Data Dispersion in Economics(II)--- Inevitability and Consequences of Restrictions

This article reviews and improves the theorems of the existence of restrictions near the boundaries of finite numerical segments and of the probability scale in the presence of non-zero dispersion. The non-zero dispersion may be caused, for example, by the influence of observation noises. Applications of the theorems to experiments, which are typical of the utility theory, are briefly presented. Similar experiments may be associated with the old problems of utility theory, such as the underweighting of high and the overweighting of low probabilities, risk aversion, loss aversion, the Allais paradox, the equity premium puzzle, the "four-fold pattern" paradox, etc. It is shown that the restrictions as the consequences of the theorems should be taken into account in the explanation of such experiments. The restrictions may facilitate such explanations including explanations by utility models.