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Many descriptive theories of judgment and decision making under risk assume that people align with normative theory in that they add up the possible outcomes weighted by their adherent probabilities (or decision weights). Yet, few studies test this assumption by a systematic comparison between all of the plausible integration models that may connect the outcomes and probabilities in the prospects. In two experiments, we explore if people spontaneously weight outcomes by their adherent probabilities in evaluations of duplex prospects that involve two independent events, taking the plausible integration models into account. Based on a Brunswikian conception of analysis and intuition and the observed response distributions, we also examine if people perform this additive weighting by analytic thought-processes, explicitly “number-crunching” the value, or by intuitive processes. The results show that people often spontaneously weight the outcome values by the probabilities also in duplex gambles – and mainly by intuitive integration in the form of an anchoring-and-adjustment strategy – but with individual differences in the extent to which they spontaneously engage in this integration, which seem most strongly predicted by culturally acquired beliefs related to economy (e.g., financial literacy).  The results carry important implications for modeling and interpreting behavior in judgment and decision making under risk in that risk preferences elicited from monetary lotteries are strongly contaminated by information-processing demands of the task. The results also question the notion that people switch from additive weighting to heuristics because they are unable to engage in weighting strategies.

The rationality of decision making under risk is of central concern in psychology and other behavioral sciences. In real-life, the information relevant to a decision often arrives sequentially or changes over time, implying nontrivial demands on memory. Yet, little is known about how this affects the ability to make rational decisions and a default assumption is rather that information about outcomes and probabilities are simultaneously available at the time of the decision. In 4 experiments, we show that participants receiving probability- and outcome information sequentially report substantially (29 to 83%) higher certainty equivalents than participants with simultaneous presentation. This holds also for monetary-incentivized participants with perfect recall of the information. Participants in the sequential conditions often violate stochastic dominance in the sense that they pay more for a lottery with low probability of an outcome than participants in the simultaneous condition pay for a high probability of the same outcome. Computational modeling demonstrates that Cumulative Prospect Theory (Tversky & Kahneman, 1992) fails to account for the effects of sequential presentation, but a model assuming anchoring-and adjustment constrained by memory can account for the data. By implication, established assumptions of rationality may need to be reconsidered to account for the effects of memory in many real-life tasks.

Expected utility theory, the normative benchmark for evaluation of risky prospect, implies that the evaluation is linear in probability, that it is concave in the outcome, and that probabilities and outcomes are multiplied. The present study examines how the evaluations of risky prospects are affected by the availability of comparative anchors. We report an experiment comparing a within-subjects design (WSD), in which 20 participants evaluated 36 prospects, with a single-subject design (SSD), in which each of 720 participants evaluated a single prospect. The results of fitting cumulative prospect theory (Tversky & Kahneman, 1992) to data showed that in the WSD, there was a roughly linear probability weighting function and a concave value function, as suggested by expected utility theory. In the SSD, on the other hand, there was a linear value function and a severely nonlinear weighting function for probability. The participants thus found it difficult to maintain the linear use of single-event probability disclosed in the WSD when they made evaluations in an SSD without access to comparative anchors. We argue that people may have much of the normative competence captured by expected utility theory, but this competence can only be manifested as normative performance given the availability of relevant comparative anchors. We discuss the possibility that this could explain why some economic markets are deemed rational, whereas others are not.