Generalization of Classical Decision Theory

Abstract

The decision theory of today is a mixture of several independent theories, such as utility theory, statistical decision theory, and game theory. This paper tries to give an outline of a more general decision theory founded upon some aspects of basic research. it is mainly the personalistic view of decision-making under uncertainty and risk based upon human valuation, clearly expressed by Savage, who said that valuation (utility) is the first and probability the second. The following reasoning takes further into account that there are two fundamental attitudes towards the surrounding world. Firstly, man can be conscious of a part of the world by recognition. Especially scientific recognition means mapping a part of the world (D) into his mental consciousness, i.e. into symbols of language to find out the empirical structure of this part (D) of the world. Secondly, man can be conscious of a part (D) of the world by evaluation. Evaluation means mapping of objects, actual states of the world, of actions into his mental consciousness, i.e. into symbols of language, to find out the order created by ordering relations of preference (Pref). There is a fundamental difference between the basic ordering of an empirical set M₀ of things a′₁, a′₂, …, a′ _n by empirical relations, as ‘a′ _i is greater than a′ _j and a′ _j is equal to a′ _k ’, and the ordering by relations of preference, as ‘a′ _i is preferred to a′ _j ’ (P(a′ _i , a′ _j ) in symbols), or ‘a′ _i is indifferent to a′ _i ’ (i(a′ _i , a′ _j )).