486 research outputs found
Recommended from our members
A quantum geometric model of similarity
No other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality, and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tverskyâs (1997) main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general
Recommended from our members
A quantum theoretical explanation for probability judgment errors
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning
Recommended from our members
Quantum cognition and decision theories: A tutorial
Models of cognition and decision making based on quantum theory have been the subject of much interest recently. Quantum theory provides an alternative probabilistic framework for modelling decision making compared with classical probability theory, and has been successfully used to address behaviour considered paradoxical or irrational from a classical point of view.
The purpose of this tutorial is to give an introduction to quantum models, with a particular emphasis on how to build these models in practice. Examples are provided by the study of order effects on judgements, and we will show how order effects arise from the structure of the theory. In particular, we show how to derive the recent discovery of a particular constraint on order effects implied by quantum models, called the Quantum Question (QQ) Equality, which does not appear to be derivable from alternative accounts, and which has been experimentally verified to high precision. However the general theory and methods of model construction we will describe are applicable to any quantum cognitive model. Our hope is that this tutorial will give researchers the confidence to construct simple quantum models of their own, particularly with a view to testing these against existing cognitive theories
Recommended from our members
Social Projection and a Quantum Approach for Behavior in Prisoner's Dilemma
Modeling Concept Combinations in a Quantum-theoretic Framework
We present modeling for conceptual combinations which uses the mathematical
formalism of quantum theory. Our model faithfully describes a large amount of
experimental data collected by different scholars on concept conjunctions and
disjunctions. Furthermore, our approach sheds a new light on long standing
drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward
a completely novel possible solution to the 'combination problem' in concept
theory. Additionally, we introduce an explanation for the occurrence of quantum
structures in the mechanisms and dynamics of concepts and, more generally, in
cognitive and decision processes, according to which human thought is a well
structured superposition of a 'logical thought' and a 'conceptual thought', and
the latter usually prevails over the former, at variance with some widespread
beliefsComment: 5 pages. arXiv admin note: substantial text overlap with
arXiv:1311.605
Recommended from our members
The dynamics of decision making when probabilities are vaguely specified
Consider a multi-trial game with the goal of maximizing a quantity Q(N). At each trial N, the player doubles the accumulated quantity, unless the trial number is Y, in which case all is lost and the game ends. The expected quantity for the next trial will favor continuing play, as long as the probability that the next trial is Y is less than one half. Y is vaguely specified (e.g., someone is asked to fill a sheet of paper with digits, which are then permuted to produce Y). Conditional on reaching trial N, we argue that the probability that the next trial is Y is extremely small (much less than one half), and that this holds for any N. Thus, single trial reasoning recommends one should always play, but this guarantees eventual ruin in the game. It is necessary to stop, but how can a decision to stop on N be justified, and how can N be chosen? The paradox and the conflict between what seem to be two equally plausible lines of reasoning are caused by the vagueness in the specification of the critical trial Y. Many everyday reasoning situations involve analogous situations of vagueness, in specifying probabilities, values, and/or alternatives, whether in the context of sequential decisions or single decisions. We present a computational scheme for addressing the problem of vagueness in the above game, based on quantum probability theory. The key aspect of our proposal is the idea that the range of stopping rules can be represented as a superposition state, in which the player cannot be assumed to believe in any specific stopping rule. This scheme reveals certain interesting properties, regarding the dynamics of when to stop to play
Recommended from our members
The conjunction fallacy, confirmation, and quantum theory: comment on Tentori, Crupi, & Russo
The conjunction fallacy refers to situations when a person judges a conjunction to be more likely than one of the individual conjuncts, which is a violation of a key property of classical probability theory. Recently, quantum probability theory has been proposed as a coherent account of these and many other findings on probability judgment âerrorsâ that violate classical probability rules, including the conjunction fallacy. Tentori, Crupi, and Russo (2013) present an alternative account of the conjunction fallacy based on the concept of inductive confirmation. They present new empirical findings consistent with their account, and they also claim that these results are inconsistent with the quantum probability theory account. This comment proves that our quantum probability model for the conjunction fallacy is completely consistent with the main empirical results from Tentori et al. (2013). Furthermore, we discuss experimental tests that can distinguish the two alternative accounts
Markov versus quantum dynamic models of belief change during evidence monitoring
This work is licensed under a Creative Commons Attribution 4.0 International License.Two different dynamic models for belief change during evidence monitoring were evaluated: Markov and quantum. They were empirically tested with an experiment in which participants monitored evidence for an initial period of time, made a probability rating, then monitored more evidence, before making a second rating. The models were qualitatively tested by manipulating the time intervals in a manner that provided a test for interference effects of the first rating on the second. The Markov model predicted no interference, whereas the quantum model predicted interference. More importantly, a quantitative comparison of the two models was also carried out using a generalization criterion method: the parameters were fit to data from one set of time intervals, and then these same parameters were used to predict data from another set of time intervals. The results indicated that some features of both Markov and quantum models are needed to accurately account for the results
Recommended from our members
Quantum probability updating from zero priors (by-passing Cromwellâs rule)
Cromwellâs rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayesâ rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwellâs rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwellâs rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwellâs rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments
- âŠ