Strict scalability of choice probabilities

This paper introduces the concept of strict scalability, which lies between the classical notions of simple scalability (Krantz, 1964; Tversky and Russo, 1969) and monotone scalability (Fishburn, 1973). For binary choices, strict scalability is precisely characterised by the well-known axiom of weak substitutability (at least for countable domains). We also introduce a multinomial extension of weak substitutability that characterises strict scalability for multinomial choice.