Prospect Theory in Betweenness Form for Binary Lotteries

Cumulative Prospect Theory (PT) has been introduced in Tversky and Kahneman (1992), as a revision of its first version (Kahneman and Tversky 1979). The reported evidence for probability weighting in their main experiment consists of binary lotteries only. For positive and negative binary prospects, however, PT can be rewritten in betweenness form, observing that the inverse-S-shaped weighting in PT is numerically nearly indistinguishable from the linear-in-log-odds pattern, exactly the class that betweenness for binary lotteries accommodates. Moreover, using the mixes in the evidence to estimate the remaining loss aversion parameter, it turns out that the betweenness model has an even better fit than PT. We come to the conclusion that there is no evidence of probability weighting in this seminal paper. This puts the current debate on rank-dependency in probability weighting in a different light, and poses questions on ambiguity models and source theory taking starting point in biseparable utility.