A Prospect Theory Account of the “Hot” Columbia Card Task

Abstract

The investigation of decisions under risk has mainly followed one of two approaches.One relies on observing choices between lotteries in which economic primitives (outcome magnitudes, probabilities, and domains (i.e., gains and losses)) are varied systematically, and this information is described to participants. The systematic variation of the economic primitives allows to formally describe behavior with expectation-based models such as expected utility theory or cumulative prospect theory (CPT), arguably the most prominent descriptive theories of risky choice. One drawback, however, is that lottery tasks can seem artificial, likely reducing the external or ecological validity. A second more naturalistic approach employs dynamic paradigms that mimic features of real-life risky situations and are assumed to have higher ecological validity. Because key information are often not provided to the decision maker, it is impossible to apply the same models as in the first approach. The goal of the present work is to integrate both approaches, by developing models for the "hot" Columbia Card Task (CCT), a task that combines a dynamic decision situation with systematic trial-to-trial variation in economic primitives. In a model comparison on the basis of the data of 191 participants, we identified a best-performing model that describes behavior as a function of CPT’s main components, outcome sensitivity, probability weighting, and loss aversion. Our work therefore provides a framework that allows the description of risk-taking behavior in a naturalistic dynamic task based on key psychological constructs (e.g., loss aversion, probability weighting) that are rooted in the factorial variation of economic primitives.

Development of a novel computational model for the Balloon Analogue Risk Task: The Exponential-Weight Mean-Variance Model

“…The reduced subjective utility for pump decreases the probability that the participant will pump the balloon, so the average number of pumps decreases. This simulation result is consistent with a previous study using the Columbia Card Task (Pedroni et al, 2018). In contrast, the risk-taking propensity obviously has a positive correlation with the adjusted BART score because the risk-taking propensity is proportional to the optimal number of pumps according to the Equation (3).…”

Are choices based on conditional or conjunctive probabilities in a sequential risk‐taking task?

“…Accordingly, the objective gains only change for each state, and hence, values undergo the same subjective transformation irrespective of starting condition. The same principle holds, if one adopts a different reference point for the computation of the accumulated gains (e.g., decision‐updated vs. round‐updated reference point; Pedroni et al, ). It is noteworthy, though, that our estimated value‐function parameters indicated an increasing rather than decreasing marginal utility.…”

“…Admittedly, though, a purely behavioral analysis seems insufficient to determine the use of either probability representation. We therefore fit CPT models (Tversky & Kahneman, ; see also Pedroni et al, ) to the data. Specifically, we used conditional or conjunctive probabilities as basis for the probability weighting function, and identified the best fitting model across the five experiments.…”

“…A Cumulative Prospect Theory (CPT; Tversky & Kahneman, ) model with four parameters was used as basis for modeling the choice behavior in the CCT (see also Pedroni et al, ). Three models were fit to individual data for all experiments.…”

“…In short, we used a parameter recovery procedure similar to the one in Wallsten et al () for modeling data of the BART. Our implementation corresponds to what Pedroni et al () referred to as RU‐reference point model. For each of the five experiments, we fit a conditional probability model (Model 1), in which probabilities as outlined in Figure a (solid line) entered the probability weighting function.…”