How Does Prospect Theory Reflect Heuristics' Probability Sensitivity in Risky Choice?

How Does Prospect Theory Reflect Heuristics’ Probability Sensitivity in Risky Choice? Renata S. Suter (suter@mpib-berlin.mpg.de) Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany Thorsten Pachur (pachur@mpib-berlin.mpg.de) Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany Ralph Hertwig (hertwig@mpib-berlin.mpg.de) Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany Abstract Two prominent approaches to describing how people make decisions between risky options are algebraic models and heuristics. The two approaches are based on fundamentally different algorithms and are thus usually treated as antithetical, suggesting that they may be incommensurable. Using cumulative prospect theory (CPT; Tversky & Kahneman, 1992) as an illustrative case of an algebraic model, we demonstrate how algebraic models and heuristics can mutually inform each other. Specifically, we highlight that CPT describes decisions in terms of psychophysical characteristics, such as diminishing sensitivity to probabilities, and we show that this holds even when the underlying process is heuristic in nature. Our results suggest that algebraic models and heuristics might offer complementary rather than rival modeling frameworks and highlight the potential role of heuristic principles in information processing for prominent descriptive constructs in risky choice. Keywords: cumulative prospect theory; probability sensitivity; computational modeling; heuristics; risky choice. Introduction How can risky decision making—in which people have to choose between options offering different outcomes with certain probabilities—best be modeled? Two prominent approaches in decision research are algebraic models and heuristics (e.g., Brandstatter, Gigerenzer, & Hertwig, 2006; Payne, 1973; Payne, Bettman, & Johnson, 1993). Algebraic models follow the principle of expectation maximization and use an algorithm that integrates (some function of) probability and outcome information multiplicatively to describe people’s risky choices. Arguably the most prominent model in this tradition is cumulative prospect theory (CPT; Tversky & Kahneman, 1992). According to CPT, options are evaluated independently of each other. The model invokes psychophysical constructs such as probability sensitivity and loss aversion to account for characteristic phenomena in choice, and quantifies them using adjustable parameters. Heuristics, by contrast, are based on simple principles of information processing, such as sequential and limited search, dimensional comparison, and aspiration levels; in contrast to algebraic models, heuristics often go without integrating information, and ignore part of the information (e.g., Payne et al., 1993; Thorngate, 1980). Models of heuristics for risky choice include the semiorder rule (Luce, 1956), the similarity heuristic (Leland, 1994; Rubinstein, 1988), elimination- by-aspects (Tversky, 1972), and the priority heuristic (Brandstatter et al., 2006). Algebraic models and heuristics are often treated as antithetical (e.g., Brandstatter et al., 2006; Payne, 1973; Svenson, 1979). As pointed out by Lopes (1995), however, this opposition may be unnecessary: “Some models focus on the algebraic pattern of people’s risk preferences, others on the content of their choice processes [models of heuristics]. Although one might suppose that these two kinds of accounts are alternate ways of describing the same thing—indeed, that one kind of model might eventually be reducible to the other—the approaches have tended to be disjoint” (p. 177). To date, however, the relationship between algebraic models and heuristics has yet to be elaborated. To close that gap, we use CPT (Tversky & Kahneman, 1992) as an illustrative case highlighting that algebraic models offer a tool for describing characteristics of the decision process in psychophysical terms; here, we focus on the sensitivity to differences in probabilities. We argue that diminished sensitivity to probability information—as captured in CPT’s weighting functions—can result from lexicographic and noncompensatory processing of heuristics. As such, CPT may offer a useful framework to represent heuristic decision making in terms of established constructs such as sensitivity to probability information. Conversely, as heuristics are explicit with regard to the information- processing steps underlying a decision, elaborating the relationship between heuristics and CPT might contribute to a better understanding of the cognitive mechanisms potentially underlying the characteristic shapes of CPT’s weighting and value functions (cf. Hogarth & Einhorn, 1990). Overall, we thus suggest that the relationship between the algebraic and heuristic models of risky choice is complementary rather than adversarial.