Constraint-Induced Redistribution of Social Influence in Nonlinear Opinion Dynamics
This work addresses collective decision-making in social or autonomous networks with constraints, but it appears incremental as it builds on existing nonlinear opinion dynamics frameworks.
The paper tackles the problem of how hard constraints on agents' decisions affect collective choices in heterogeneous groups, showing that these constraints create an effective weighted social graph that reshapes agent centrality and group sensitivity to inputs.
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.