An empirical test of gain-loss separability in prospect theory

Abstract

We investigate a basic premise of prospect theory, that the valuation of gains and losses is separable. In prospect theory, gain-loss separability implies that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble. Two experimental studies demonstrate a systematic violation of the double matching axiom, an axiom that is necessary for gain-loss separability. We document a reversal between preferences for mixed gambles and the associated gain and loss gambles-mixed gamble A is preferred to mixed gamble B, but the gain and loss portions of B are preferred to the gain and loss portions of A. The observed choice patterns are consistent with a process in which individuals are less sensitive to probability differences when choosing among mixed gambles than when choosing among either gain or loss gambles.

New paradoxes of risky decision making.

“…Intuitively, if you prefer the good part of B to the good part of A, and if you prefer the bad part of B to the bad part of A, then you should prefer B to A. Wu and Markle (2005) devised a test from a choice in Levy and Levy (2002, Experiment 2), shown in Choice Problems 12.1, 12.2, and 12.3 in Table 5. Wu and Markle (2005) found that the majority prefers B ϩ ՝ A ϩ and B Ϫ ՝ A Ϫ ; however, the majority does not prefer B ՝ A, contrary to CPT/RSDU and any model that satisfies gain-loss separability, including OPT.…”

“…Wu and Markle (2005) devised a test from a choice in Levy and Levy (2002, Experiment 2), shown in Choice Problems 12.1, 12.2, and 12.3 in Table 5. Wu and Markle (2005) found that the majority prefers B ϩ ՝ A ϩ and B Ϫ ՝ A Ϫ ; however, the majority does not prefer B ՝ A, contrary to CPT/RSDU and any model that satisfies gain-loss separability, including OPT. This example is consistent with the TAX model, with the simplifications listed in the note of Table 5, including the use of just one ␦ and u(x) ϭ x.…”

“…Some authors have criticized CPT (Baltussen, Post, & van Vliet, 2006;Barron & Erev, 2003;Blavatskyy, 2005;Brandstätter, Gigerenzer, & Hertwig, 2006;Gonzalez & Wu, 2003;González-Vallejo, 2002;Hertwig, Barron, Weber, & Erev, 2004;Humphrey, 1995;Levy & Levy, 2002;Lopes & Oden, 1999;Luce, 2000;Neilson & Stowe, 2002;Payne, 2005;Starmer, 1999Starmer, , 2000Starmer & Sugden, 1993;Weber & Kirsner, 1997;Wu, 1994;Wu & Markle, 2005;Wu, Zhang, & Abdelloui, 2005). Not all criticisms of CPT have been received without controversy (Baucells & Heukamp, 2006;Fox & Hadar, 2006;Wakker, 2003), however, and some conclude that CPT is the "best," if imperfect, description of decision making under risk and uncertainty (Camerer, 1998;Harless & Camerer, 1994;Starmer, 2000;Wu, Zhang, & Gonzalez, 2004).…”

Aspirational Preferences and Their Representation by Risk Measures

“…Table 2 shows application of ESAM with zero target to a set of experiments from Wu and Markle (2008). For comparison, we also show application of the entropic satisficing measure (Brown and Sim 2009;see Example 3) with zero target to these choices.…”

“…For act f , the notation f + denotes the act f + s = max f s 0 for all s ∈ S, i.e., the gain part of the act, and the notation f − denotes the act f − s = min f s 0 for all s ∈ S, i.e., the loss part of the act. Wu and Markle (2008) show violations of gainloss separability by finding experimental violations of double matching. Double matching is the requirement f + High ∼ f + Low and f − High ∼ f − Low ⇒ f High ∼ f Low , and is a necessary requirement for gain-loss separability (thus violations of double matching are even stronger than are violations of gain-loss separability).…”