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)

Nadezhnostʹ matematicheskogo dokazatelʹstva -- Nadezhnostʹ logicheskikh norm -- Ontologicheskoe obosnovanie matematiki -- Sistemnoe obosnovanie matematiki.

Quantum cognition in decision making is a recent and rapidly growing field. In this paper, we develop an expected utility theory in a context of non-classical uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework, we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neumann–Lüders postulate (...) applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion. (shrink)

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)

Proper interpretation of the problem of contradiction in motion has acquired pressing importance in recent years in conjunction with the development of dialectical materialist concepts of motion, space and time, continuity and discontinuity, infinity, and the like, and also in relations to problems of dialectical logic. In a number of writings , we have attempted to demonstrate that internal contradiction is inherent in motion that inseparably connected with it are such contradictory factors as variability and stability, movement and rest, with (...) variability playing the leading role. Moreover, generally speaking, the concept of preservation, stability or rest means the preservation or maintenance of the very state of motion. (shrink)

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