Luce's choice axiom

A geometric approach is introduced to explain phenomena that can arise with Luce's choice axiom; e.g., differences occur when determining the likelihood of a ranking by starting with the ``best-first,'' or ``worst-first'' alternative. As shown, the problem is caused by the way we compute pairwise probabilities: it forces ``best-first'' and ``worst-first'' computations to use different information from a profile. Thus agreement holds only should the different information agree: this happens only with complete indifference. An alternative ``best-first'' and ``worst-first'' comparison, which always holds, is developed. Ways to increase the applicability of the choice axiom are introduced; e.g., profiles admitted by Luce's formulation for ten alternatives have nine degrees of freedom; the approach described here allows millions of degrees of freedom. New ways to compute probabilities, which combine ``best-first'�...

• Type: Journal
• Year: 2008
• Where: SCHOLARPEDIA
• Authors: Duncan Luce
• Keywords: Choice Axiom, Compute Pairwise, Geometric Approach, SCHOLARPEDIA 2008