# Transparent use of statistical methods can help detect rigged electronic voting machines

## Suitable modifications can be made to account for differences in sizes of constituencies while deciding on the required proportion of tallying V-VPAT with EVMs.

analysis Updated: Apr 27, 2018 11:39 ISTNew Delhi

Shift from paper ballots to electronic voting machines (EVMs) has reduced the expenses and logistical problems involved in conducting elections in India.

This achievement can be jeopardised if allegations of EVM tampering are not addressed in a satisfactory manner. Parties such as the Aam Aadmi Party (AAP) and the Bahujan Samaj Party (BSP) have levelled allegations of EVM tampering in the recent past.

The March plenary session of the Congress party also demanded that India revert to the use of paper ballots in elections. Even the Bharatiya Janata Party (BJP) had made allegations against EVMs after the 2009 elections. Whether or not such allegations are true, they threaten the credibility of the electoral process in the eyes of common people.

The Election Commission of India (ECI) organised a hackathon challenge in June 2017 to satisfy concerns of political parties about integrity of EVMs. Although no political party could hack the machines, allegations about EVMs being tampered have not stopped.

It is welcome that the ECI has announced that it will be using Voter-Verifiable Paper Audit Trail machines (V-VPAT) for all EVMs in the 2019 elections. A V-VPAT machine generates a unique paper slip with the name and symbol of the candidate for each vote which has been cast in the machine.

Tallying the results from V-VPAT with aggregate count from respective EVMs is the best way to test whether or not EVMs have been tampered with. About 1.8 million EVMs are used across 543 Lok Sabha constituencies. Tallying all V-VPAT machines with EVMs would defeat the very purpose of shifting from paper ballots to EVMs.

In a press note dated May 20, 2017, the ECI said that “The Commission will count V-VPAT slips up to a definite percentage, which will be determined by the Commission. The ECI will be shortly evolving an appropriate framework in this regard.”

The question is: What should this proportion be?

A slight digression to explain the concepts of sampling and probability in statistics might be useful to understand the issue at hand here.

Sampling is a procedure by which we usually try to estimate any population’s features by inspecting a small proportion of individuals, where complete enumeration is either impossible or a daunting task, even if it is doable. Barring the decennial census, almost all important statistical indicators in the country involve some sampling.

An example can give an idea about the relation between sample-size and population-size. National Sample Survey Office (NSSO) surveys are considered to be the most authoritative sources on employment statistics in India. The 2009-10 NSSO survey on employment covered around 100,000 households and 460,000 persons. According to the 2011 census, there were 247 million households in the country. So the NSSO essentially covered just 0.19% of the Indian households. Yet nobody doubts the veracity of employment numbers given by the NSSO.

This is because the NSSO’s sample is considered to be “representative” of the country’s population. If all 100,000 households in the NSSO’s employment survey had been selected from richer areas such as Delhi or Mumbai, we would not get a very good picture about employment situation in the country, but because the sample is spread across states and rural-urban areas, the findings of the survey are not influenced by extreme cases.

In the case of EVMs, the natural choice of sampling units should be a parliamentary/assembly constituency. Within each constituency, the ECI will have to lay down a clearly predefined criterion to select EVMs for which vote-counts would be tallied with V-VPAT slips. This would mean creating sub-categories within each constituency and then randomly selecting an EVM from a given sub-category. This process will ensure that EVMs selected for V-VPAT tallying are “representative” of the constituency, yet potential EVM riggers cannot know in advance which EVMs would be selected for checking.

Now, to come to the question of how checking just a few EVMs can successfully detect any potential EVM tampering. The concept of probability is useful here.

Suppose a box contains 95 red balls along with five blue balls. The probability that a randomly drawn (i.e. drawn without any bias) ball will be red, is just the proportion of red balls in the box, which is 95/100. Once this ball has been taken out, the probability of drawing another red ball would be 94/99. Suppose the first nine drawn balls are all red. The box now contains 91 balls, of which 86 are red. The chance of drawing a red ball in the 10th draw will be 86/91.

Probability theory tells us that the chances of drawing 10 red balls in succession would be the product of these fractions. This number comes out to be 58.4%. What is the probability that there would be at least one blue ball in the first 10 draws from the box? It is 41.6%, which is the difference between 100% and probability of drawing all 10 red balls.

Now assume that the box contains all the EVMs in an election. The blue balls can be considered as tampered EVMs (if at all) and the red balls might correspond to the EVMs which are not tampered. Let us assume that we want a 95% probability, which is a widely accepted level in many sampling procedures, of getting a potentially rigged EVM in tallying V-VPAT count with EVMs.

Let us take four different possibilities of level of potential rigging into account at the constituency level: 25%, 10%, 5% and 0.5%. We assume an equal distribution of 1.8 million EVMs across 543 constituencies. Tallying 11, 29, 58 and 534 V-VPATs per constituency would allow us to find a rigged EVM with 95% probability for each of these four scenarios.

Suitable modifications can be made to account for differences in sizes of constituencies while deciding on the required proportion of tallying V-VPAT with EVMs. It is reasonable to assume that any acts of EVM rigging would be done in a large scale than just at the booth levels.

Provided the process is carried out in a transparent and democratic manner, it could help dispel all fears of EVM tampering and facilitate smooth conduct of elections in our country.

*(Atanu Biswas is a professor of statistics at Indian Statistical Institute, Kolkata)*