When 0 + 1/3+1/3>2/3, but 0 + 0 +1/3 <1/3. How the median outcome impacts lottery valuation?

Abstract

This paper presents the results of two experiments that exhibit monotonicity violations: some lotteries with three equally likely outcomes are valued more than a superior two-outcome lottery, while others are valued less than an inferior two-outcome lottery. Moreover the experimental data provide compelling evidence that lottery valuation strongly depends on the value(s) of the middle outcome(s). This contradicts the claim of Cumulative Prospect Theory (CPT) that middle outcomes are assigned lower weights than the extreme ones. Both effects can be observed in the case of four-outcome lotteries. The patterns are persistent for various payoff schedules, and have been observed for subjects from both Poland and California. Incorporating the median outcome value into any modeling of risky decision-making enables these effects to be explained. This paper demonstrates that a simple weighted Expected Utility - Median model describes data involving two- three-, and four-outcome lotteries more accurately than CPT. Moreover, it offers an alternative explanation of ''overweighting'' of small probabilities, and ''underweighting'' of large ones – phenomena postulated by CPT.