 Completeness and transitivity of preferences on mixture setsTsogbadral Galaabaatar, M. Khan and Metin Uyanık Mathematical Social Sciences, 2019, vol. 99, issue C, 49-62 Abstract: This paper contributes to the interplay of the behavioral assumptions on a binary relation and the structure of the choice space on which it is defined: the (ES) research program of Eilenberg (1941) and Sonnenschein (1965) to which Schmeidler (1971) is an especially influential contribution. We show that the presence of the Archimedean and mixture-continuity properties, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without decisiveness (completeness), or decisiveness without consistency, or in the presence of a weak consistency condition, both indecisiveness and inconsistency altogether. Second, we delineate how semi-transitivity of a relation is already hidden in linearity assumptions; and third, offer sufficient conditions that yield an isomorphism theorem that reduces a general setting to the usual order on an interval, and thereby yields the classic theorem of Herstein–Milnor (1953). We remark on extensions to a generalized mixture set of Chipman–Fishburn. Date: 2019 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:99:y:2019:i:c:p:49-62 DOI: 10.1016/j.mathsocsci.2019.03.004 Access Statistics for this article Mathematical Social Sciences is currently edited by J.-F. Laslier More articles in Mathematical Social Sciences from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.