An axiomatic system for multidimensional preferences

An axiomatic system TP is developed which allows the amalgamation of linear preferences (preferences in respect to different criteria) according to the weights of those criteria. Section 1 deals with linear preferences. In Section 2 an axiomatic system for the ordering of classes of criteria is formulated. Section 3 explains the development of system TP. Two TP-systems are distinguished, based on two different linear preference systems. The preference relation of TP is shown to be nontransitive, while the linear preference relation is transitive. In 3.7 an alternative-system TP′ is given. Section 3.8 deals with formulas concerning the disjunction of alternatives, which are not valid in TP, even though they are valid in a linear preference system. In Section 4 types of preference relations and types of alternatives are distinguished to get the opportunity to express preferences between preferences.