The bounded rationality of probability distortion: the bounded log-odds model

Abstract

AO_SCPLOWBSTRACTC_SCPLOWIn decision-making under risk (DMR) participants choices are based on probability values systematically different from those that are objectively correct. Similar systematic distortions are found in tasks involving relative frequency judgments (JRF). These distortions limit performance in a wide variety of tasks and an evident question is, why do we systematically fail in our use of probability and relative frequency information? We propose a Bounded Log-Odds Model (BLO) of probability and relative frequency distortion based on three assumptions: (1) log-odds: probability and relative frequency are mapped to an internal log-odds scale, (2) boundedness: the range of representations of probability and relative frequency are bounded and the bounds change dynamically with task, and (3) variance compensation: the mapping compensates in part for uncertainty in probability and relative frequency values. We compared human performance in both DMR and JRF tasks to the predictions of the BLO model as well as eleven alternative models each missing one or more of the underlying BLO assumptions (factorial model comparison). The BLO model and its assumptions proved to be superior to any of the alternatives. In a separate analysis, we found that BLO accounts for individual participants data better than any previous model in the DMR literature. We also found that, subject to the boundedness limitation, participants choice of distortion approximately maximized the mutual information between objective task-relevant values and internal values, a form of bounded rationality. SO_SCPLOWIGNIFICANCEC_SCPLOW SO_SCPLOWTATEMENTC_SCPLOWPeople distort probability in decision under risk and many other tasks. These distortions can be large, leading us to make markedly suboptimal decisions. There is no agreement on why we distort probability. Distortion changes systematically with task, hinting that distortions are dynamic compensations for some intrinsic "bound" on working memory. We first develop a model of the bound and the compensation process and then report an experiment showing that the model accounts for individual human performance in decision under risk and relative frequency judgments. Last, we show that the particular compensation in each experimental condition serve to maximize the mutual information between objective decision variables and their internal representations. We distort probability to compensate for our own working memory limitations.