Opinion | An ideal EVM verification ratio for accurate election results

From paper ballots, we moved to Electronic Voting Machines or EVMs (Voting 2.0) and then to the Voter Verifiable Paper Audit Trail or VVPAT era (Voting 2.1). With this transition, possibly the most important socio-political concern in India now is: How many EVMs should be VVPAT-audited? As the Supreme Court has refused to review its judgment of tallying five EVMs for every assembly constituency with the corresponding VVPAT counts, this would be the gold-standard for the time being.

In an opinion piece in Hindustan Times, I used two types of balls—blue for defective EVMs and red for non-defective EVMs—to illustrate how drawing a few randomly chosen balls from an opaque urn can ensure a high probability of obtaining at least one defective (blue) ball in the sample, even if the proportion of defectives is small.

Twenty-one political parties have demanded that 50% (or at least 25%) of all EVMs be VVPAT-audited. On the other hand, a three-member team (henceforth called the “ISI team”), with one member each from the Indian Statistical Institute (ISI) Delhi, Chennai Mathematical Institute, and the Central Statistical Organization, has asserted that the paper tallying of just 479 randomly chosen machines across India (out of 1.035 million machines in total) is enough to ensure a 99.99% probability of obtaining at least one defective EVM. The ISI team basically treated it like a multiple sampling plan, which is often used by companies for product quality control.

Here, the idea is to find the required sample size (n) out of N (1.035 million) items having a certain percentage of defectives to obtain at least one defective item with a fixed probability (99.99%). Interestingly, according to statistical theory, the value of n would always be almost the same whatever be N, as long as N is large enough. Thus, n will be close to 479 if N is 10,000, 10 million or 10 billion. Even if one intends to find n separately for each Lok Sabha constituency with roughly 2,000 EVMs at the same confidence level, the required number of EVMs to be paper-audited would be close to 479. Thus, how we define the sample—whether we verify 479 EVMs across India or in each constituency—depends on the assumption of what an electoral unit is. Are Indian elections a single election or 543 separate elections—one in each Lok Sabha constituency? While that might be an interesting political debate, let’s address it from the sole perspective of EVM-related problems.

It seems that the ISI team assumed that an EVM-VVPAT mismatch might occur only due to manufacturing defects in the machines; also, that they’d behave similarly in different parts of the country. The statistical exercise of the ISI team was only about the efficacy of EVMs. The Election Commission of India (EC) maintains that EVMs are tamper-proof and the analysis of the ISI team is based on that assumption. On the other hand, the spectre of EVM-tampering haunts Indian politics. If these can be tampered with—although one is not saying so—the situation would be completely different. In any case, the outcome of a constituency with a huge victory margin, say more than 300,000, is much less likely to be altered by defective/tampered EVMs, as it would require at least a few hundred such EVMs to change the result. Assuming that at most 1,000 votes, on an average, can be altered by a single such EVM, one would need at least 300 such machines. On the other hand, only a few defective/tampered EVMs have the potential to change the winner in constituencies where the victory margin is a few thousand votes. One may argue that this is one way in which polls differ from constituency to constituency.

Also, there might be another practical problem in assuming the entire election as a single one. A few EVM-VVPAT mismatches might raise questions over the credibility of the entire process. On the other hand, under the assumption of different elections in different constituencies, the credibility of the results in those with no mismatches would remain beyond question.

If 25% EVM-VVPAT tallying is done, the probability of obtaining at least one mismatch would be more than 99% separately for each of the Lok Sabha’s 543 constituencies, even if the percentage of defective/tampered EVMs is as small as 1%. But, 25% is 259,000 EVMs, and tallying all of them would be a daunting task indeed. More importantly, is such a small defective/tampering EVM percentage relevant in every constituency?

Interestingly, the EC proposed tallying one EVM-VVPAT per assembly constituency, which in most cases translates to seven per Lok Sabha constituency, and 4,125 in the entire country. By proposing this, EC conveyed the message that each constituency is possibly different in nature. Stratified sampling is advocated when the strata possibly possess different characteristics. So, is the EC differentiating constituencies on the basis of defective/tampered EVMs or different victory margins? If so, that might be contrary to the assumption of the ISI team that EVMs would behave similarly in all constituencies.

And when the apex court ordered 5 EVMs to be VVPAT-audited per assembly segment—again a stratified sampling technique—the inherent message was the same. This would ensure 99% probability of obtaining at least one defective/tampered EVM in a Lok Sabha constituency with 13% defect and/or tampering proportion. If the proportion of defectives/tampered EVMs is as low as 2%, this probability would still be 51%.

While 21 parties are eager to enhance the ratio of EVM-VVPAT tallying, some people argue that different sample sizes are required in different constituencies to ensure that the winner via EVMs is also the winner via VVPAT counts. Hence, this is perhaps not the end of the EVM-VVPAT saga. However, the 5 EVMs per assembly segment order certainly strikes a balance until the verification rule is further modified.

Atanu Biswas is professor of statistics at the Indian Statistical Institute, Kolkata