The profile structure for Luce's choice axiom

The Profile Structure for 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 “bestfirst” and “worst-first” computations to use different information from a...

Relationship between Luces Choice Axiom, Thurstones Theory of Comparative Judgment, and Double Exponential- Distribution

The Axiom of Choice

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...

The Axiom of Choice

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...

A Substitute for the Axiom of Choice

This theorem is well known to be equivalent to the axiom of choice (though there does not seem to be a proof of this fact in the literature) and it has been suggested as an alternative for this axiom. The purpose of this note (which is purely methodological) is to propose a simpler but equivalent formulation of (A) as a substitute for the Zermelo axiom. The simplicity lies in the fact that we m...