Choice on the simplex domain

Walter Bossert and Hans Peters

No 30, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

Abstract: One unit of a good has to be divided among a group N of individuals 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 resulting rules are what we refer to as N-path choice functions. If there are only three individuals, the monotonicity property can be weakened. We also consider the issue of rationalizability and show that, for the threeagent case, excluding cycles of length three in the revealed preference relation implies the strong axiom of revealed preference, that is, the exclusion of cycles of any length.

JEL-codes: D11 D71 (search for similar items in EconPapers)
Date: 2017-12-05
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-upt
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Journal Article: Choice on the simplex domain (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:unm:umagsb:2017030

DOI: 10.26481/umagsb.2017030

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