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In its most basic form, decision-making can be viewed as a computationalprocess that progressively eliminates alternatives, thereby reducinguncertainty. Such processes are generally costly, meaning that the amount ofuncertainty that can be reduced is limited by the amount of availablecomputational resources. Here, we introduce the notion of elementarycomputation based on a fundamental principle for probability transfers thatreduce uncertainty. Elementary computations can be considered as the inverse ofPigou-Dalton transfers applied to probability distributions, closely related tothe concepts of majorization, T-transforms, and generalized entropies thatinduce a preorder on the space of probability distributions. As a consequencewe can define resource cost functions that are order-preserving and thereforemonotonic with respect to the uncertainty reduction. This leads to acomprehensive notion of decision-making processes with limited resources. Alongthe way, we prove several new results on majorization theory, as well as onentropy and divergence measures.

Bounded rational decision-making from elementary computations that reduce uncertainty