Institute for Mathematical Behavioral Sciences

A geometric approach is developed to explain several phenomena that arise with Luce’s choice axiom such as where differences occur when a ranking is determined from best, or worst, first. New ways to compute probabilities and to increase the applicability of the choice axiom are introduced; e.g., with ten alternatives, Luce’s formulation allows nine degrees of freedom for profiles while the approach described here allows millions of degrees of freedom. A profile decomposition identifies and explains the e_ects of using di_erent methods to determine outcomes and compute ranking probabilities. Three and four alternatives are emphasized for reasons of exposition, but most of the conclusions hold for any number of alternatives.