In Douglas Adams’s irreverent sci-fi classic The Hitchhiker’s Guide to the Galaxy, the supercomputer Deep Thought, after spending seven-and-a-half million years on it, derives the ‘Answer to the Ultimate Question of Life, the Universe and Everything’. It is the number 42.Deep Thought also clarifies that the answer is meaningless because the people who programmed the computer didn’t actually know what the question was.Closer to home, a few judges of our Supreme Court and many renowned lawyers sought to understand the meaning of the number ‘479’, obtained ostensibly from an Indian Statistical Institute report to the Election Commission of India. The three learned authors of this report spent seven-and-a-half months to come up with this number, which indicates the number of EVMs that should be randomly checked with VVPAT.On a careful reading of the report, we now understand the question to which the answer is 479. It is the answer to a question of statistical quality-control. Indeed, this would have been the same answer to the question of how many pencils need to be checked to ensure that in a pencil factory, the weekly production of 15 lakh pencils doesn’t have more than 2% defects – or in other words, whether the EVMs when they were produced had manufacturing defects or not.Before we move to other aspects of this report, we first point out a fundamental flaw in the assumptions on which this report is based. The report considers all the EVMs of India to be a single population, among which defects have to be searched. India does not have a presidential system of elections. Instead, we choose representatives in each constituency to send to Parliament. In such a model, a voter from a particular constituency has to be satisfied that their representative has legitimately won the elections and the result is not because of machine tampering. Thus, the random checks have to be done among the machines at constituency-level, which constitutes the relevant population. Once this fact is noted, then following the ‘hypergeometric model’ of the report, and assuming 1,500 EVM-VVPATs in each constituency with 2% having defects, one comes to a figure of approximately 350 per constituency as the number of EVMs whose VVPATs have to be tallied. This gives an overall number for the country of around 2 lakh of randomly selected EVMs whose VVPATs have to be cross-checked. However, this number of 350 per constituency, which is arrived at from the hypergeometric model used in the report, is flawed.Indeed suppose that there are 15 lakh voters in each of two distinct constituencies ‘A’ and ‘B’. Also assume that in constituency A the winning margin is 1.5 lakh votes, while in constituency B the winning margin is 15,000 votes, and this is not an unrealistic scenario, as a perusal of past election data will suggest. It is not rocket science to realise that even a small error may change the outcome in constituency B, while it will need a larger error to change the outcome in constituency A. For constituency B, tampering of 7,500 votes is enough to change the outcome, while for constituency A there has to be tampering of 75,000 votes. In percentages terms, an error in the count of 0.5% of the electorate of constituency B is enough to change the outcome, whereas in constituency A the percentage required is 5%. Thus the number of samples to be checked for constituency B has to be much larger than that for constituency A. Indeed the sample size has to depend on the size of the winning margin. A ‘one size fits all’ cannot be a solution as is done in the said report where a uniform 2% error is used. A quick calculation, assuming there are 1,500 EVMs in the constituencies (each EVM on an average handles 1000 votes), it will be enough to check 150 VVPATs for the constituency ‘A’, while to obtain a precision given in the report, it will be required to check about 950 VVPATs for the constituency ‘B’.The report also proceeds to give a sequential scheme of checking in case of mismatch between the VVPAT and the EVM counts. If there is only one mismatch in the 479 randomly selected EVMs, the report suggests that an extra 128 EVMs be randomly selected and their VVPATs checked for mismatches. If there are two mismatches in the original 479 and the additional 128, then another extra 110 are to be selected and their VVPATs tallied to check for mismatches, etc. Again, clearly, if there is a mismatch in an EVM used in a particular constituency, in the random choice of the EVMs for the additional checks, the chosen machines may come from completely different constituencies. This hardly makes any sense.There is one more fallacy of checking a fixed number (1 or 5) of EVM-VVPATs for each assembly segment of a parliamentary constituency. For example, each parliamentary constituency in UP has five assembly segments and hence, assuming five VVPATs are to be verified per assembly segment, we need to check 25 machines. On the other hand, Mizoram has one parliamentary constituency with 40 assembly segments, leading to checking of 200 of them. Given the objection of the ECI about the difficult terrain, checking 200 machines in Mizoram should have been a bigger concern than checking only five in UP. An even more interesting conundrum arises in the five parliamentary seats in the union territories without any assembly.Recall what professor P.C. Mahalanobis said to the 125th meeting of the American Statistical Association, about the difficulty of applying “Statistics as a Key Technology” to the official systems in India. The Father of Indian Statistics lamented: “The very idea of having crosschecks is frightening as conflicting results arising from independent checks would be ‘confusing’ and must be resisted and is being resisted even today.” How correct and contextual Mahalanobis sounds, even 54 years later.Antar Bandyopadhyay, Krishanu Maulik and Rahul Roy work at the Theoretical Statistics and Mathematics Division of the Indian Statistical Institute. The views expressed here are personal.
