Stochastic representation decision theory: How probabilities and values are entangled dual characteristics in cognitive processes

Abstract

Humans are notoriously bad at understanding probabilities, exhibiting a host of biases and distortions that are context dependent. This has serious consequences on how we assess risks and make decisions. Several theories have been developed to replace the normative rational expectation theory at the foundation of economics. These approaches essentially assume that (subjective) probabilities weight multiplicatively the utilities of the alternatives offered to the decision maker, although evidence suggest that probability weights and utilities are often not separable in the mind of the decision maker. In this context, we introduce a simple and efficient framework on how to describe the inherently probabilistic human decision-making process, based on a representation of the deliberation activity leading to a choice through stochastic processes, the simplest of which is a random walk. Our model leads naturally to the hypothesis that probabilities and utilities are entangled dual characteristics of the real human decision making process. It predicts the famous fourfold pattern of risk preferences. Through the analysis of choice probabilities, it is possible to identify two previously postulated features of prospect theory: the inverse S-shaped subjective probability as a function of the objective probability and risk-seeking behavior in the loss domain. It also predicts observed violations of stochastic dominance, while it does not when the dominance is “evident”. Extending the model to account for human finite deliberation time and the effect of time pressure on choice, it provides other sound predictions: inverse relation between choice probability and response time, preference reversal with time pressure, and an inverse double-S-shaped probability weighting function. Our theory, which offers many more predictions for future tests, has strong implications for psychology, economics and artificial intelligence.

Artificial intelligence versus surgeon gestalt in predicting risk of emergency general surgery

“…13,17,18 This is because subjective risk estimation is also influenced by the importance of the event. 19 The emotional and professional consequences of failing to predict a mortality weigh heavily on surgeons' judgment, which cause them to attribute more weight to worst-case scenarios. A 2020 systematic review by Dilaver et al 18 found that surgeons overestimate mortality risk but are more accurate in predicting morbidity, the latter arguably having a less consequential impact than the former.…”

On the use of discrete-time quantum walks in decision theory

“…As our present focus is on preferential choice under uncertainty, we will summarize how decision field theory (DFT, [ 6 ]) works. Also, given that some of the results we present here rely on insights from stochastic representation decision theory (SRDT, [ 7 ]), we will give a short account of it.…”

“…In our first analysis, we choose the unbiased parameter configuration ξ = 0, η = 0. [7]), where the inverse double-S-shaped subjective probability arises through the interplay of value-distortion (probability of an event influenced by its magnitude) and time pressure. The model here does not need value distortion, but assumes that the underlying stochastic process is quantum in nature, thus with intrinsic interference between different positions along the deliberation paths.…”

“…As for preferential choice under uncertainty, the most famous accumulator model is Decision Field Theory (DFT), where the decision process is represented by a (sophisticated) random walk [ 6 ]. Two of the present authors recently developed a model in the same fashion, called Stochastic Representation Decision Theory (SRDT [ 7 ]). Here, the choice set determines the topology of the space in which the representative random walk wanders.…”

“…In light of the descriptive inadequacy of Expected Utility Theory, two approaches, among others, have been shown to accurately describe human decision-making. The first class of models, known as accumulator models [5][6][7], represents the deliberation activity leading to a decision as a noisy accumulation of evidence over time. According to the models, choice is triggered once evidence accumulated in favor of one alternative reaches a given threshold.…”