Problems of utility and prospect theories. A ”certain-uncertain” inconsistency of the random-lottery incentive system

Three main groups of results have been obtained: 1) The question is emphasized whether the probability weighting function W(p) is continuous. If W(p) reveals a discontinuity at p=1, then this is a topological feature. This can qualitatively change (at least) the mathematical aspects of the utility and prospect theories. This is supported by a number of the evidences of the qualitative difference between subjects’ treatments of the probabilities of probable and certain outcomes. 2) Purely mathematical theorems prove (under several conditions) that if the dispersion of data (the noise) is non-zero, then the non-zero discontinuity take place at the probability p=1. 3) In the prevailing random-lottery incentive system of the experiments of the utility and prospect theories, the choices of certain outcomes are stimulated by uncertain lotteries. Because of this evident “certain-uncertain” inconsistency, the deductions from the random-lottery incentive experiments, those include the certain outcomes, cannot be unquestionably correct. The experiment of Starmer and Sugden (1991) evidently supports this consideration.