We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

Издание предназначено для студентов, магистрантов, аспирантов филологических факультетов вузов и широкого круга читателей.

t. 1. Igry rynka -- t. 2. Torgovet︠s︡ v Khrame.

В доступной форме ученики и последователи В. И. Свидерского рассказывают об этом выдающемся "генераторе" новых философских идей, о значении этих идей в преодолении кризисных явлений в современной философии.

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

In his critique of empiriocriticism, V. I. Lenin also considered it necessary to characterize its relationship to religion in order to show more fully the social significance of this school, which was fashionable in its time. In contrast to those who took at face value the pretensions of Machism to present the scientific thought of the nineteenth century and who hastened to put it in place of "obsolete" materialist dialectics, V. I. Lenin unmasked the "completely reactionary character" of this essentially (...) subjective-idealistic current, which played into the hands of fideism despite the fact that E. Mach considered himself an atheist. (shrink)