It is Whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice

Abstract

the opportunity to improve such a gamble is provided by a manipulation that adds value to one outcome versus another outcome, particularly when the opportunity to add value to one outcome versus another outcome changes the overall probability of a gain or the overall probability of a loss? Such a choice provides a simple test of the expected utility model (EU), original prospect theory (OPT), and cumulative prospect theory (CPT). A study of risky choices involving 375 respondents indicates that respondents were most sensitive to changes in outcome values that either increased the overall probability of a strict gain or decreased the overall probability of a strict loss. These results indicate more support for OPT rather than CPT and EU under various assumptions about the shape of the utility and value and weighting functions. Most importantly, the main difference between the various expectation models of risky choice occurs for outcomes near the reference value. A second study of risky choice involving 151 respondents again demonstrated the sensitivity of subjects to reducing the probability of a strict loss even at the cost of reduced expected value. Consequently, we argue that theories of how people choose among gambles that involve three or more consequences with both gains and losses need to include measures of the overall probabilities of a gain and of a loss. Keywords: decision, risk, preference JEL Classification: D81The past fifty years have seen much theoretical and empirical work devoted to developing and testing models of risky choice behavior. However, developing a descriptive model of risky decision-making has proven much more difficult than originally assumed. In particular, "the issue of a suitable descriptive theory for gambles with three or more consequences is very much up in the air" (Luce, 2000, p. 286). This is unfortunate, since many important decisions involve risky options with multiple outcomes.This paper provides evidence that any descriptive theory of choice among gambles with multiple outcomes will need to include measures of the overall probability of a gain and the overall probability of a loss. Although the psychological meaningfulness of constructs reflecting the overall probabilities of winning or losing may seem obvious, such constructs are not part of the traditional expected utility model nor of more recent nonlinear expectation

An Empirical Test of Gain-Loss Separability in Prospect Theory

“…Nevertheless, we do not regard our results as providing a general picture of how decision makers choose among mixed gambles. The mixed gambles in Study 1 have a very special configuration that may contribute to a "perceived" dominance: the highest outcome in H is better than the highest outcome in L, and the lowest outcome in H is also better than the lowest outcome in L. Even though Study 2's indirect test of double matching demonstrates that this configuration is not a necessary condition for producing violations of gain-loss separability, Payne's (2005) findings suggest that other heuristics might operate as well. Although a comprehensive study of gain-loss separability is beyond the scope of this paper, we encourage extensions of our tests to mixed gambles with different structures.…”

“…Indeed, Payne (2005) found that participants faced with a multiple-outcome mixed gamble preferred to improve the $0 outcome rather than the best gain, contrary to some parametric specifications of cumulative prospect theory. These results suggest that, individuals may use a heuristic of maximizing the probability of gain, or minimizing the probability of loss, when faced with a complicated mixed gamble.…”

“…While these data appear to be inconsistent with a bilinear form, the analytical procedure used in these investigations is quite complex and relies on parametric assumptions about the form of the value function and the probability weighting function. Payne (2005) documented choice patterns for mixed gambles that are inconsistent with cumulative prospect theory assuming typical parameter values. Payne argued that these patterns demonstrate that individuals sometimes use a heuristic of selecting the mixed gamble with the highest probability of a gain.…”

From anomalies to forecasts: Toward a descriptive model of decisions under risk, under ambiguity, and from experience.

“…These studies highlight new anomalies that emerge in this setting but cannot be captured with CPT. For example, Ert and Erev (2013; see Row 7 in Table 1) showed that low stakes eliminate the tendency to exhibit loss aversion; Thaler and Johnson (1990) documented a "break-even" effect (more risk seeking when only the risky choice can prevent losses; see Row 8 in Table 1); Payne (2005) documented a "getsomething" effect (less risk seeking when only the safe prospect guarantees a gain; see Row 9…”

Fearing the worst: the importance of uncertainty for inequality

“…As regards the latter aspect, it has been argued on the basis of experimental evidence that a major concern for individuals in evaluating risky prospects is the overall chances of success and failure. For example, Edwards (1954) shows that individuals prefer low probabilities of large losses to high probabilities of small losses, whilst Langer and Weber (2001) and Payne (2005) reveal that individuals pay special consideration to the probabilities of winning and losing as a whole.…”