A category theory approach to derived preference relations in some decision making problems

A decision making problem is considered from algebraic point of view. The set of outcomes (consequences) is supposed to be 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) over another, i.e., to describe suitable preference relations (called derived preference relations) on the set of the decision maker's strategies. This problem is formalized by using a category theory approach and is reduced to a pure algebraical question. An effective method is suggested for constructing all reasonable derived preference relations and some examples are presented which illustrate how the method is applied.