Luce's choice axiom

13 years 4 months ago

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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'�...

Duncan Luce

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