Spread of opinions and proportional voting.

Election results are determined by numerous social factors that affect the formation of opinion of the voters, including the network of interactions between them and the dynamics of opinion influence. In this work we study the result of proportional elections using an opinion dynamics model similar to simple opinion spreading over a complex network. Erdös-Rényi, Barabási-Albert, regular lattices, and randomly augmented lattices are considered as models of the underlying social networks. The model reproduces the power law behavior of a number of candidates with a given number of votes found in real elections with the correct slope, a cutoff for a larger number of votes, and a plateau for a small number of votes. It is found that the small world property of the underlying network is fundamental for the emergence of the power law regime.