Bounded rational decision-making from elementary computations that reduce uncertainty
This work provides a foundational framework for understanding decision-making under computational constraints, which is incremental in extending majorization theory.
The paper tackles the problem of modeling bounded rational decision-making by introducing the concept of elementary computations based on probability transfers that reduce uncertainty, leading to a framework for decision processes with limited resources. It proves new results in majorization theory and entropy measures.
In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou-Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. As a consequence we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.