59,267 research outputs found
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
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
Identifying Quantum Structures in the Ellsberg Paradox
Empirical evidence has confirmed that quantum effects occur frequently also
outside the microscopic domain, while quantum structures satisfactorily model
various situations in several areas of science, including biological, cognitive
and social processes. In this paper, we elaborate a quantum mechanical model
which faithfully describes the 'Ellsberg paradox' in economics, showing that
the mathematical formalism of quantum mechanics is capable to represent the
'ambiguity' present in this kind of situations, because of the presence of
'contextuality'. Then, we analyze the data collected in a concrete experiment
we performed on the Ellsberg paradox and work out a complete representation of
them in complex Hilbert space. We prove that the presence of quantum structure
is genuine, that is, 'interference' and 'superposition' in a complex Hilbert
space are really necessary to describe the conceptual situation presented by
Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision
processes in economics and decision theory, and allows to deal with different
Ellsberg-type generalizations, e.g., the 'Machina paradox'.Comment: 16 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1208.235
The Quantum Challenge in Concept Theory and Natural Language Processing
The mathematical formalism of quantum theory has been successfully used in
human cognition to model decision processes and to deliver representations of
human knowledge. As such, quantum cognition inspired tools have improved
technologies for Natural Language Processing and Information Retrieval. In this
paper, we overview the quantum cognition approach developed in our Brussels
team during the last two decades, specifically our identification of quantum
structures in human concepts and language, and the modeling of data from
psychological and corpus-text-based experiments. We discuss our
quantum-theoretic framework for concepts and their conjunctions/disjunctions in
a Fock-Hilbert space structure, adequately modeling a large amount of data
collected on concept combinations. Inspired by this modeling, we put forward
elements for a quantum contextual and meaning-based approach to information
technologies in which 'entities of meaning' are inversely reconstructed from
texts, which are considered as traces of these entities' states.Comment: 5 page
Quantum Structure in Cognition
The broader scope of our investigations is the search for the way in which
concepts and their combinations carry and influence meaning and what this
implies for human thought. More specifically, we examine the use of the
mathematical formalism of quantum mechanics as a modeling instrument and
propose a general mathematical modeling scheme for the combinations of
concepts. We point out that quantum mechanical principles, such as
superposition and interference, are at the origin of specific effects in
cognition related to concept combinations, such as the guppy effect and the
overextension and underextension of membership weights of items. We work out a
concrete quantum mechanical model for a large set of experimental data of
membership weights with overextension and underextension of items with respect
to the conjunction and disjunction of pairs of concepts, and show that no
classical model is possible for these data. We put forward an explanation by
linking the presence of quantum aspects that model concept combinations to the
basic process of concept formation. We investigate the implications of our
quantum modeling scheme for the structure of human thought, and show the
presence of a two-layer structure consisting of a classical logical layer and a
quantum conceptual layer. We consider connections between our findings and
phenomena such as the disjunction effect and the conjunction fallacy in
decision theory, violations of the sure thing principle, and the Allais and
Elsberg paradoxes in economics.Comment: 58 pages, 1 figure. Reworked version after review proces
Quantum Structure in Competing Lizard Communities
Almost two decades of research on applications of the mathematical formalism
of quantum theory as a modeling tool in domains different from the micro-world
has given rise to many successful applications in situations related to human
behavior and thought, more specifically in cognitive processes of
decision-making and the ways concepts are combined into sentences. In this
article, we extend this approach to animal behavior, showing that an analysis
of an interactive situation involving a mating competition between certain
lizard morphs allows to identify a quantum theoretic structure. More in
particular, we show that when this lizard competition is analyzed structurally
in the light of a compound entity consisting of subentities, the contextuality
provided by the presence of an underlying rock-paper-scissors cyclic dynamics
leads to a violation of Bell's inequality, which means it is of a non-classical
type. We work out an explicit quantum-mechanical representation in Hilbert
space for the lizard situation and show that it faithfully models a set of
experimental data collected on three throat-colored morphs of a specific lizard
species. Furthermore, we investigate the Hilbert space modeling, and show that
the states describing the lizard competitions contain entanglement for each one
of the considered confrontations of lizards with different competing
strategies, which renders it no longer possible to interpret these states of
the competing lizards as compositions of states of the individual lizards.Comment: 28 page
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