The Price of Uncertainty for Social Consensus

TL;DR

This paper investigates how small uncertainties in neighbor color counts significantly impede consensus achievement in social networks, providing tight bounds on the 'price of uncertainty' affecting network consensus.

Contribution

It introduces a theoretical framework quantifying the impact of uncertainty on social consensus, establishing tight bounds on the 'price of uncertainty' in network games.

Findings

Small perturbations in neighbor counts greatly hinder consensus.

Tight bounds on the 'price of uncertainty' are established.

Uncertainty significantly affects the ability to reach social consensus.

Abstract

How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus, which is when the colors of all agents align. Agents attempt to do this locally through steps in which an agent changes their color to the color of the majority of their neighbors. In real life, agents may not know exactly how many of their neighbors are red or blue, which introduces uncertainty into this process. Modeling uncertainty as perturbations of relative magnitude $1+\varepsilon$ to these color neighbor counts, we show that even small values of $\varepsilon$ greatly hinder the ability to achieve consensus in a social network. We prove theoretically tight upper and lower bounds on the \emph{price of uncertainty}, a metric defined in previous work by Balcan et al. to quantify the effect of uncertainty in network games.