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Maximizing the minimum voter satisfaction on spanning trees

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  • Darmann, Andreas
  • Klamler, Christian
  • Pferschy, Ulrich

Abstract

This paper analyzes the computational complexity involved in solving fairness issues on graphs, e.g., in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, i.e., spanning trees, can be determined efficiently given the goal of maximin voter satisfaction. In particular, we show that computing spanning trees for maximin voter satisfaction under voting rules such as approval voting or the Borda count is -complete for a variable number of voters whereas it remains polynomially solvable for a constant number of voters.

Suggested Citation

  • Darmann, Andreas & Klamler, Christian & Pferschy, Ulrich, 2009. "Maximizing the minimum voter satisfaction on spanning trees," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 238-250, September.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:238-250
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    References listed on IDEAS

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    1. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    2. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
    3. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 151-162, June.
    4. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    5. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
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    1. Darmann, Andreas & Klamler, Christian & Pferschy, Ulrich, 2010. "A note on maximizing the minimum voter satisfaction on spanning trees," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 82-85, July.
    2. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.
    3. Klamler, Christian & Pferschy, Ulrich & Ruzika, Stefan, 2012. "Committee selection under weight constraints," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 48-56.
    4. Darmann, Andreas, 2013. "How hard is it to tell which is a Condorcet committee?," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 282-292.

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