Representation of Binary Choice Probabilities. Part I: Scalability

Matthew Ryan ()
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Matthew Ryan: School of Economics, Auckland University of Technology, NZ

No 2016-04, Working Papers from Auckland University of Technology, Department of Economics

Abstract: Scalability refers to the existence of a utility scale on alternatives, with respect to which binary choice probabilities are suitably monotone. This is a fundamental concept in psychophysical theory (Falmagne, 1985). We introduce a new notion of scalability which we call strict scalability, and establish axiomatic foundations for this concept. Strict scalability lies between the classical notion of simple scalability, which was axiomatised by Tversky and Russo (1969), and the weaker notion of monotone scalability, which was axiomatised by Fishburn (1973). When the set of alternatives is countable, a binary choice probability is strictly scalable if and only if it satis?es the familiar condition of weak substitutability.

Pages: 16 pages
Date: 2016-04
New Economics Papers: this item is included in nep-upt
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