 Choice on the simplex domainWalter Bossert and Hans Peters Journal of Mathematical Economics, 2019, vol. 84, issue C, 63-72 Abstract: One unit of a good has to be divided among a group of agents who each are entitled to a minimal share, and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic; the last condition means that if an agent receives its minimal share and that share increases, then no other agent benefits. In line with Kıbrıs (2012) we show that these rules are rationalizable and representable by a real-valued function. On the issue of rationalizability, we also consider weakenings of our conditions. In particular, we show that in general, excluding cycles of any fixed length does not imply the strong axiom of revealed preference, that is, the exclusion of cycles of any length. For continuous three-agent choice rules, however, excluding cycles of length three implies the strong axiom of revealed preference. Keywords: Choice rules; Simplex domain; Rationalizability; Representability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:84:y:2019:i:c:p:63-72 DOI: 10.1016/j.jmateco.2019.07.002 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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