Explaining versus describing human decisions: Hilbert space structures in decision theory

Abstract

Despite the impressive success of quantum structures to model long-standing human judgement and decision puzzles, the quantum cognition research programme still faces challenges about its explanatory power. Indeed, quantum models introduce new parameters, which may fit empirical data without necessarily explaining them. Also, one wonders whether more general non-classical structures are better equipped to model cognitive phenomena. In this paper, we provide a realistic–operational foundation of decision processes using a known decision-making puzzle, the Ellsberg paradox, as a case study. Then, we elaborate a novel representation of the Ellsberg decision situation applying standard quantum correspondence rules which map realistic–operational entities into quantum mathematical terms. This result opens the way towards an independent, foundational, rather than phenomenological, motivation for a general use of quantum Hilbert space structures in human cognition.

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Fig. 1

Notes

  1. 1.

    One of the axioms is the famous sure-thing principle, which is violated in the Ellsberg paradox. The other axioms are: ordinal event independence, comparative probability, non-degeneracy, small event continuity and dominance, and have a technical nature (Savage 1954). However, these axioms are not relevant to the present purposes, and hence, we will not dwell on them, for the sake of brevity.

  2. 2.

    Some authors identify the notion of “state” with the notion of “belief state” of the individual participating in the cognitive experiment, e.g. taking the decision (see, e.g. Busemeyer and Bruza 2012; Blutner and beim Graben 2016; Haven and Khrennikov 2013). We instead neatly distinguish states from measurements here. A state is defined by a preparation procedure of the cognitive entity under investigation. The participant in the experiment acts as a (measurement) context that interacts with the cognitive entity and changes its state.

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Correspondence to Sandro Sozzo.

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The author has no conflict of interest to declare.

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This work was supported by QUARTZ (Quantum Information Access and Retrieval Theory), the Marie Skłodowska-Curie Innovative Training Network 721321 of the European Union’s Horizon 2020 research and innovation programme.

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Communicated by F. Holik.

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Sozzo, S. Explaining versus describing human decisions: Hilbert space structures in decision theory. Soft Comput 24, 10219–10229 (2020). https://doi.org/10.1007/s00500-019-04140-x

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Keywords

  • Quantum structures
  • Cognitive science
  • Decision theory
  • Ellsberg paradox
  • Operational realism