Elections across the world display a universal feature: voter turnout drives victory margins
Pune, 11th January 2025: In a paper published in the journal Physical Review Letters, Prof. M.S. Santhanam’s research group from IISER Pune reported a universal trend in elections across the world, the analysis of which can help flag large-scale electoral malpractices.
Across the world, elections are a volatile mix of emotions, competing ideologies, and sometimes even violence. But what if, beneath this apparent chaos and cacophony, elections share some universal characteristics irrespective of where and when they are held? And, what if these characteristics are useful for pinpointing fraudulent election practices?
It is this curiosity that led Prof M.S. Santhanam to analyse election data along with PhD students Ritam Pal and Aanjaneya Kumar. The team carried out an extensive analysis of election data drawn from 34 countries from 6 continents and spanning several decades of national elections and developed a new Random Voting Model, which is a probability rule that governs how voters choose a candidate.
By using available data on actual voter turnout for a given election, the team predicted statistical distribution of victory margin for the election. Using this approach, they analysed a total of 581 elections conducted previously in 34 countries. The team found that the predictions derived from their model completely matched with the actual election results in each of the corresponding countries.
One of the authors of the paper, Ritam Pal, a PhD student at IISER Pune, said, “While complex interactions at different levels make the outcomes of elections inherently unpredictable, at the microscopic level, the rules for how people vote for a candidate are often simple as far as margin distributions are concerned. Our model leverages this simplicity to predict the statistical distribution of margins with remarkable accuracy.”
The analysis of election data showed that the statistical distribution of an election’s margin of victory could be predicted solely from the voter turnouts, regardless of the electorate size (from municipal elections to state-level and Parliamentary elections), country, region, or the finer details of how the elections are conducted.
When the analysis was applied to election data from Indian elections (both state and general elections) from 1952 to 2019, the team found that the margin distributions were in complete agreement with the expected universal trend observed for elections in other countries.
The research also uncovered cases where this universal trend broke down. Elections in Ethiopia and Belarus (in the last decade) showed deviations from the universal norm for margin distribution. These elections were indeed previously flagged by reputed international media outlets and civil organisations as potentially fraudulent.
Thus, by comparing their model and analysis with the past election outcomes, the authors suggest that this analysis could be valuable for identifying possible instances of electoral malpractice across the world.
Speaking on the significance of the paper, Prof. Santhanam said, “These findings offer an intriguing glimpse into how voter turnout shapes elections everywhere, and how science might help protect the integrity of elections”.
This research was supported by a MATRICS Grant from Science and Engineering Research Board (SERB), DST, Government of India, during the early stages of the work. The analysis shown in this paper was carried out at the National Supercomputing Mission’s PARAM Brahma supercomputer facility at IISER Pune.
Citation:
Ritam Pal, Aanjaneya Kumar, and M. S. Santhanam (2025). Universal statistics of competition in democratic elections. Physical Review Letters 134, 017401. DOI: https://doi.org/10.1103/PhysRevLett.134.017401
Associated Web Resource for the Paper:
Gives more information on the contents of the paper
https://www.iiserpune.ac.in/~santh/election/index.html
Information about the Authors of the Paper
(Left to Right) Ritam Pal, Aanjaneya Kumar, and M.S. Santhanam
Ritam Pal is a PhD student in the Physics Department of the Indian Institute of Science Education and Research (IISER) Pune. (Email: [email protected])
Aanjaneya Kumar was a PhD student at IISER Pune, and is currently a post-doctoral fellow at Santa Fe Institute and Princeton University. U.S.A. (Email: [email protected])
M.S. Santhanam is a professor of physics at IISER Pune. (Email: [email protected])
Pre-print link:
Universal Statistics of Competition in Democratic Elections
Ritam Pal, Aanjaneya Kumar, and M. S. Santhanam
https://www.arXiv.org/abs/2401.05065
Representative Image from the Analysis carried out in the Paper:
Universality of election data: This figure shows that election data from India, Germany, the UK, Canada, and South Korea are consistent with the expected universality (represented by the purple line). However, data from elections in Ethiopia in the year 2010 strongly deviates from this line and the analysis supports news reports of election fraud. (Image Credit: Ritam Pal, Aanjaneya Kumar, and M.S. Santhanam)
