RESPONSE STRENGTHS AND CHOICE PROBABILITY. A CONSIDERATION OF TWO COMBINATION RULES
STANFORD UNIV CA APPLIED MATHEMATICS AND STATISTICS LABS
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Consideration is given to the following problems given two competing responses with known strength, what is the composition, or combination, rule by which choice probability is related to the strengths of the separate responses. Two theories are considered 1 Thurstones theory which assumes that the probability of choosing response A over B is an increasing function of the over difference in strengths of the two responses, and 2 Luces theory which assumes that the choice of A over B is determined by the ratio of their strengths. The discussion shows that there are extra constraints on the decision about suitable rules by which alternative response strengths may be combined. The extra constraint arises from a detailed analysis and representation of the component behaviors of a subject during the act of choosing. A model of what goes on during a single act of choice by an individual is presented. Some direct empirical support for this model are discussed, and Luces ratio test is shown to fall directly as a theorem from this representation of the behavior of a subject at a choice point.