opinion

Updated: Jul 31, 2019 06:01 IST

wo months after the declaration of Lok Sabha election results, conspiracy theories about possible tampering of Electronic Voting Machines (EVMs) are still doing the rounds. That important opposition leaders have demanded a return to paper ballots and even openly supported EVM-rigging theories has lend credence to the latter – although some of their behavior can be attributed to just being bad losers.

Still, doubts about EVMs have been planted, despite the fact that none of the Voter Verifiable Paper Audit Trail (VVPAT) machines showed a mismatch with the EVM count . The Supreme Court ordered the Election Commission of India (ECI) that five VVPATs per assembly constituency (AC) should be matched with the EVM count of votes. Statistically speaking this is adequate to remove doubts about possible tampering of EVMs. In an earlier article in HT dated April 27, 2018, this author had argued that tallying just

11, 29, 58 and 534 VVPATs per parliamentary constituency (PC) would allow us to find a rigged EVM with 95% probability for scenarios where 25%, 10%, 5% and 0.5% of the EVMs were tampered in a given PC.

Are EVM rigging fears an example of conspiracy theories defeating statistical methods? Ironical as it may sound; an eighteenth century concept in statistics known as Bayes’ theorem can help us understand why matching a sample of VVPATs with EVMs is failing to generate confidence in the credibility of EVMs.

The Bayes’ theorem basically tells us how to calculate the probability of an event given that another event has happened. This is how it works in mathematical terms. If A and B are two events, we know the probabilities of A and B; and also the probability of B given that A has already happened; then Bayes’ theorem can be used to calculate the probability of A given that B has already happened.

An example can make this clear. Let us assume the following: Virat Kohli hits a century in 4 out of 10 one day internationals (ODIs), India wins 6 out of 10 ODIs it plays, and Kohli hits a century in 5 out of 10 ODIs India wins. This means that the probability of Kohli hitting a century is 0.4, India winning is 0.6 and Kohli hitting a century given that India won an ODI is 0.5. The Bayes’ theorem allows us to calculate the probability of India winning an ODI given that Kohli has hit a century by dividing the product of probability of India winning an ODI (0.6) and Kohli hitting a century given India won (0.5) by the probability of Kohli hitting a century (0.4). The value comes out to 0.75, which basically means that India will win 75% of the times Kohli hits a century. Anecdotally speaking, that’s most likely true.

How is the Bayes’ theorem relevant in case of EVM tampering and VVPATs? It comes into play because people might have a prior belief about the possibility of EVM tampering. In case this value is greater than zero, then the final belief (probability) of EVM tampering even after a sample of VVPATs show no tampering is a number which can be derived from the Bayes’

theorem. A rudimentary example can illustrate this. Let us suppose that there is an AC with two EVMs. Logically, there are three possibilities; no EVMs are tampered, one EVM is tampered and both the EVMs are tampered. However, different persons might have different beliefs about the credibility of EVMs. Suppose there are two persons A and B, where A is more sceptical about EVMs and B has relatively greater trust in them. Let us assume that A thinks that the probability of no tampering, one EVM being tampered and both the EVMs being tampered is 10%, 40% and 50%. Let these numbers for B be 50%, 30% and 20% respectively.

Without VVPAT tallying, the probability of finding an un-tampered EVM, if one out of two EVMs is picked, for A and B will be 0.3 and 0.65. Now let us assume that one out of the two EVMs is matched with a VVPAT machine and there is no discrepancy in the count. Bayes’ theorem tells us that both A and B will revise their beliefs about EVMs being tamper-proof given the fact that one out of the two EVMs has been found to be un-tampered and nothing is known about the other. These values will be

33% for person A and 77% for

person B.

The point is if a section of the population is more biased against the claim of EVMs being tamper-proof, then even a successful sample based VVPAT tallying will not bring their trust in EVMs at par with another set of people, who are bigger believers in the credibility of EVMs.

If there is no unanimity among political parties on the credibility of EVMs, then it is to be expected that people with different political beliefs will have different degrees of scepticism about the possibility of EVM tampering. In such a scenario, even if EVMs are tamper-proof, nothing less than a tallying of all VVPAT machines, which basically entails a shift to paper ballots, will restore complete faith in EVMs. This underlines the importance of institutions such as the Election Commission of India taking more efforts to allay fears of EVM tampering beyond the VVPAT mechanism.

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