Phase transitions in voting simulated by an intelligent Ising model

TL;DR

This paper introduces an intelligent Ising model with nonlinear feedback to simulate voting behavior, revealing phase transitions influenced by feedback strength and demonstrating how adaptive interactions can cause biased outcomes in voting systems.

Contribution

It develops a novel intelligent Ising model with dynamic interaction strength based on total magnetization, showing new phase transition behaviors in voting simulations.

Findings

Positive feedback induces phase transitions at any finite temperature.

System transitions from second-order to first-order phase transitions with increasing feedback.

Unbiased feedback can lead to spontaneous symmetry breaking and biased voting outcomes.

Abstract

Voting is an important social activity for expressing public opinions. By conceptually considering a group of voting agents to be intelligent matter, the impact of real-time information on voting results is quantitatively studied by an intelligent Ising model, which is formed by adding nonlinear instantaneous feedback of the overall magnetization to the conventional Ising model. In the new model, the interaction strength becomes a variable depending on the total magnetization rather than a constant, which mimics the scenario that the decision of an individual during vote influenced by the dynamically changing polling result during the election process. Our analytical derivations along with Mote Carlo simulations reveal that, with a positive feedback, the intelligent Ising model exhibits phase transitions at any finite temperatures, a feature lacked in the conventional one-dimensional Ising model. In all dimensions, by varying the feedback strength, the system changes from going through a second-order phase transition to going through a first-order phase transition with increasing temperature, and the two types of phase transitions are connected by a tricritical point. This study on the one hand demonstrates that the intelligent matter with a nonlinear adaptive interaction can exhibit qualitatively different phase behaviors from conventional matter, and on the other hand shows that, during voting, even unbiased feedback may possibly induce spontaneous symmetry breaking, leading to a biased outcome where one side of the vote becomes favored.