Consistent aggregation of simply scalable families of choice probabilities

Proabilistic choice models that have two (or more) fixed ratio scales associated with each choice option are characterized, which suppose only local boundedness, non-constancy and an injectivity condition.

Abstract

We characterize probabilistic choice models that have two (or more) fixed ratio scales associated with each choice option. A version of Luce’s choice model with fixed scales and exponents, which we also characterize, is included. The characterizing properties are: Simple scalability, i.e. the choice probabilities depend upon a priori arbitrary combinations of the two scale values attached to each choice option. Aggregation equations express that both the probabilities and the scales are aggregated from individual to overall values. Generalized homogeneity type equations appear because we deal with ratio scales. As regards regularity, we suppose only local boundedness, non-constancy and an injectivity condition.