In 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 11 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.

In decision under risk 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. 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. The key assumption is that the dynamic range of representation of probability and relative frequency is limited. We tested the model experimentally and found that BLO accounts for individual participants' data better than all previous models in the literature. We also show that subject to the dynamic range limitation, participants' choice of distortion serves to maximize the mutual information between objective and internal values, a form of bounded rationality.

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