[en] We establish a surprising connection between a family of conservative semigroups, which includes the class of idempotent uninorms, and the concepts of single-peakedness and single-plateaudness, introduced in social choice theory by D. Black. We also introduce a generalization of single-peakedness to partial orders of join-semilattices and show how it is related to the class of idempotent and commutative semigroups. Finally, we enumerate those orders when the corresponding semigroups are finite.
Disciplines :
Mathematics
Author, co-author :
Devillet, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Generalizations of single-peakedness
Publication date :
30 January 2019
Event name :
2nd Symposium Mathematics for Decision and Discovery (M4D2)
Event organizer :
Laboratoire lorrain de recherche en informatique et ses applications (LORIA)