 

  • Das P, Chakraborti NR, Chaudhuri PK (2001) Spherical minimax location problem. Computational Optimization and Applications 18:311–326

    Article  Google Scholar 

  • Feld SL, Grofman B (1988) The Borda count in \(n\)-dimensional issue space. Public Choice 59:167–176

    Article  Google Scholar 

  • Hansen P, Thisse JF (1981) Outcomes of voting and planning: Condorcet, Weber and Rawls locations. Journal of Public Economics 16:1–15

    Article  Google Scholar 

  • Harris JW, Stocker H (1998) Handbook of Mathematics and Computational Science. Springer-Verlag, New York

    Book  Google Scholar 

  • Katz IN, Cooper L (1980) Optimal location on a sphere. Computers & Mathematics with Applications 6:175–196

    Article  Google Scholar 

  • Kawamori T, Yamaguchi K (2010) Outcomes of bargaining and planning in single facility location problems. Mathematical Social Sciences 59:38–45

    Article  Google Scholar 

  • Wendell RE, Thorson SJ (1974) Some generalizations of social decisions under majority rule. Econometrica 42:893–912

    Article  Google Scholar 

  • Zhang L (2003) On the convergence of a modified algorithm for the spherical facility location problem. Operations Research Letters 31:161–166

    Article  Google Scholar 

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Acknowledgments

The author is grateful to managing editor Clemens Puppe, an anonymous associate editor, and two anonymous referees for their useful comments.

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Authors and Affiliations

  1. Faculty of Economics, Rissho University, 4-2-16 Osaki, Shinagawa-ku, Tokyo, 141-8602, Japan

    Kazuo Yamaguchi

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  1. Kazuo Yamaguchi
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Correspondence to Kazuo Yamaguchi.

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Yamaguchi, K. Borda winner in facility location problems on sphere. Soc Choice Welf 46, 893–898 (2016). https://doi.org/10.1007/s00355-015-0940-1

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  • DOI: https://doi.org/10.1007/s00355-015-0940-1

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