Choice Probabilities and Choice Functions.

摘要

Although there are sizable literatures on the connections between choice probabilities and preference relations, and between preference relations and choice functions, little has been done--apart from their common ties to preference relations--to connect choice probabilities and choice functions. The latter connection is studied in this report. A family of choice functions that depends on a threshold parameter is defined from a choice probability function. It is then shown what must be true of the choice probability function so that the choice functions satisfy three traditional rationality conditions. Conversely, it is shown what must be true of the choice functions so that the choice probability function satisfies a version of Luce's axiom for individual choice probabilities. (Author)