Representation of Binary Choice Probabilities. Part I: Scalability - Matthew Ryan (Auckland University of Technology (AUT), Faculty of Business, Economics and Law, 2016)
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.
Keywords: 330