A new foundation of quantum decision theory

Abstract: Quantum decision theory is introduced here, and a new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, and next on arguments for the Born rule, that is, the basis for calculating quantum probabilities. A basic notion behind the quantum theory foundation is that of theoretical variables, that are divided into accessible and inaccessible ones. This is here specialized to decision variables. It is assumed that each accessible variable can be seen as a function of a specific inaccessible variable. Another assumption is that there exist two maximal accessible theoretical variables in the given situation. Two basic assumptions behind the Born rule are 1) the likelihood principle, 2) the actor in question has motivations that can be modeled by a hypothetical perfectly rational higher being. The theory is illustrated by a medical example. Finally, a broad discussion of decision processes is given.