A Quantum-Inspired Framework for Subjective Evaluation: Cognitive Polarization and Entropic Measures

TL;DR

This paper introduces a quantum-inspired mathematical framework to model and analyze subjective preferences and evaluation processes, using entropy measures to quantify indecisiveness and coherence.

Contribution

It presents a novel quantum-inspired approach employing Hilbert space and entropy measures to model subjective evaluation and preference polarization.

Findings

Entropy measures reveal internal indecisiveness.

The framework quantifies collective incoherence.

Simulated data demonstrates the model's conceptual utility.

Abstract

We propose a quantum-inspired framework to model subjective evaluation processes using state vectors in Hilbert space. In this approach, individual preferences are represented as cognitive states polarized between 'like' and 'dislike', enabling a continuous interpretation of evaluative attitudes. The evolution of these states is characterized on the Bloch sphere, and the cognitive coherence is interpreted geometrically. To further analyze the uncertainty and diversity in subjective preferences, we introduce both Shannon entropy (at the individual level) and Von Neumann entropy (at the group level) into the framework. A small-scale simulated dataset is used to conceptually demonstrate how these entropy measures can reveal internal indecisiveness and collective incoherence. The model offers a physically grounded and mathematically expressive tool for quantifying subjectivity.