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Algorithms for Voting and Competitive Location on a Network

Author

Listed:
  • Pierre Hansen

    (RUTCOR, Rutgers University, New Brunswick, New Jersey 08903)

  • Martine Labbé

    (Erasmus Universiteit Rotterdam, Posbus 1738, 3000 DR Rotterdam, The Netherlands, and CORE, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium)

Abstract

Consider a network with weights associated to its vertices. When a facility must be located through a voting procedure, these weights may be interpreted as the numbers of users located on the vertices. When a facility must be located in a competitive setting, i.e., when a concurrent facility will be located later and will capture all clients closer to it, these weights may be viewed as the purchasing power of the clients. A Condorcet point is any point of the network, i.e., a vertex or a point on an edge, such that the set of vertices closer to any other point has a total weight not larger than the half sum of the weights of all the vertices. A Simpson point is a point of the network which minimizes the largest total weight of the set of vertices closer to another point. Polynomial algorithms are provided to determine the sets of Condorcet and of Simpson points of a network.

Suggested Citation

  • Pierre Hansen & Martine Labbé, 1988. "Algorithms for Voting and Competitive Location on a Network," Transportation Science, INFORMS, vol. 22(4), pages 278-288, November.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:4:p:278-288
    DOI: 10.1287/trsc.22.4.278
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    Citations

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    Cited by:

    1. Labbe, Martine & Hakimi, S. Louis, 1989. "Market And Locational Equilibrium For Two Competitors," Econometric Institute Archives 272383, Erasmus University Rotterdam.
    2. 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.
    3. Abdullah Dasci & Gilbert Laporte, 2005. "A Continuous Model for Multistore Competitive Location," Operations Research, INFORMS, vol. 53(2), pages 263-280, April.
    4. Fernández, Elena & Pozo, Miguel A. & Puerto, Justo & Scozzari, Andrea, 2017. "Ordered Weighted Average optimization in Multiobjective Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 260(3), pages 886-903.
    5. Elena Fernández & Justo Puerto & Antonio Rodríguez-Chía, 2013. "On discrete optimization with ordering," Annals of Operations Research, Springer, vol. 207(1), pages 83-96, August.

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