  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 analysed 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.
