Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty

Abstract

This paper reports the results of an experimental parameter-free elicitation and decomposition of decision weights under uncertainty. Assuming cumulative prospect theory, utility functions were elicited for gains and losses at an individual level using the tradeoff method. Subsequently, decision weights were elicited through certainty equivalents of uncertain two-outcome prospects. Furthermore, decision weights were decomposed using observable choice instead of invoking other empirical primitives, as in previous experimental studies. The choice-based elicitation of decision weights allows for a quantitative study of their characteristics, and also allows, among other things, for the examination of the sign-dependence hypothesis for observed choice under uncertainty. Our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice-based subjective probabilities. We also find evidence for sign dependence of decision weights.decision under uncertainty, Choquet expected utility, cumulative prospect theory, decision weights, choice-based probabilities, probability weighting

A parametric analysis of prospect theory’s functionals for the general population

“…For losses, the point estimate isδ − = 1.022 which is higher than one, also suggesting pessimism in the loss domain (ŵ − (1/2) = 0.505 > .5), but we cannot reject the hypothesis that δ = 1 (z = 0.27, p-value = 0.787). The elevation of the weighting function for losses is significantly higher than that of gains (z = 4.54, p-value = 0.000) as was also found by Abdellaoui (2000); Abdellaoui et al (2005), and Fehr-Duda et al (2006), and we cannot reject the hypothesis that the elevation parameter is different from the literature average (Table 1) ofδ − = 1.09 (z = .81, p-value = 0.418). Contrary to Etchart-Vincent (2004), who find more elevation for losses with higher stakes, we did not find any effect of the magnitude of the stakes on the degree of pessimism of the respondents.…”

“…It should be noted that most recent estimates of utility curvature are much closer to linearity (Abdellaoui 2000;Etchart-Vincent 2004;Abdellaoui et al 2005;Fehr-Duda et al 2006;Abdellaoui et al 2007b;Andersen et al 2006;Abdellaoui et al 2008) than what is suggested by the average estimate calculated from Table 1. Hence, our estimates fall within the range of contemporaneous estimates that find the power of the value function to be between .8 and 1.…”

Parametric weighting functions

“…A few parametric forms have been proposed for inverse-S shaped weighting functions (Karmarkar 1978, 1979, Goldstein and Einhorn 1987, Currim and Sarin 1989, Lattimore, Baker and Witte 1992, Tversky and Kahneman 1992, Prelec 1998, and their parameters have been estimated in many empirical studies (Camerer and Ho 1994, Tversky and Fox 1995, Wu and Gonzalez 1996, Gonzalez and Wu 1999, Abdellaoui 2000, Bleichrodt and Pinto 2000, Kilka and Weber 2001, Etchart-Vincent 2004, Abdellaoui, Vossmann and Weber 2005. Most of these parametric forms lack an appropriate axiomatic underpinning.…”

“…More generally, because the afore mentioned weighting functions each involve a single parameter, they cannot accommodate at the same time probabilistic risk seeking and probabilistic risk aversion within the probability interval. That is, they are incompatible with the inverse-S shaped form, concave for small probabilities and convex for large probabilities, that received extensive empirical support (e.g., Camerer and Ho 1994, Wu and Gonzalez 1996, Tversky and Fox 1995, Gonzalez and Wu 1999, Abdellaoui 2000, Bleichrodt and Pinto 2000, Kilka and Weber 2001, Abdellaoui, Vossmann and Weber 2005.…”

Testing independence conditions in the presence of errors and splitting effects

“…Whereas certain configural weight models and extended original prospect theory imply that DI holds, it should be violated according to RDU and CPT, at least if the weighting function is not linear, as commonly 13 implied by empirical research (Camerer and Ho, 1994;Wu and Gonzalez, 1996;Tversky and Fox, 1995;Gonzalez and Wu, 1999;Abdellaoui, 2000;Bleichrodt and Pinto, 2000;Kilka and Weber, 2001;Abdellaoui, Vossmann, and Weber, 2005 Birnbaum (2005b). The evidence reported in that paper and in Birnbaum and Chavez (1997) indicates that one should observe either no violations or violations contrary to CPT with inverse-S weighting function.…”