A General Framework for Distributed Vote Aggregation

TL;DR

This paper introduces a comprehensive framework for opinion dynamics in social networks, analyzing convergence properties and extending existing gossip models to broader settings with proven convergence results.

Contribution

It presents a general model for opinion dynamics, proves convergence in various settings, and extends gossip models with new convergence insights.

Findings

Almost sure convergence of the proposed dynamics

Convergence of top-$k$ selective gossip in general settings

Extended models with analyzed limiting behavior

Abstract

We present a general model for opinion dynamics in a social network together with several possibilities for object selections at times when the agents are communicating. We study the limiting behavior of such a dynamics and show that this dynamics almost surely converges. We consider some special implications of the convergence result for gossip and top-$k$ selective gossip models. In particular, we provide an answer to the open problem of the convergence property of the top-$k$ selective gossip model, and show that the convergence holds in a much more general setting. Moreover, we propose an extension of the gossip and top-$k$ selective gossip models and provide some results for their limiting behavior.