A Normative Probabilistic Design of a Fair Government Decision Strategy

摘要

A government (a global decision maker) is supposed to search for a fair strategy generating its decisions influencing a population of citizens (local decision makers). The strategy should respect the fact that each citizen has their personal preferences as well as observation and decision spaces. A non-standard problem formulation and its solution are proposed. Specifically, each citizen (male, female, possibly child) is supposed to express his wishes and restrictions in the way that can be translated into an ideal distribution of data he observes and influences. He is recommended to select his decision strategy so that the real distribution of these data is close to his ideal distribution. This approach is called fully probabilistic design. The government is assumed to be able to influence a few data entries that have an impact on each citizen. The government optimal decision strategy is also formulated in the fully probabilistic sense with its ideal defined as a mixture of the ideal distributions of citizens. Portions of different types of citizens are taken as weights of components forming the mixture. The paper characterizes individual problem elements and information flow, provides an approximate feasible solution and specializes it to normal government model and normal ideal distributions of citizens. Qualitative consequences with respect to rational governing are drawn.