Modeling Human Decision-Making: An Overview of the Brussels Quantum Approach

Abstract

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing ‘fallacies of human reasoning’, namely, the ‘conjunction fallacy’ and the ‘disjunction effect’. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of ‘emergent reasoning’ and ‘logical reasoning’, where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. ‘contextuality’, ‘emergence’, ‘entanglement’, ‘interference’ and ‘superposition’. As such, it is alternative to the Kahneman–Tversky research programme, which instead aims to explain human fallacies in terms of ‘individual heuristics and biases’.

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Notes

  1. 1.

    A normalized function \(p: E \in \mathscr {A} \longrightarrow [0,1]\) is said ‘Kolmogorovian’ if it satisfies the following axioms: (i) \(p(\Omega )=1\) and (ii) \(p(\cup _{i}E_i)=\sum _{i}p(E_i)\), for every sequence \(\{E_i\}_i\) of pairwise disjoint events \(E_i\) (Kolmogorov 1933).

  2. 2.

    The monotonicty law of Kolmogorovian probability is globally expressed by the inequalities \(p(E_A \cap E_B)\le p(E_A),p(E_B)\le p(E_A\cup E_B)\).

  3. 3.

    We remind that an orthogonal projection operator is a liner operator which satisfies hermiticity, i.e. \(M^{\dag }=M\), and idempotency, i.e. \(M^2=M\cdot M=M\).

  4. 4.

    Indeed, \(|A\rangle\) and \(|B\rangle\) are orthogonal vectors, and also \(M|A\rangle\) and \((1\!\!1-M)|A\rangle\) and \(M|B\rangle\) and \((1\!\!1-M)|B\rangle\) are, representing three data points \(\mu (A)\), \(\mu (B)\) and \(\mu (A \ \mathrm{and} \ B)\) requires a Hilbert space of at least dimension 3.

  5. 5.

    The situation in which \(\mu (A)=0\) or \(\mu (B)=0\) requires some further technicalities and a more complex Hilbert space structure, the ‘Fock space’, which will be introduced later. We do not dwell on this aspect here, for the sake of brevity.

  6. 6.

    In Kolmogorovian probability, one proves the law of total probability, namely, \(p(E_A)=p(E_B)p(E_A|E_B)+p(E'_{B})p(E_A|E'_B)\), where \(E'_B=\Omega \setminus E_B\) denotes the ‘complement event’ with respect to \(E_B\).

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Correspondence to Massimiliano Sassoli de Bianchi.

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Aerts, D., Sassoli de Bianchi, M., Sozzo, S. et al. Modeling Human Decision-Making: An Overview of the Brussels Quantum Approach. Found Sci (2018). https://doi.org/10.1007/s10699-018-9559-x

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Keywords

  • Quantum structures
  • Cognition
  • Concept theory
  • Decision theory
  • Human reasoning