Consistent aggregation of simply scalable families of choice probabilities (Q1566506)

Suppose an individual hears a sequence of three pure tone bursts of the same frequency but with different intensities and duration. He then ranks the three bursts according to (perceived) loudness. Each tone burst can be specified by two scale values, perceived intensity and duration (different pairs of values can be perceived as equivalent). Suppose now that we have data from \(m\) individuals and that we have to create a representation of the performance of an `average' person. The ranking at the individual level is done according to a probabilistic model called `two-scale Luce model with exponents.' In this paper, the `average' person is supposed to respect this probabilistic model and the question which is explored is the following: under which aggregation condition can this `aggregate' choice be written as an `aggregate' of the component (individual) probabilistic model? This question is answered and, furthermore, a characterization is provided.