Models of Choice Between Multioutcome Lotteries

Abstract

Multiplicative-summing decision theories were compared by assessing their fit to choice data obtained from 559 subjects, each providing 16–60 problems. The problems were 212 pairs of multioutcome monetary lotteries, including 86 for gains, 86 for losses, and 40 mixed lotteries with gains and losses. Lotteries of each pair had the same expected value. The fit of each theory to the data was measured by the percent of problems with agreement between the observed majority preference and the lottery with the higher calculated expected utility (or Value); ‘percent concordance’ indicates percent of agreement. Parameter fitting showed that a linear probability function provided excellent representation of the data, and was superior to the rank-dependent weighted probability functions of cumulative prospect theory. Modeling is successful when the utility function is S-shaped, concave in the gain and convex in the loss domains, across a wide range of curvatures (from u(x)=x0.05 to x0.85). Surprisingly, the best modeling was with severe curvature (u(x)=x0.05). Addition of loss aversion to the model and steeper slopes for losses than for gains provided no or very little increases of concordances between theory and data. Conclusions are that for this data set of choices between multioutcome monetary lotteries, the most descriptive of the multiplicative-summing theories was a hybrid model which combines the linear probability of classical expected utility and a symmetrical S-shaped utility function borrowed from cumulative prospect theory. A rank-dependent weighted probability function did not improve the fit of model to data. Variance modeling also described choices very well. © 1997 by John Wiley & Sons, Ltd.

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