Algebraic Properties of Blackwell's Order and a Cardinal Measure of Informativeness

I establish a translation invariance property of the Blackwell order over experiments for dichotomies, show that garbling experiments bring them closer together, and use these facts to define a cardinal measure of informativeness. Experiment A is inf-norm more informative (INMI) than experiment B if the infinity norm of the difference between a perfectly informative experiment and A is less than the corresponding difference for B. The better experiment is closer to the fully revealing experiment; the norm of the distance from the identity matrix is interpreted as a measure of informativeness. This measure coincides with Blackwell’s order whenever possible, is complete, order invariant, prior-independent, and computationally simple