  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.
