Acyclic domains of linear orders: a survey
AbstractAmong the many significant contributions that Fishburn made to social choice theory some have focused on what he has called "acyclic sets", i.e. the sets of linear orders where majority rule applies without the "Condorcet effect" (majority relation never has cycles). The search for large domains of this type is a fascinating topic. I review the works in this field and in particular consider a recent one that allows to show the connections between some of them that have been unrelated up to now.
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Bibliographic InfoPaper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00198635.
Date of creation: Feb 2009
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Publication status: Published, The Mathematics of Preference, Choice and Order, Essays in honor of Peter C. Fishburn, Springer (Ed.), 2009, 139-160
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acyclic set; alternating scheme; distributive lattice; effet Condorcet; linear order; maximal chain; permutoèdre lattice; single-peaked domain; weak Bruhat order; value restriction.;
Other versions of this item:
- Bernard Monjardet, 2006. "Acyclic domains of linear orders : a survey," Cahiers de la Maison des Sciences Economiques b06083, Université Panthéon-Sorbonne (Paris 1).
- Bernard Monjardet, 2006. "Acyclic domains of linear orders : a survey," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00130205, HAL.
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- Olivier Hudry & Bernard Monjardet, 2010.
"Consensus theories: an oriented survey,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories : An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Post-Print halshs-00119141, HAL.
- Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Post-Print halshs-00309825, HAL.
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