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.