Stochastic Token Theory

This paper presents a theory encompassing a collection of stochastic models developed earlier and concerning the evolution of subjective preferences under the influence of a stream of elementary events. The theory relies on two basic concepts. (1) The states: Each individual in the population of reference is regarded as evolving in real time through a sequence of internal states. These states can be probed by interviewing the subjects at some arbitrarily chosen times t1,  em leader, tn. Each of these interviews yields a response which is a reflection of the current state. (2) The tokens: The individual is subjected to a stochastic stream of unobservable or unrecorded "particles" of information, called tokens. Each token has the potential of modifying the current state, and is accordingly formalized by a transformation on the set of states. The core of the theory and the major concern of this paper is the particular semigroup generated by all such transformations. Combinatorial and stochastic axioms are formulated which lead to testable conditions. The theorems of this paper generalize earlier results by the author and others.