On categorical approach to derived preference relations in some decision making problems

Abstract

A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of his strategies (or acts) to another, i.e. it is to describe so called derived preference relations. This problem is formalized by using category theory approach and reduced to a pure algebraical question. An effective method is suggested to build all reasonable derived preferences relations and to compare them with each other.