24 research outputs found
Processing Information in Quantum Decision Theory
A survey is given summarizing the state of the art of describing information
processing in Quantum Decision Theory, which has been recently advanced as 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 intended
actions. The theory characterizes entangled decision making, non-commutativity
of subsequent decisions, and intention interference. The self-consistent
procedure of decision making, in the frame of the quantum decision theory,
takes into account both the available objective information as well as
subjective contextual effects. This quantum approach avoids any paradox typical
of classical decision theory. Conditional maximization of entropy, equivalent
to the minimization of an information functional, makes it possible to connect
the quantum and classical decision theories, showing that the latter is the
limit of the former under vanishing interference terms.Comment: Review article, 49 pages, Latex fil
Preference reversal in quantum decision theory
We consider the psychological effect of preference reversal and show that it
finds a natural explanation in the frame of quantum decision theory. When
people choose between lotteries with non-negative payoffs, they prefer a more
certain lottery because of uncertainty aversion. But when people evaluate
lottery prices, e.g. for selling to others the right to play them, they do this
more rationally, being less subject to behavioral biases. This difference can
be explained by the presence of the attraction factors entering the expression
of quantum probabilities. Only the existence of attraction factors can explain
why, considering two lotteries with close utility factors, a decision maker
prefers one of them when choosing, but evaluates higher the other one when
pricing. We derive a general quantitative criterion for the preference reversal
to occur that relates the utilities of the two lotteries to the attraction
factors under choosing versus pricing and test successfully its application on
experiments by Tversky et al. We also show that the planning paradox can be
treated as a kind of preference reversal.Comment: Latex file, 15 page
Reframing Convergent and Divergent Thought for the 21st Century
Convergent thought is defined and measured in terms of the ability to perform
on tasks where there is a single correct solution, and divergent thought is
defined and measured in terms of the ability to generate multiple different
solutions. However, this characterization of them presents inconsistencies, and
despite that they are promoted as key constructs of creativity, they do not
capture the capacity to reiteratively modify an idea in light of new
perspectives arising out of an overarching conceptual framework. Research on
formal models of concepts and their interactions suggests that different
creative outputs may be projections of the same underlying idea at different
phases of this kind of 'honing' process. This leads us to redefine convergent
thought as thought in which the relevant concepts are considered from
conventional contexts, and divergent thought as thought in which they are
considered from unconventional contexts. Implications for the assessment of
creativity are discussed.Comment: 7 pages; 2 figures
Inconclusive quantum measurements and decisions under uncertainty
We give a mathematical definition for the notion of inconclusive quantum
measurements. In physics, such measurements occur at intermediate stages of a
complex measurement procedure, with the final measurement result being
operationally testable. Since the mathematical structure of Quantum Decision
Theory has been developed in analogy with the theory of quantum measurements,
the inconclusive quantum measurements correspond, in Quantum Decision Theory,
to intermediate stages of decision making in the process of taking decisions
under uncertainty. The general form of the quantum probability for a composite
event is the sum of a utility factor, describing a rational evaluation of the
considered prospect, and of an attraction factor, characterizing irrational,
subconscious attitudes of the decision maker. Despite the involved
irrationality, the probability of prospects can be evaluated. This is
equivalent to the possibility of calculating quantum probabilities without
specifying hidden variables. We formulate a general way of evaluation, based on
the use of non-informative priors. As an example, we suggest the explanation of
the decoy effect. Our quantitative predictions are in very good agreement with
experimental data.Comment: Latex file, 16 page
How brains make decisions
This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum
Decision Theory (QDT) that we have developed in a series of publications since
2008. We formulate a general mathematical scheme of how decisions are taken,
using the point of view of psychological and cognitive sciences, without
touching physiological aspects. The basic principles of how intelligence acts
are discussed. The human brain processes involved in decisions are argued to be
principally different from straightforward computer operations. The difference
lies in the conscious-subconscious duality of the decision making process and
the role of emotions that compete with utility optimization. The most general
approach for characterizing the process of decision making, taking into account
the conscious-subconscious duality, uses the framework of functional analysis
in Hilbert spaces, similarly to that used in the quantum theory of
measurements. This does not imply that the brain is a quantum system, but just
allows for the simplest and most general extension of classical decision
theory. The resulting theory of quantum decision making, based on the rules of
quantum measurements, solves all paradoxes of classical decision making,
allowing for quantitative predictions that are in excellent agreement with
experiments. Finally, we provide a novel application by comparing the
predictions of QDT with experiments on the prisoner dilemma game. The developed
theory can serve as a guide for creating artificial intelligence acting by
quantum rules.Comment: Latex file, 20 pages, 3 figure