On the Monotonicity of Information Costs

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.