A generalized extensive structure that is equipped with a right action and its representation

Publication date: Available online 22 September 2017 Source:Journal of Mathematical Psychology Author(s): Yutaka Matsushita In intertemporal choice, it has been found that if the receipt time is closer to the present, then people tend to grow increasingly or decreasingly impatient. This paper develops an axiom system to construct a weighted additive model reflecting nonconstant impatience. By presupposing that an increment in duration is subjectively assessed according to the periods at which advancement occurs, we denote the one-period advanced receipt of outcomes by multiplying the outcomes by the increment on the right. By this right multiplication, we can regard the effect of advance as the decomposition into two factors, i.e., the factor of step-by-step advance accompanied by subdivided durations and the factor of advance based on the total duration. First, the conditions for enabling right multiplication are proposed for the Cartesian product of the underlying set of a generalized extensive structure and a set of durations. Second, the properties derived under these conditions yield a right action on the generalized extensive structure. Finally, the weighted additive model is obtained as a representation of the generalized extensive structure equipped with the right action.

Source: Journal of Mathematical Psychology - September 22, 2017 Category: Psychiatry & Psychology Source Type: research