Reconciling dominance and stochastic transitivity in random binary choice

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

No 2020-05, Working Papers from Auckland University of Technology, Department of Economics

Abstract: 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.

Keywords: stochatic choice; risk; stochatic dominance; scalability; Fechner (search for similar items in EconPapers)
JEL-codes: D01 D81 (search for similar items in EconPapers)
Date: 2020-06
New Economics Papers: this item is included in nep-ore
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