On information value and mean-preserving transformations

The methods of defining and evaluating evolution of information in economic systems are often based on abstract measure-theoretic mean-preserving transformations (MPTs), also known as second-order stochastic dominance. This study first points out that such abstract MPTs have distributional equivalents and then shows that the distributional MPTs often provide analytical settings that are more accessible than those provided by their measure-theoretic analogs. It is shown that a number of abstract results on information value could be readily obtained via the distributional MPTs. The focus is on the central issue of negative value for information.