Auckland University of Technology (AUT), Faculty of Business, Economics and Law, Auckland
Ryan (2017) introduces a condition on binary stochastic choice between lotteries which we call Weak Transparent Domniance (WTP). Consider a binary choice set containing two different mixtures over a "best" and "worst" possible prize, so that one option transparently dominates the other. The WTD axiom says that the probability of choosing the dominant alternative depends only on the difference in chance of winning the "best" prizea across the two lotteries. A person whose choices always respect first-order stochastic dominance (FOSD) will satisfy this condition, but WTD is a weaker requirement. We show that WTD and strong stochastic transitivity (SST), together with a mild technical condition, ensure the existence of a Fechner model for choice probabilities. this implies, in particular, that for choice probabilities satisfying WTD and our technical condition, there is no observable difference between scalability (Kants, 1964; Tversky and Russo, 1969) and compatability with a Fechner model.