Acyclic domains of linear orders : a survey
AbstractAmong the many significant contributions of Fishburn to social choice theory some have borne on what he has called «acyclic sets», i.e. these sets of linear orders where majority rule applies without «Condorcet effect» (majority relation never has cycles). Search for large such domains is a fascinating topic. I review the works in this field and in particular a recent one allowing to show the connections between some of them unrelated up to now.
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Date of creation: Dec 2006
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Acyclic set; alternating scheme; distributive lattice; effet Condorcet; maximal chain; permutoedre lattice; 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, 2009. "Acyclic domains of linear orders: a survey," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00198635, HAL.
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- 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.
- Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00504974, HAL.
- 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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