Institute for Mathematical Behavioral Sciences

Understanding the psychological interpretation of numbers is of both practical and theoretical interest. In classical magnitude estimation, respondents match numbers to sensations and in magnitude production they select tones that stand in a prescribed numerical ratio to a given tone. The present work focusses on evaluating serveral possible, and related, forms for this numerical distortion function, or weighting function, w. The main form, of which a power function is a special case, is the Prelec exponential/power representation. Behavioral equivalents to power and to Prelec functions are described, tested, and rejected. Thus, either the mathematical form or the assumption of W(1) = 1 is wrong. Whereas, the axiomatic literature has focussed exclusively on the former inference, we explore the possibility that W(1)≠ 1. Behavioral axioms are formulated in each case and experimentally tested. We conclude that most respondents satisfy a general power function and that those who do not, appear to satisfy the more general Prelec function.