Abstract
This paper is in two parts: 1. (1) A review of tests of Luce's choice axiom reveals a surprising lack of direct statistical tests. A simple statistical test of the choice axiom is proposed and applied to two sets of data. Clarke's data, which originally suggested the axiom, demonstrates a statistically significant departure from that axiom, though it must also be mentioned that Clarke's data was pooled over individual subjects. 2. (2) A long-standing objection to the choice axiom is that it is unsuitable when choice is multistage. A number of propositions are therefore given (and tested statistically) for a two-stage mechanism of choice, and the choice axiom adapted to such a two-stage situation.
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