Constraint-Induced Redistribution of Social Influence in Nonlinear Opinion Dynamics

TL;DR

This paper investigates how intrinsic decision constraints in social agents influence collective opinion dynamics, revealing that such constraints induce an effective weighted social graph that impacts group influence and sensitivity.

Contribution

The study introduces a framework encoding agent constraints as projections, proving invariant subspaces and analyzing how heterogeneous constraints reshape social influence in nonlinear opinion dynamics.

Findings

Constraints induce invariant subspaces where opinions evolve.

Heterogeneous constraints create an effective weighted social graph.

The effective graph alters agent centrality and group sensitivity.

Abstract

We study how intrinsic hard constraints on the decision dynamics of social agents shape collective decisions on multiple alternatives in a heterogeneous group. Such constraints may arise due to structural and behavioral limitations, such as adherence to belief systems in social networks or hardware limitations in autonomous networks. In this work, agent constraints are encoded as projections in a multi-alternative nonlinear opinion dynamics framework. We prove that projections induce an invariant subspace on which the constraints are always satisfied and study the dynamics of networked opinions on this subspace. We then show that heterogeneous pairwise alignments between individuals' constraint vectors generate an effective weighted social graph on the invariant subspace, even when agents exchange opinions over an unweighted communication graph in practice. With analysis and simulation studies, we illustrate how the effective constraint-induced weighted graph reshapes the centrality of agents in the decision process and the group's sensitivity to distributed inputs.