Before revision: In this paper, I first showed that an indirect information measure is supported by expected learning cost minimizationif and only if it satisfies: 1. monotonicity in Blackwell order, 2. sub-additivity in compound experiment and 3. linearity in mixing with no information.
After revision: We study the indirect cost of information from sequential information cost minimization. A key sub-additivity in compound experiment and 3. linearity in mixing with no information.