Choice functions over a finite set: A summary
type: Item
instance of: scholarly article
title: Choice functions over a finite set: A summary
zbMATH Open document ID: 0576.90004
DOI: 10.1007/BF00437315
author: H. Moulin
published in: Social Choice and Welfare
publication date: 1985-01-01T00:00:00Z
review text: Let A be a finite set of outcomes and B a nonempty subset of A. Let S be a choice function, such that S(B) is nonempty for all S. The following conditions on S are crucial: Chernoff: \(B\subset B'\to S(B')\cap B\subset S(B)\). Expansion: S(B)\(\cap S(B')\subset S(B\cup B')\). Aizerman: [S(B')\(\subset B\subset B']\to [S(B)\subset S(B')].\) The main results are the following. S is rationalizable if and only if it satisfies the Chernoff and Expansion conditions. S is Pareto- rationalizable if and only if it satisfies the Aizerman and Expansion conditions. Finally, S is pseudo-rationalizable if and only if it satisfies the Chernoff and Aizerman conditions. Although these results have existed in Russian for some time, this is the first time that they have been readily available in the West.
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 3922310
zbMATH Keywords: rationalizability
zbMATH Keywords: Chernoff condition
zbMATH Keywords: choice function
zbMATH Keywords: Expansion conditions
zbMATH Keywords: Aizerman conditions
MaRDI profile type: Publication
cites work: General theory of best variants choice: Some aspects
full work available at URL: https://doi.org/10.1007/bf00437315
OpenAlex ID: W2016120321
description: scientific article; zbMATH DE number 3922310