Two ex-IAS officers have suggestions for how EC can count votes and avoid EVM controversy
Opinion

Two ex-IAS officers have suggestions for how EC can count votes and avoid EVM controversy

The officers looked at three elements of VVPAT-based audit of EVMs and found Election Commission’s system wanting in all three aspects.

Polling officials collect EVMs and other material in Jaipur | PTI

Polling officials collect EVMs and other material in Jaipur | PTI

The Supreme Court’s order last month increasing the physical verification of EVMs by counting voter slips from one randomly selected EVM per assembly constituency to five EVMs per assembly constituency, and its refusal this month to review that order, may have settled the controversy from a legal standpoint but it will not appeal to a conscientious statistician.

The audit of Electronic Voting Machines (EVMs) through VVPAT, or Verified Voter Paper Audit Trail, is a simple problem of statistical quality control, and has to be dealt with statistically. The issue is very similar to the “lot acceptance sampling” technique widely used in industry and trade for assuring the quality of incoming and outgoing goods. If the number of defectives found in the sample is less than or equal to a specified acceptance number, the lot (or ‘population’) is accepted; otherwise, the lot is rejected.

Unlike industry and trade where, depending upon the quality norms, the presence of a few defectives in the sample is usually tolerated, the acceptance number will have to be zero in the context of elections. In other words, even if a single EVM from a randomly drawn sample of EVMs shows a ‘defect’ (the electronic vote count does not match with the VVPAT’s manual count of voter slips either due to EVM malfunction or EVM manipulation), then the manual counting of VVPAT slips should be done for all the remaining EVMs of the ‘population’ (from which the sample was drawn). In such scenarios, the election results should be declared only on the basis of the VVPAT count.

It follows, therefore, that VVPAT-based audit of EVMs involves three essential elements: (1) a clear definition of the ‘population’ of EVMs; (2) determination of a statistically correct sample size for the specified population; and (3) the ‘decision rule’ to be applied to the specified population if one or more defective EVMs turn up in the chosen sample.


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The system put in place by the Election Commission of India (ECI) was found wanting in all the three aspects — the ECI did not specify the ‘population’ to which its sample size relates; its sample size was statistically incorrect by a big margin; and it chose to be vague about its ‘decision rule’. Thus, the ECI’s system completely failed in fulfilling the second of what security technologist Bruce Schneier’s holds as purpose of elections, namely, convincing the losers. “The first, and obvious, purpose is to accurately choose the winner… To the extent that an election system is not transparently and auditably accurate, it fails in that second purpose,” Schneier says.

Even though the Supreme Court’s prescribed sample size (five EVMs per assembly constituency) is superior to what the Election Commission had prescribed (one EVM per assembly constituency), it is nevertheless an arbitrary, non-statistical sample size that will some of the time fail to detect miscounts, which will affect the election outcome. More importantly, the Supreme Court’s order does not touch upon the following two critical issues: (1) what is the ‘population’ to which the sample size relates? (2) what is the ‘decision rule’ to be followed if one or more defective EVMs turn up in the sample? A system of VVPAT audit in which these two issues have been left vague or unaddressed is non est and unworkable.

(Note: In the discussion that follows, the percentage of defective EVMs in the population is assumed to be one per cent, and the sample sizes have been calculated using the Hypergeometric distribution to say that there would be a 99 per cent probability of detecting at least one defective EVM.)

EVM population and sample size

There are various ways of defining the ‘population’ of EVMs. If “EVMs deployed in an assembly constituency” are defined as the population, then the population size will vary from about 20 to about 300, and the corresponding sample size required will range from 20 to 235 EVMs per assembly constituency. This is administratively unviable. Likewise, if “EVMs deployed in a parliamentary constituency” are defined as the population, then the population size will vary from about 300 to about 2200, and the sample size required will range from 235 to 414 EVMs per parliamentary constituency, which is again administratively unviable.


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This leaves us only with the option of defining “EVMs deployed in a state as a whole” as the population.

In this case, the population size (of EVMs) will vary from 589 (Sikkim) to 23,672 (Chhattisgarh, the median state) to 1,50,000 (Uttar Pradesh) and the sample size required for a state as whole will vary from 315 (Sikkim) to 454 (Chhattisgarh) to 458 (Uttar Pradesh). If the population is defined as above, the Supreme Court’s sample size is adequate for the 20 bigger states (whose population of EVMs exceeds 10,000) and the probability of it failing to detect a defective EVM in respect of these states will be 1.2 per cent or less.

But the Supreme Court’s sample size is not adequate for the 9 smaller states (whose population of EVMs is less than 10,000) and the probability of it failing to detect a defective EVM varies from 14.8 per cent (Sikkim) to 3 per cent (Himachal Pradesh). However, since the 20 bigger states account for over 80 per cent of the Lok Sabha seats, for the purposes of the present election, we will have to go with the Supreme Court’s formulation, presuming that even if there is EVM malfunction (or manipulation) in these nine smaller states, it is unlikely to affect the final outcome significantly.

Decision Rules for the ECI

Since we have defined “EVMs deployed in a state as a whole” as the population, it follows that if a defective EVM turns up in the chosen sample, the manual counting of VVPAT slips of all the remaining EVMs in the state should be done. This is the first ‘decision rule’.

While large scale rigging of EVMs is not possible, it may not even be necessary because potential attackers need to target only select EVMs to tip the balance in a few marginal, closely fought constituencies. We, therefore, recommend that for constituencies where the margin of victory is below 2 per cent of the votes cast or 1,000 votes (whichever is less), full manual counting of VVPAT slips should be done for all the EVMs in the constituency even if no defective EVM turns up in the sample. This is the second ‘decision rule’.


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It is occasionally noticed that there are discrepancies between the polling station-wise figures of voter turnout and the votes as counted in EVMs, possibly due to EVM malfunction. The Election Commission’s standard argument that some presiding officers ‘forgot’ to initialise the EVM count to zero at the end of the mock poll demonstration before the regular polling commenced, does not explain why there are positive as well as negative discrepancies. We, therefore, recommend that full manual counting of VVPAT slips should be done for those polling stations where the discrepancy between the votes polled in EVMs and votes as counted in EVMs is more than 2 per cent of the votes cast. This is the third ‘decision rule’.

It follows that a proper VVPAT-based audit of EVMs entails the definition of “EVMs deployed in a state as a whole” as the population and the application of the three ‘decision rules’ indicated above. In the interests of transparency and of “convincing the losers”, we hope that the Election Commission of India will go beyond the Supreme Court’s order and implement these recommendations on the counting day (23 May) of the ongoing Lok Sabha elections.

Ramani Venkatesan is a retired IAS officer of Maharashtra cadre and the former Director General of YASHADA, Pune.

K. Ashok Vardhan Shetty is a retired IAS officer of Tamil Nadu cadre and a former Vice Chancellor of the Indian Maritime University, a Central University. 

Both authors have experience in the conduct and supervision of elections in India at various levels.