# Bounded rational decision-making from elementary computations that reduce uncertainty

## TL;DR

This paper models decision-making as elementary computations that reduce uncertainty within resource constraints, introducing a framework based on majorization and entropy to analyze bounded rationality.

## Contribution

It introduces elementary computations based on probability transfers that reduce uncertainty, linking majorization theory with resource-limited decision processes.

## Key findings

- Develops a formal framework for elementary uncertainty-reducing computations.
- Proves new results on majorization, entropy, and divergence measures.
- Defines resource cost functions that are monotonic with uncertainty reduction.

## Abstract

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.