Power Networks — A Network Approach to Voting Theory

Ádám Telek¹

In this paper I study elections where the preferences of the voters are derived from their position in the social network. I argue that in some cases studying the ideology of the electorate is not the right way to understand the result of an election. In small electorates or in committees the personal connections can be much more important than political ideology. I develop a voting model where these personal connections add up to a social network and I study what network properties and the social structures lead to a voting equilibrium. I show that single peaked preferences on chain and tree networks are inherent in my model, then I define a set of networks where the equilibrium is robust to changes in the intensity of a connection. Finally I provide a method to locate potential Condorcet winners in the network. In the discussion I relate my approach to the practice of using centrality measures (betweenness or eigenvector centrality) in the analysis and in an illustrative example I calibrate my model to predict the victory of the Medici family in a medieval power struggle.