A 'Certain-Uncertain' Inconsistency of the Main Experimental System of Utility and Prospect Theories and Models

In the main random-lottery incentive system of experiments, the choices of certain outcomes are stimulated by random, uncertain lotteries. This “certain-uncertain” inconsistency is quite evident, but only recently revealed. Because of this inconsistency, conclusions from a random-lottery incentive experiment, which includes a certain outcome, cannot be unquestionably correct. The well-known experiment and purely mathematical theorems support this evidently. So, the main result of the article is that the prevailing experimental system of utility and prospect theories and models may need additional independent analyses in the content of the “certain-uncertain” inconsistency. Because of this inconsistency, one cannot exclude that, at the probability p=1, this system hides such a topological feature as a discontinuity of the probability weighting function. Such a discontinuity is also supported by the theorems and experiment. Owing to this discontinuity, these theories and models can be qualitatively changed. For example, the probability weighting (Prelec) function can transform from the inverse S-shaped curve into a roughly straight approximation of its own middle part