The Supreme Court has now set new guidelines for counting the Voter-Verified Paper Audit Trail (VVPAT) slips and matching them with the corresponding Electronic Voting Machine (EVM) counts. Five EVMs are to be VVPAT-audited in each Assembly constituency, which, for most of the cases, would come out to be 35 per Lok Sabha constituency. Of course, the SC didn’t doubt the EVMs.
However, there has been a widespread dissatisfaction among different political parties, and boosting the confidence of the 900 million electorates over EVMs is possibly no less important than making the voting machines tamper-free. The Court observed that it “would be of greater satisfaction not only for political parties but also for the entire electorate”.
According to reports, a proposal for verification of 479 randomly selected EVMs across the country was examined (which possibly treated it a single election across the country), whereas the ECI rules recommended VVPAT verification for one booth in every Assembly constituency (where the idea is to treat every constituency separately), which is a total of 4,125 EVMs in the country. Finally, this number has been enhanced to a total number of 20,625, by the Hon’ble SC bench headed by CJI Ranjan Gogoi.
Let’s try to understand how these numbers would work in terms of detecting EVM tampering. Let’s first assume that each of the 543 Lok Sabha seats are separate units, and the objective is to establish the sanctity of EVMs in each of these constituencies. We can treat each Lok Sabha constituency as a combination of seven-eight baskets (Assemblies in this case), and a few hundred EVMs are placed in each basket, and only a few among them are possibly tampered.
Certainly, if we tally each and every EVM with the corresponding VVPAT count, we’d be able to find whether all the EVMs are okay or not. That’s complete enumeration, and would destroy the sole purpose of transition from paper ballot to EVM. Sampling is advocated instead, where the idea is to mix the EVMs within each basket properly, and draw only a few among them ‘randomly’ (which would ensure equal probability of selecting each EVM in the sample).
The objective is to get hold of at least one tampered EVM with high probability. If we get one mismatch of the EVM and the corresponding VVPAT counts, the election of that Lok Sabha constituency maybe treated to be rigged.Take a hypothetical Lok Sabha constituency having seven Assemblies, each with 460 EVMs. Assume that 10 per cent of the EVMs are tampered, and these are randomly distributed among the seven Assembly constituencies.
Thus, on an average, 46 EVMs are tampered in each Assembly, and if one EVM is randomly chosen for VVPAT-auditing from each Assembly, the chance of it being not tampered is a=(460-46)/460, which is the proportion of non-tampered EVMs in that Assembly. Similarly, if five EVMs are randomly chosen, the proportion of non-tampered EVMs is b=0.589, according to calculations. Consequently, the chance of getting at least one EVM-VVPAT mismatch is 1-a^7=0.522.
And if we go by the SC’s directive, the chance is 1-b^7=0.975. So, as in the present case, the probability of choosing a tampered EVM—according to the current ECI rule—is 52.5 per cent. But after the Supreme Court verdict, the probability would be 97.5 per cent. We can define these probabilities as the ‘tampering-detection capacities’. Thus, the SC verdict would undoubtedly enhance the confidence of the electorates in the sense that the chance of getting at least one tampered EVM would increase considerably. In case of a 5 per cent EVM tampering, the tampering-detection capacity of ECI rule is 30.2 per cent, while that of the SC verdict would become 83.5 per cent. However, for a 15 per cent EVM tampering in any Lok Sabha constituency, these probabilities would become 67.9 per cent and 99.7 per cent.
On the other hand, let’s treat an entire state, say with 39 Lok Sabha seats, as the unit of EVM-VVPAT cross-checking. Then, the probability of detecting a tampered EVM is almost 100 per cent in both cases. In other words, the SC ruling will not change anything significantly. However, both the ECI and the SC analysed smaller units for the election process; elections in different constituencies are treated differently. This may not be without reason.
Note that the above sampling scheme is not the same as randomly drawing 35 EVMs from a pool of 460x7=3,220 EVMs, rather it’s a stratified sampling where 3,220 EVMs are divided into 7 strata, and 5 EVMs are randomly chosen from each stratum. If the proportion of EVM-tampering is small, one needs more VVPAT-auditing to ensure high probability of finding at least one tampered EVM in the sample.
Reportedly, the SC increased the number of EVMs to be VVPAT-audited ensuring that it would neither require additional manpower nor delay the results of the Lok Sabha elections. Now, will the number ‘five’ per Assembly constituency satisfy all the concerned parties – electorates and all political parties? An important six-weeks-long social experiment begins today.