The impact of middle outcomes on lottery valuations

This paper presents the results of two experiments that violate implications of expected utility (EU) and cumulative prospect theories (CPT). First, some lotteries with three equally likely branches are valued more than strictly better or objectively equivalent binary lotteries, while others are valued less than strictly worse or objectively equivalent binary lotteries. Second, experimental data provide evidence that lottery valuations strongly depend on the value of the middle monetary outcome(s), whereas CPT as fit to binary lotteries implies that middle outcomes are given lower weights relative to extreme ones. This leads to self-contradiction when CPT is used to fit the data: the probability weighting function takes an inverse S-shape when estimated using binary lotteries, and an S-shape when estimated using lotteries with three or four branches. Both effects are replicated with four-branch lotteries, with different highest outcome values, and with subjects from both Poland and California. It is argued that the violations of coalescing and stochastic dominance observed in the experiments cannot be explained by any rank-dependent weighted utility model, including CPT, but can be described by other rank-affected weighted utility models.