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# Mathematical programming formulations for the efficient solution of the k-sum approval voting problem

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 dc.creator Ponce López, Diego es dc.creator Puerto Albandoz, Justo es dc.creator Ricca, Federica es dc.creator Scozzari, Andrea es dc.date.accessioned 2018-09-21T06:38:10Z dc.date.available 2018-09-21T06:38:10Z dc.date.issued 2018-10 dc.identifier.issn 0305-0548 es dc.identifier.issn 1873-765X es dc.identifier.uri https://hdl.handle.net/11441/78690 dc.description.abstract In this paper we address the problem of electing a committee among a set of m candidates and on the basis of the preferences of a set of n voters. We consider the approval voting method in which each voter can approve as many candidates as she/he likes by expressing a preference profile (boolean m-vector). In order to elect a committee, a voting rule must be established to ‘transform’ the n voters’ profiles into a winning committee. The problem es is widely studied in voting theory; for a variety of voting rules the problem was shown to be computationally difficult and approximation algorithms and heuristic techniques were proposed in the literature. In this paper we follow an Ordered Weighted Averaging approach and study the k-sum approval voting (optimization) problem in the general case 1 ≤ k < n. For this problem we provide different mathematical programming formulations that allow us to solve it in an exact solution framework. We provide computational results showing that our approach is efficient for medium-size test problems (n up to 200, m up to 60) since in all tested cases it was able to find the exact optimal solution in very short computational times. dc.description.sponsorship Ministerio de Economía y Competitividad es dc.description.sponsorship Fondo Europeo de Desarrollo Regional es dc.format application/pdf es dc.language.iso eng es dc.publisher Elsevier es dc.relation.ispartof Computers & Operations Research, 98, 127-136. dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject Approval voting es dc.subject Ordered Weighted Averaging (OWA) es dc.subject k-sum optimization problems es dc.title Mathematical programming formulations for the efficient solution of the k-sum approval voting problem es dc.type info:eu-repo/semantics/article es dc.type.version info:eu-repo/semantics/submittedVersion es dc.rights.accessrights info:eu-repo/semantics/openAccess es dc.contributor.affiliation Universidad de Sevilla. Departamento de Estadística e Investigación Operativa es dc.relation.projectID MTM2013-46962-C02-01 es dc.relation.projectID MTM2016-74983-C02-01 es dc.relation.publisherversion https://ac.els-cdn.com/S0305054818301370/1-s2.0-S0305054818301370-main.pdf?_tid=e8f9ce41-a431-4398-b466-c09b33cc3916&acdnat=1537511149_5b8dd4a3e5ecf3b31454e96c3ed05465 es dc.identifier.doi 10.1016/j.cor.2018.05.014 es dc.contributor.group Universidad de Sevilla. FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa es idus.format.extent 20 p. es dc.journaltitle Computers & Operations Research es dc.publication.volumen 98 es dc.publication.initialPage 127 es dc.publication.endPage 136 es dc.contributor.funder Ministerio de Economía y Competitividad (MINECO). España dc.contributor.funder European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
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