Quantum-Like Tug-of-War Model for Context-Dependent Decision Dynamics

Overview

Decision making frequently exhibits context dependence, which poses challenges for representation within a single non-invasive classical probability model. This research introduces a quantum-like extension of the Tug-of-War (QTOW) decision-making model. The primary objective is to investigate the conditions under which such context dependence can be effectively represented by a singular, constrained internal state.

Research Context

Classical probability models struggle to accommodate context dependence in decision making without resorting to methods like introducing explicit context labels, storing historical data, or expanding state descriptions. The paper addresses this by exploring an alternative framework drawn from quantum probability, suggesting its potential to offer a more compact representational approach for contextual operations.

Approach

The QTOW construction utilizes a qutrit state as its foundational element. Within a unified state space, the model incorporates several operational components:

• A state-disturbing generalized decision instrument.
• Decision-conditioned and reward-conditioned norm-preserving feedback mechanisms.
• Optional probing operations.

This qutrit representation is designed to admit specific probe families, specifically KCBS-type probe families. This design also allows for the existence of states that violate a non-contextuality bound. Such a violation serves as a witness, indicating that the specified family of operations cannot be embedded within a single non-contextual classical probability space.

Findings

The quantum-like extension of the Tug-of-War (QTOW) model provides a mechanism through which context dependence in decision making can be represented by a single constrained internal state. Key findings include:

• The QTOW construction, utilizing a qutrit state and associated operations, successfully models context dependence.
• The qutrit representation supports KCBS-type probe families and identifies states that infringe upon a non-contextuality bound.
• The presence of this non-contextuality witness suggests that the operation family specified by the QTOW model cannot be described by a single non-contextual classical probability space.
• While classical reconstructions can achieve descriptive adequacy via explicit context labels, stored history, or enlarged state descriptions, or by restricting the admissible probe set to avoid the non-contextuality witness, quantum probability offers a compact, single-state realization for the contextual operation family under consideration.

Why This Matters

From the perspective of both natural and artificial intelligence, the results illuminate an architectural-level trade-off in representation. Specifically, contextual information can be carried intrinsically through transformations of a shared internal state, as suggested by the quantum-like approach. Alternatively, this information can be externalized into additional state and memory resources, as is characteristic of classical approaches that expand state descriptions or add context labels.