caa a22 4500 465774881 CHVBK 20180323111939.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02204855 doi (NATIONALLICENCE)springer-10.1007/BF02204855 Linear extension majority cycles on partial orders [Elektronische Daten] [William Gehrlein, Peter Fishburn] Let P define a partial order on a set X of cardinalityn. A linear extensionL ofP is a linear order withP G L, and $$\mathcal{L}(P)$$ is the set of all linear extensions ofP. $$\mathcal{L}(x,y)$$ denotes that subset of $$\mathcal{L}(P)$$ withxLy forx, y ∈X. A linear extension majority (LEM) relationM onX is defined byxMy if $${}^\# \mathcal{L}(x,y) > {}^\# \mathcal{L}(y,x)$$ . Similarly,M′ is defined byxM′y if $${}^\# \mathcal{L}(x,y) \geqslant {}^\# \mathcal{L}(y,x)$$ . An LEM cycle exists if there arex, y, z ∈X withxMyMzMx, and an LEM quasi-cycle exists ifxM′yM′zM′x and the equality part of the definition ofM′ holds for exactly one pair in the triple. The study shows that no semiorders have LEM cycles or LEM quasi-cycles, and that every interval order has a maximal element under theM relation. LEM cycles and LEM quasi-cycles are also considered for partial orders with specific structures. Simulation is used to determine the relative likelihood with which LEM cycles and LEM quasi-cycles are observed when connected partial orders are generated at random by a specific procedure. J.C. Baltzer AG, Scientific Publishing Company, 1990 Gehrlein William Department of Business Administration, University of Delaware, 19716, Newark, DE, USA aut Fishburn Peter AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA aut Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 23/1(1990-12-01), 311-322 0254-5330 23:1<311 1990 23 10479 https://doi.org/10.1007/BF02204855 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02204855 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gehrlein William Department of Business Administration, University of Delaware, 19716, Newark, DE, USA aut NATIONALLICENCE 700 1- Fishburn Peter AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 23/1(1990-12-01), 311-322 0254-5330 23:1<311 1990 23 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer