The optimality of coarse categories in decision-making and information storage

TL;DR

This paper demonstrates that, under certain conditions, binary criteria or bits are the most efficient choice for decision-making and information storage, minimizing costs in the absence of preferences.

Contribution

It establishes that binary criteria are optimal for decision-making and storage efficiency, highlighting the importance of symmetry conditions in such optimal sets.

Findings

Binary criteria are optimal under mild conditions.

Bits are the most efficient for information storage.

Symmetry conditions are crucial for efficiency.

Abstract

An agent who lacks preferences and instead makes decisions using criteria that are costly to create should select efficient sets of criteria, where the cost of making a given number of choice distinctions is minimized. Under mild conditions, efficiency requires that binary criteria with only two categories per criterion are chosen. When applied to the problem of determining the optimal number of digits in an information storage device, this result implies that binary digits (bits) are the efficient solution, even when the marginal cost of using additional digits declines rapidly to 0. This short paper pays particular attention to the symmetry conditions entailed when sets of criteria are efficient.