Models of best–worst choice and ranking among multiattribute options (profiles)

We develop and characterize new representations for the maxdiff model (Marley & Louviere, 2005) for best–worst choice between multiattribute options; in particular, we state conditions under which the scale value of a multiattribute option is a product of independent ratio scales on each attribute. We show that there is a vector of simple “scores” that are sufficient for the model, with each score a closed-form function of the maximum likelihood estimates of the model’s parameters. Several related models are developed for rank orders obtained by repeated best and/or worst choices, and two of these models are tested on stated preferences between mobile phones. ► We axiomatize the maxdiff model for best–worst choice between multiattribute options. ► We show that the scale value of each option is a product of independent ratio scales. ► We show that there is a vector of simple “scores” that are sufficient for the model. ► We develop models for rank orders obtained by repeated best and/or worst choices. ► Two ranking models are tested on stated preferences between mobile phones.