On the Monotonicity of Information Costs

TL;DR

This paper investigates the conditions under which information costs increase with informativeness, providing necessary and sufficient criteria for monotonicity based on Blackwell and Lehmann orders, and analyzing existing cost functions.

Contribution

It offers a unified framework for understanding when information costs are monotone with respect to standard informativeness orders, grounded in garbling characterizations.

Findings

Derived necessary and sufficient conditions for monotonicity.

Analyzed well-known cost functions against these conditions.

Clarified the relationship between informativeness and costs in information theory.

Abstract

We study the monotonicity of information costs: more informative experiments must be more costly. As criteria for informativeness, we consider the standard information orders introduced by Blackwell (1951, 1953) and Lehmann (1988). We provide simple necessary and sufficient conditions for a cost function to be monotone with respect to each order, grounded in their garbling characterizations. Finally, we examine several well-known cost functions from the literature through the lens of these conditions.