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A Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making

M. Canan

Published Jan 1, 2017• 1 citation
Publisher

Abstract

Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs. individual context, time, resources, and technology. At the individual level, the differences in attaining separate actions by accessing shared information may not be considered as an anomaly from the perspective of rational decision-making. But for group behavior, reacting differently to the shared information can give rise to conflicts and deviations from an expected behavior, and are categorized as an anomaly or irrational behavior. The lack of proper recognition of the reasons for differences can even impede the shared action towards attaining a common objective. The manifestation of differences becomes noticeable in complex situations. The shared awareness approaches that originate from available situational awareness models fail to recognize the reasons of an unexpected decision in these situations. One reason for this is that in complex situations, incompatible events can become dominant. Human information processing is sensitive to the compatibility of the events. This, and various other human psychological characteristics, require models to be developed that include comprehensive formalisms for both compatible and incompatible events in complex situations. Quantum probability provides a geometrical probabilistic formalism to study the decision and the dynamic cognitive systems in complex situations. The event representation in Hilbert space provides the necessary foundation to represent an individual's knowledge of a situation. Hilbert space allows representing awareness as a superposition of indefinite states. These states form a complete N-dimensional Hilbert space. Within the space generated, events are represented as a subspace. By using these characteristics of Hilbert space and quantum geometrical probabilities, this study introduces a representation of self and other-than-self in a situation. An area of awareness with the possibility of projection onto the same event allows representing shared awareness geometrically. This formalism provides a coherent explanation of shared awareness for both compatible and incompatible events. Also, by using the superposition principles, the dissertation introduces spooky action at a distance concept in studying shared awareness.

DOI
10.25777/mc4a-8y68

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Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs. individual context, time, resources, and technology. At the individual level, the differences in attaining separate actions by accessing shared information may not be considered as an anomaly from the perspective of rational decision-making. But for group behavior, reacting differently to the shared information can give rise to conflicts and deviations from an expected behavior, and are categorized as an anomaly or irrational behavior. The lack of proper recognition of the reasons for differences can even impede the shared action towards attaining a common objective. The manifestation of differences becomes noticeable in complex situations. The shared awareness approaches that originate from available situational awareness models fail to recognize the reasons of an unexpected decision in these situations. One reason for this is that in complex situations, incompatible events can become dominant. Human information processing is sensitive to the compatibility of the events. This, and various other human psychological characteristics, require models to be developed that include comprehensive formalisms for both compatible and incompatible events in complex situations. Quantum probability provides a geometrical probabilistic formalism to study the decision and the dynamic cognitive systems in complex situations. The event representation in Hilbert space provides the necessary foundation to represent an individual's knowledge of a situation. Hilbert space allows representing awareness as a superposition of indefinite states. These states form a complete N-dimensional Hilbert space. Within the space generated, events are represented as a subspace. By using these characteristics of Hilbert space and quantum geometrical probabilities, this study introduces a representation of self and other-than-self in a situation. An area of awareness with the possibility of projection onto the same event allows representing shared awareness geometrically. This formalism provides a coherent explanation of shared awareness for both compatible and incompatible events. Also, by using the superposition principles, the dissertation introduces spooky action at a distance concept in studying shared awareness.
Shared awareness is an essential concept in the joint decision-making context. Typically, it is oversimplified and associated with shared information. To share an understanding in totality is to say that there is a sharing of meaning and awareness, not only of information. However, existing shared awareness models fail to explain situations in which two people view the same event but attend to different information or act differently based on the same information. Although several categorization models of shared awareness exist, the models are ad-hoc or inadequate to generalization. This paper presents a theoretical discussion of shared awareness based on its cognitive structure. We apply the pragmatic idealism framework, which provides a theoretical construct where the domain of awareness is an abstraction of reality. This framework supports the existence of multiple incompatible perspectives and understandings. We discuss the ontology of this abstract concept with the mathematical tools of quantum probability theory. We discuss the cognitive processes that transform a simple situation into a complex situation. The presented model of shared awareness includes a quantification of the degree of sharing in complex situations.
Artificial Intelligence is set to encompass additional decision space that has traditionally been the purview of humans. However, this decision space remains contested. Incongruencies between artificial intelligence and human rationalization processes introduce uncertainties in human decision-making, which require new conceptualizations that capture these distinct types of uncertainties. Hence, developing new ways to model human and artificial intelligence interactions are necessary to account for such uncertainties and improve situation awareness and decision-making. In this paper, we outline current conceptualizations of human and machine rationalities. Next, we offer the concept of rational prediction deviations (via quantum probability theory) for capturing uncertainty in situational awareness. Lastly, we propose a human-in-the-loop construct to explicate how applications of quantum probability theory in decision science can ameliorate situation awareness models by providing a novel way to capture distinct dynamics of decision making.
FINDING: Quantum cognition applies non-Kolmogorov probability (Hilbert-space amplitudes) to model human decision-making under context and conflict, replacing classical Boolean logic with superposition and interference. | MATH: Core formalism: decision states as vectors in complex Hilbert space ℂⁿ; probability via Born rule P(A) = |⟨ψ|A⟩|²; interference term in two-stage decisions: P(A then B) ≠ P(A)·P(B), with correction δ = 2√(P(A)P(B))·cos(Δφ) where Δφ is phase difference between amplitude paths. Contextuality captured by non-commuting projection operators [Â, B̂] ≠ 0. Social agent model (arXiv:1202.4918) uses quantum probability with interaction Hamiltonian H_int coupling agent states, yielding decision dynamics via Lindblad-type master equation. | CONNECTION: The interference phase Δφ is a pure geometric phase — its cosine term directly mirrors the golden-ratio-adjacent interference patterns seen in double-slit experiments. When Δφ = 2π/5 (72°), cos(Δφ) = 0.309 (≈ 1/φ² = 0.382 minu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The present thesis (mostly) concerns the application of alternative mathematical methods to understand patterns in human cognition and to model them. The different chapters presented in this thesis show research that concerns the application of quantum probability (QP) theory in the modeling of human decision-making. Quantum probability (QP) theory is a theory for how to assign probabilities to events. QP theory can be thought of as the probability rules from quantum mechanics, without any of the physics. This work is not about the application of quantum physics to brain physiology. Rather, we are interested in QP theory as a mathematical framework for cognitive modelling. This theory is potentially relevant in any behavioural situation that involves uncertainty. QP theory is analogous to classical probability theory, though QP theory and classical probability (CP) theory are founded from different sets of axioms (the Kolmogorov and Dirac/von Neumann axioms respectively) and so are subject to alternative constraints. In this thesis we show that especially over the last decade, there has been a growing interest in decision-making and cognitive models using a quantum probabilistic (QP) framework. We see how this development encompasses publications in major journals (see Pothos and Busemeyer, 2013; Wang et al., 2014; and Yearsley and Pothos, 2014; among others), special issues, and dedicated workshops, as well as several comprehensive books (Busemeyer and Bruza, 2012; Khrennikov, 2010; and Haven and Khrennikov, 2010). However, uncertainty itself is neither ethical nor unethical – yet it is inherent to most situations in which, for instance, moral judgments and decisions have to be made. For a descriptive understanding of judgment and decisions in moral situations, it is an important lesson to acknowledge both the cognitive side (bounded rationality) and the environment (ecological rationality) – and thus the uncertainty of the world and how the mind deals with it. This thesis also shows significant interest in moral and social psychology. Specifically, we consider present technologies that suggest a need for evaluating alternative contexts for ethical decision-making. How the research on human-machine interaction feeds back into humans’ understanding of themselves as moral agents? This key question ultimately relates to the nature of ethical theory itself. Overall, this dissertation presents and addresses not only standard aspects of decision- making processes, such as similarity judgments (Chapters 1 to 4) or the constructive role of articulating impressions (Chapter 5), but also standard aspects of social psychology, such as moral judgments (Chapters 6 and 7) and game theory (Chapter 8). As stated in the Declarations section, the present thesis is a combination of a standard and a publication- based dissertation.
Recent results from cognitive psychology suggest that human behavior can be, in some situations, better described by laws known from physical quantum theory. This work responds to this development and seeks to answer the question of how quantum models of cognition and decision-making can contribute to our understanding of the social world. We introduce the approaches to the application of quantum theory in social sciences - quantum consciousness, quantum reasoning and quantum metaphor and further develop the second, in the context of strategic interaction in game theory. We show that the quantum model corresponds to both the psychological intuition and many empirically known anomalies such as the order effect, disjunction effect, or context effect. In this work, we derive a specific model of strategic interaction between two players, and we test it in the experimental Prisoner's Dilemma game. The model is based on the rational choice theory, which is nevertheless re-defined when it is shown how the strategic choice is changed if the quantum probability (C*-algebra) is used as the underlying theory instead of classical probability (σ-algebra). The results obtained support the quantum model and showed a different representation of the game among various groups of players. The quantum model of...
Human cognition is a complex process facilitated by the intricate architecture of human brain. However, human cognition is often reduced to quantum theory based events in principle because of their correlative conjectures for the purpose of analysis for reciprocal understanding. In this paper, we begin our analysis of human cognition via formal methods and proceed towards quantum theories. Human cognition often violate classic probabilities on which formal representation of conceptual spaces are built. Further, geometric representation of conceptual spaces proposed by Gardenfors discusses the underlying content but lacks a systematic approach (Gardenfors, 2000; Kitto et. al, 2012). However, the aforementioned views are not contradictory but different perspective with a gap towards sufficient understanding of human cognitive process. A comprehensive and systematic approach to model a relatively complex scenario can be addressed by vector space approach of conceptual spaces as discussed in literature. In this research, we have proposed an approach that uses both formal representation and Gardenfors geometric approach. The proposed model of high dimensional formal representation of conceptual space is mathematically analysed and inferred to exhibit quantum aspects. Also, the proposed model achieves cognition, in particular, consciousness. We have demonstrated this process of achieving consciousness with a constructive learning scenario. We have also proposed an algorithm for conceptual scaling of a real world scenario under different quality dimensions to obtain a conceptual scale.