A raised hand effect as a decision making process

TL;DR

The paper addresses how groups of agents decide to follow or ignore rules under mutual interactions and external information, modeling the situation as a quantum-dynamical system with a two-state per-agent structure. A mean-field Hamiltonian $H_N$ with terms $H_1^{(N)}$, $H_2^{(N)}$, and $H_3^{(N)}$ is analyzed under $p_{i,j} \to p/N$, $J_{i,j}\to J/N$; the external input is represented by $B$. The analysis employs KMS states in the GNS representation to derive conditions for nontrivial solutions $m_3$, showing that for $J<0$ and suitable $B$, an educated majority can emerge, but $m_3=1$ is not achieved. The work links the raised-hand effect to a tunable parameter $B$ that biases decision making, highlighting the potential and limits of a quantum-like framework for social dynamics and prompting future exploration of different Hamiltonians, states, and parameter roles.

Abstract

In this paper we will analyse a group of agents and their attitude to follow, or not, some rules. The model is based on some quantum-like ideas, and in particular on an Hamiltonian operator $H$ describing the dynamics of the agents, assuming they are driven by some mutual interactions and that they are subjected to an external source of "information" used by the agents to decide whether to obey or not these rules. We will discuss how the relative strengths of the parameters of $H$ determine this attitude and we will discuss in particular the role of the external information. We will also apply our general idea to a specific situation, involving drivers and pedestrians trying to cross a road.