Conceptual relations between expanded rank data and models of the unexpanded rank data

Louviere et al. (2008. J. of Choice Modelling, 1, 126-163) present two main empirical examples in which a respondent rank orders the options in various choice sets by repeated best, then worst, choice. They expand the ranking data to various "implied" choices in subsets and fit the expanded data in various ways; they do not present models of the original rank data, except in one case (that of the rank ordered logit). We build on their work by constructing models of the original rank data that are consistent with the "weights" implied by the data expansions. This results in two classes of models: the first includes the reversible ranking model and has useful "score" properties; the second includes the rank ordered logit model and has natural "process" interpretations. Finally, we summarize known and new results on relations between the two classes of models