Commentry
Yutaka Matsushita
Abstract
In this paper, focusing on a problem involved in extensive structures, a two-step generalization of extensive structures is discussed. Extensive structures can be useful in measuring attributes possessing an invariant unit, whereas they will not be adequate for measuring attributes in the case of a unit varying according to time, as inferred from the observation that the value of money (a unit) changes with the passage of time. To solve this problem, extensive structures are generalized such that the concatenation operation can be non-associative and noncommutative. This generalization yields a weighted additive function that enables us to explain preferences among temporal sequences as long as the degree of consumers’ impatience is constant regardless of the receipt period of each component (outcome). However, it is well known that the state of constant impatience is often violated in intertemporal choice. This problem can be solved by expressing the advanced (resp. postponed) receipt of outcomes by right multiplication (resp. right division) by “subjective” durations. The subjective duration is assessed for each period in such a way that the duration becomes longer when a person feels impatient during a particular period. By the introduction of right multiplication (right division), the weighted additive function is a generalized form of the weight being a function of durations, and hence we can evaluate intertemporal choice problems accompanied by non-constant impatience.