Democratic Consensus and the Local Majority Rule

Abstract

In this paper we study a rather generic communication/ <br />coordination/ computation problem: in a finite network of agents,<br />each initially having one of the two possible states, can the majority<br /> initial state be computed and agreed upon (i.e., can a democratic<br /> consensus be reached) by means of iterative application of<br />the local majority rule. We show that this task is failure-free only<br />in the networks that are nowhere truly local. In other words, the<br />idea of solving a truly global task (reaching consensus on majority<br />) by means of truly local computation only (local majority rule)<br />is doomed for failure.<br />We also show that even well connected networks of agents that<br />are nowhere truly local might fail to reach democratic consensus<br />when the local majority rule is applied iteratively. Structural<br />properties of democratic consensus computers, i.e., the networks<br />in which iterative application of the local majority rule always<br />yields consensus in the initial majority state, are presented.