Universal Statistics of Competition in Democratic Elections

Abstract

Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge independent of microscopic details. Despite the availability of empirical election data, such universality, valid at all scales, countries, and elections, has not yet been observed. In this work, we propose a parameter-free voting model and analytically show that the distribution of the victory margin is driven by that of the voter turnout, and a scaled measure depending on margin and turnout leads to a robust universality. This is demonstrated using empirical election data from $34$ countries, spanning multiple decades and electoral scales. The deviations from the model predictions and universality indicate possible electoral malpractices. We argue that this universality is a stylized fact indicating the competitive nature of electoral outcomes.