Publications

Universal Statistics of Competition in Democratic Elections

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.

Voter Turnouts Govern Key Electoral Statistics

Elections, the cornerstone of democratic societies, are usually regarded as unpredictable due to the complex interactions that shape them at different levels. In this work, we show that voter turnouts contain crucial information that can be leveraged to predict several key electoral statistics with remarkable accuracy. Using the recently proposed random voting model, we analytically derive the scaled distributions of votes secured by winners, runner-ups, and margins of victory, and demonstrating their strong correlation with turnout distributions. By analyzing Indian election data -- spanning multiple decades and electoral scales -- we validate these predictions empirically across all scales, from large parliamentary constituencies to polling booths. Further, we uncover a surprising scale-invariant behavior in the distributions of scaled margins of victory, a characteristic signature of Indian elections. Finally, we demonstrate a robust universality in the distribution of the scaled margin-to-turnout ratios.

Indian General Elections 2024: A preliminary health-check on the electoral process

Usually, election analysis for public consumption is focused on who the winner will be or if there will be a change of incumbent. On the date we prepared this article, the votes were yet to be counted, and we have limited access to the turnout data in the general elections of 2024 (GE-2024). Based on the available turnout data, in this article, we steer clear of predicting winner or loser, but instead, we make predictions for the scaled margin distribution, which is a potent indicator of electoral competitiveness. We employ RVM simulation in conjunction with the turnout data of GE-2024 to derive this prediction. We contrast this prediction with the historical Lok Sabha election data during 1999-2019. In summary, this is like a preliminary health check on the mammoth election exercise that has just concluded.

The physics and maths of keeping elections fair and representative