Probabilistic models of set-dependent and attribute-level best-worst choice

We characterize a class of probabilistic choice models where the choice probabilities depend on two scales, one with a value for each available option and the other with a value for the set of available options. Then, we develop similar results for a task in which a person is presented with a profile of attributes, each at a pre-specified level, and chooses the best or the best and the worst of those attribute-levels. The latter design is an important variant on previous designs using best-worst choice to elicit preference information, and there is various evidence that it yields reliable interpretable data. Nonetheless, the data from a single such task cannot yield separate measures of the “importance” of an attribute and the “utility” of an attribute-level. We discuss various empirical designs, involving more than one task of the above general type, that may allow such separation of importance and utility.