A Cyclic Representation of Discrete Coordination Procedures

TL;DR

This paper demonstrates that any discrete opinion pooling method with positive weights can be approximated by a cyclic DeGroot process with a Hamiltonian cycle communication graph, linking influence and arc weights.

Contribution

It introduces a cyclic representation for discrete opinion pooling procedures, connecting influence weights to communication graph structure.

Findings

Any discrete opinion pooling with positive weights can be approximated by a Hamiltonian cycle-based DeGroot process.

Arc weights are inversely proportional to the influence of the target agent.

The cyclic representation provides a new perspective on opinion dynamics and influence distribution.

Abstract

We show that any discrete opinion pooling procedure with positive weights can be asymptotically approximated by DeGroot's procedure whose communication digraph is a Hamiltonian cycle with loops. In this cycle, the weight of each arc (which is not a loop) is inversely proportional to the influence of the agent the arc leads to.