Relationship between Blackwell's informativeness and supermodular precision

Abstract

In a decision problem with uncertainty the decisions are supposed to be made after obtaining information from some signals, thus the expectation conditional on signals is likely to be crucial. Therefore, the relationship between the classical Blackwell's informativeness criterion and the dispersion of conditional expectations, one of which is the so-called supermodular precision criterion, is examined here. The study shows that Blackwell's informativeness does not necessarily imply or be implied by the supermodular precision in general cases even with the monotone likelihood ratio property, although binary cases could enlighten us somehow. © 2013 Springer-Verlag.