Generalized Zipf's Law in proportional voting processes

TL;DR

This paper analyzes voting data from Brazilian elections and finds that voting distributions follow a generalized Zipf's Law, revealing differences in complexity between local and non-local voting processes within a nonextensive statistics framework.

Contribution

It demonstrates that voting distributions adhere to a generalized Zipf's Law and distinguishes the complexity levels of local versus higher-level elections using nonextensive statistics.

Findings

Voting distributions follow a generalized Zipf's Law.

City-councillor voting shows less nonextensivity than higher-level elections.

Differences relate to local and non-local voting process complexities.

Abstract

Voting data from city-councillors, state and federal deputies elections are analyzed and considered as a response function of a social system with underlying dynamics leading to complex behavior. The voting results from the last two general Brazilian elections held in 1998 and 2000 are then used as representative data sets. We show that the voting distributions follow a generalized Zipf's Law which has been recently proposed within a nonextensive statistics framework. Moreover, the voting distribution for city-councillors is clearly distinct from those of state and federal deputies in the sense that the latter depicts a higher degree of nonextensivity. We relate this finding with the different degrees of complexity corresponding to local and non-local voting processes.