Modeling Gain-Loss Asymmetries in Risky Choice: The Critical Role of Probability Weighting

Modeling Gain-Loss Asymmetries in Risky Choice: The Critical Role of Probability Weighting Thorsten Pachur (pachur@mpib-berlin.mpg.de) Center for Adaptive Rationality, Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany David Kellen (david.kellen@psychologie.uni-freiburg.de) Department of Psychology, Albert Ludwig University Freiburg, Engelbergerstr. 41 79085 Freiburg im Breisgau, Germany Abstract A robust empirical regularity in decision making is that the negative consequences of an option (i.e., losses) often have a stronger impact on people’s behavior than the positive consequences (i.e., gains). One common explanation for such a gain-loss asymmetry is loss aversion. To model loss aversion in risky decisions, prospect theory (Kahneman & Tversky, 1979) assumes a kinked value function (which translates objective consequences into subjective utilities), with a steeper curvature for losses than for gains. We highlight, however, that the prospect theory framework offers many alternative ways to model gain-loss asymmetries (e.g., via the weighting function, which translates objective probabilities into subjective decision weights; or via the choice rule). Our goal is to systematically test these alternative models against each other. In a reanalysis of data by Glockner and Pachur (2012), we show that people’s risky decisions are best accounted for by a version of prospect theory that has a more elevated weighting function for losses than for gains but the same value function for both domains. These results contradict the common assumption that a kinked value function is necessary to model risky choices and point to the neglected role of people’s differential probability weighting in the gain and loss domains. Keywords: cognitive modeling; loss aversion; risky choice; prospect theory; probability weighting Introduction For many of our decisions we are unable to tell with certainty what consequence the decision will have—for instance, when deciding between different medications that potentially lead to some side effects. Ideally, we have knowledge of the nature of the possible consequences as well as some inkling of the chances that the consequences will occur, but our decisions must necessarily remain in the “twilight of probability” (Locke, 1690/2004). Elaborating how such risky decisions are made (and how they should be made) has engaged decision scientists at least since Bernoulli’s (1738/1954) seminal work on subjective utility. One of the most influential and successful modeling frameworks of risky decision making is prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). A prominent feature of prospect theory is the assumption that the subjective disutility of a negative outcome is higher than the subjective utility of a positive outcome of the same size. In other words, prospect theory assumes an asymmetry between gains and losses in its value function, which translates objective outcomes into subjective magnitudes. This assumption of loss aversion can explain, for instance, that people dislike gambles in which one has a 50% chance to win a particular amount of money and a 50% can to lose the same amount. Similarly, loss aversion is invoked to account for the endowment effect—the phenomenon that people evaluate an object higher in a buyer perspective than in a seller perspective (e.g., Pachur & Scheibehenne, 2012; for a general overview of gain-loss asymmetries, see Peeters & Czapinski, 1990). However, the way prospect theory—more specifically, its mathematical formulation in cumulative prospect theory (CPT; Tversky & Kahneman, 1992)—is usually implemented allows for asymmetries in the evaluation of positive and negative prospects to be represented also in other ways than via the value function. For instance, the parameters of CPT’s weighting function, which translates objective probabilities into subjective decision weights, are typically estimated separately for the gain and the loss domain (e.g., Gonzalez & Wu, 1999). Furthermore, it has been argued that choice sensitivity (i.e., how accurately choices between two alternatives reflect their subjective valuations) differs between options involving losses and those involving gains only (Yechiam & Hochman, 2013a). Crucially, these possible representations of gain-loss asymmetries within CPT have never been directly pitted against each other in a model-comparison analysis (Linhart & Zucchini, 1986), where the descriptive power of a model is evaluated in light of its complexity (but see Harless & Camerer, 1994; Stott, 2006). Conducting such a model comparison is our goal in this paper. To that end, we use CPT to model data collected by Glockner and Pachur (2012), where 64 participants were asked to make choices between 138 two-outcome monetary gamble problems. 1 Fitting different implementations of CPT to this data also allows us to test specific predictions of how a gain-loss asymmetry should be reflected in specific parameter patterns, such as choice sensitivity (Yechiam & Hochman, 2013a) or probability sensitivity (Wu & Markle, 2008). Next we provide a detailed description of CPT’s parameter In Glockner and Pachur (2012) each participant made choices between 138 gamble problems at two separate sessions (separated by one week). Here we analyze the data from the first session.