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Committee selection under weight constraints

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  • Klamler, Christian
  • Pferschy, Ulrich
  • Ruzika, Stefan

Abstract

In this paper we investigate the problem of selecting a committee consisting of k members from a list of m candidates. Each candidate has a certain cost or weight. The choice of the k-committee has to satisfy some budget or weight constraint: the sum of the weights of all committee members must not exceed a given value W. While the former part of the problem is a typical question in Social Choice Theory, the latter stems from Operations Research. The purpose of this paper is to link these two research fields: we first characterize reasonable ways of ranking sets of objects, i.e., candidates, and then develop efficient algorithms for the actual computation of optimal committees.

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  • Klamler, Christian & Pferschy, Ulrich & Ruzika, Stefan, 2012. "Committee selection under weight constraints," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 48-56.
    • Handle: RePEc:eee:matsoc:v:64:y:2012:i:1:p:48-56
    DOI: 10.1016/j.mathsocsci.2011.11.006
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    References listed on IDEAS

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    1. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 2005. "Voting by committees under constraints," Journal of Economic Theory, Elsevier, vol. 122(2), pages 185-205, June.
    2. 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.
    3. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236, Elsevier.
    4. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    5. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.
    6. Caprara, Alberto & Kellerer, Hans & Pferschy, Ulrich & Pisinger, David, 2000. "Approximation algorithms for knapsack problems with cardinality constraints," European Journal of Operational Research, Elsevier, vol. 123(2), pages 333-345, June.
    7. 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.
    8. Christian Klamler & Ulrich Pferschy, 2007. "The traveling group problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 429-452, October.
    9. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    10. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
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    Cited by:

    1. 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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