Representations of votes facilitating monotonicity-based ranking rules: From votrix to votex

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• 作者：Raú ; l Pé ; rez-Ferná ; ndez^a ; ^b ; ^{raul.perezfernandez@ugent.be" class="auth_mail" title="E-mail the corresponding author} ; Michael Rademaker^a ; ^{uo205053@uniovi.es" class="auth_mail" title="E-mail the corresponding author} ; Pedro Alonso^c ; ^{palonso@uniovi.es" class="auth_mail" title="E-mail the corresponding author} ; Irene Dí ; az^d ; ^{sirene@uniovi.es" class="auth_mail" title="E-mail the corresponding author} ; Susana Montes^b ; ^{montes@uniovi.es" class="auth_mail" title="E-mail the corresponding author} ; Bernard De Baets^a ; ^{bernard.debaets@ugent.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Social choice ; Ranking rule ; Monotonicity ; Votrix ; Votex ; Monometric
• 刊名：International Journal of Approximate Reasoning
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：73
• 期：Complete
• 页码：87-107
• 全文大小：590 K

文摘

We propose a new point of view of the long-standing problem where several voters have expressed a (strict) linear order (or ranking) over a set of candidates. For a ranking class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0888613X1630007X&_mathId=si1.gif&_user=111111111&_pii=S0888613X1630007X&_rdoc=1&_issn=0888613X&md5=6539e6e56d43a18fa5df1d2723821cae" title="Click to view the MathML source">a≻b≻cclass="mathContainer hidden">class="mathCode">$a\succ b\succ c$ to represent a group's opinion, it would be natural that the strength with which class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0888613X1630007X&_mathId=si2.gif&_user=111111111&_pii=S0888613X1630007X&_rdoc=1&_issn=0888613X&md5=26e4ec64665b22d36b41d8326f64941a" title="Click to view the MathML source">a≻cclass="mathContainer hidden">class="mathCode">$a\succ c$ is supported should not be less than both the strength with which class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0888613X1630007X&_mathId=si3.gif&_user=111111111&_pii=S0888613X1630007X&_rdoc=1&_issn=0888613X&md5=00aa32e34ccf4da5bd2cf7317eb779f0" title="Click to view the MathML source">a≻bclass="mathContainer hidden">class="mathCode">$a\succ b$ and the strength with which class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0888613X1630007X&_mathId=si4.gif&_user=111111111&_pii=S0888613X1630007X&_rdoc=1&_issn=0888613X&md5=5cf05a172c714e2bc3e5a89d705145b2" title="Click to view the MathML source">b≻cclass="mathContainer hidden">class="mathCode">$b\succ c$ are supported. This intuitive property is called monotonicity and it has been recently addressed for the first time in the context of social choice. In this paper, two different representations of votes (the votrix and the votex) are considered. The former one is a formalization of the well-known reciprocal matrix of pairwise comparisons between candidates already introduced by Condorcet. The latter one is an extension of this reciprocal matrix considering hitherto unexploited information. These two representations lead to two monotonicity-based ranking rules.