A simple derivation of Prelec's probability weighting function

Since Kahneman and Tversky [(1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263-291], it has been generally recognized that decision makers overweight low probabilities. Of the several weighting functions that have been proposed, that of Prelec [(1998). The probability weighting function. Econometrica, 60, 497-528] has the attractions that it is parsimonious, consistent with much of the available empirical evidence and has an axiomatic foundation. Luce [(2001). Reduction invariance and Prelec's weighting functions. Journal of Mathematical Psychology, 45, 167-179] provided a simpler derivation based on reduction invariance, rather than compound invariance of Prelec [(1998). The probability weighting function. Econometrica, 60, 497-528]. This note introduces a behavioral assumption that we call power invariance and provides a simple derivation of Prelec's function. Thus, we have three a priori different behavioral assumptions all leading to Prelec's function.