Statistical Proof of Reliability of EVMs

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For over 20 years now, all Parliament and State Assembly elections in India are being conducted using Electronic Voting Machines (EVMs). From time to time, there have been questions raised on the trustworthiness of EVMs. 

For the 2019 Parliamentary elections, the VVPAT (Voter Verifiable Paper Audit Trail) system was incorporated in the polling process on the basis of Supreme Court (SC) directions. Based on commitments made by the Election Commission (EC) to the SC, on the day of counting, from each of the 4025 assembly segments of the 543 Lok Sabha constituencies, five booths were chosen randomly and the VVPAT votes in these 20125 booths were counted manually and compared with EVM count. 

We will argue as to how the data based on VVPAT matching done in 2019 Parliamentary elections provides a strong statistical proof that EVMs are reliable. 

HISTORY OF EVM & VVPAT 

The Election Commission (EC) along with teams of experts from Indian Institute of Technologies and Electronics Corporation of India (ECIL) developed the EVMs in India, beginning with 1977 and these were tried in a few booths in the Kerala Assembly elections in 1982. This was challenged in the court by the losing candidate and the courts ordered re-election in this constituency as the law governing elections, namely, The Representation of the People’s Act 1951, only recognised paper ballots and did not sanction EVMs. In 1989, the said law was amended empowering the EC to use EVMs for elections. The Election Commission continued to work with experts and ECIL to improve the EVMs.  

In 1999, the improved EVMs were used in Goa Assembly polls successfully and then they were also used in 46 constituencies out of 543 in the 1999 Parliamentary elections. Subsequently, EVMs have been used in all the constituencies in Assembly elections since May 2001 and in all Parliamentary elections since 2004. 

It put an end to a large number of invalid votes and booth capturing and was widely welcomed for over a decade. It is easy to see that there will be no invalid votes now, while in the paper ballot era, if the stamp was marked two times by mistake or on a line separating two candidates, it was considered invalid. On the other hand, readers may wonder as to how it could bring an end to booth capturing? After all, some armed people can intimidate security staff, officials and voters and take control of a booth. Well, an EVM allows only four votes per minute. So, while in the paper ballot era, the troublemakers could capture a booth and stuff the box with lots of votes at one go, and more onto a nearby booth, now it will take a long time to stuff one EVM with large number of fake votes and in the meanwhile, the news may reach security personnel who can take required action. 

Also, in the paper ballot era, one could get a different number while counting the votes a second time, because manual counting is subject to error. While counting notes we can see that there are possible errors in manual count! Thus, all in all, the move to EVM has eliminated several problems and as mentioned this was widely welcomed. 

Yet, all along, multiple cases have been filed under various grounds related to EVMs, which have been dismissed by the courts over the years. However, since the law states that a court can order a recount, the Supreme Court had suggested to EC to find a way of enabling recount of votes, if a court so orders, something that was not possible in an EVM.  The EC had been developing a VVPAT (Voter Verifiable Paper Audit Trail) system and conducting trials of the same with a technical expert committee for this purpose. In 2013, the technical committee approved a design of VVPAT and prepared to introduce the same. In response to this, the SC said that they are satisfied that the ‘paper trail’ is an indispensable requirement of free and fair elections. The confidence of the voters in the EVMs can be achieved only with the introduction of the ‘paper trail’. EVMs with VVPAT system ensure the accuracy of the voting system. The SC permitted the ECI to implement VVPAT in a phased manner, since ECI would have required over 8 lakh VVPATs for the 2014 Lok Sabha elections. Since the 2019 Lok Sabha elections, VVPAT has become an integral part of the EVMs used by EC.

IMPORTANT FEATURES OF EVM 

Here are the two important features of EVMs that provide their reliability: 

1.  The EVMs do not have any networking capability — no wired internet, no WiFi and no Bluetooth or any other wireless connectivity whatsoever. On the day of counting, a button is pressed and then the total votes for each candidate are displayed on the EVM and need to be copied by hand. 

2.  The names of candidates appear on the ballot screen of the ballot unit of EVM following the same scheme that existed when paper ballots were being used. The names of the candidates are divided in 3 groups: with the first group consisting of candidates of recognised political parties, second group consisting of candidates of all registered parties and the third group consisting of Independent candidates. Within each group, the candidates are listed in the alphabetical order of their names and not in the order of the party name. Thus, the order in which names appear would be decided only after the last date of the withdrawal of candidates. By then the EVMs would already be distributed to the districts and perhaps to the constituencies as well. 

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The ECI had announced in 2018 that one booth in each assembly segment will be chosen randomly on the counting day, and the VVPAT count of the chosen booth will be matched with the EVM count. This was proposed by ECI as a confidence-building measure.  This was challenged and demands were made to match 50% of EVM-VVPAT. The SC rejected the petition. However, SC suggested that 5 booths instead of one booth be chosen randomly and EVM-VVPAT matching be done. The EC accepted the suggestion and instructed the returning officers in each assembly segment to pick randomly five booths and verify if EVM count and the VVPAT count matched, and report the outcome.

The information available at EC published manuals makes it abundantly clear that EVMs incorporate all the safeguards that were in place for the paper ballot era. So, before the elections and during the period between voting day and counting day, the EVMs are stored securely and all access is strictly monitored. 

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The crux, then, is the question: Is it possible to tamper the EVMs remotely, while they are stored securely with no one having access to them. 

If it can be asserted that EVMs cannot be tampered with remotely, we can conclude that elections using EVMs are at least as reliable as the paper ballot-based elections.  Of course, if we want to assert that all EVMs are error free, one needs to count all VVPATs and match the same with EVMs. How can we test it statistically?

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STATISTICAL HYPOTHESIS TESTS 

Suppose that indeed someone does manage to find a way of tampering with the internal memory of EVM where the voting outcome is stored remotely. Then it is safe to assume that the person(s) who can do so will not stop at one or few EVMs but would try to tamper several EVMs so as to modify the outcome of the national election. It can be seen that to do so, one would need to tamper a large number of EVMs. Thus, the entity that wishes to tamper with the outcome of the national elections would need to tamper with EVMS in, say at least 25 constituencies in such a way to change the outcome, which in turn would need tampering with say 20% of the EVMs in these constituencies. Of course, the tampering itself would have to be done carefully for if it is found that a very large proportion of votes go to one candidate which is not expected, it will raise an alarm and if this happens in several booths, the losing candidate can seek recounting of votes (using VVPAT) in the entire constituency. Thus, the entity that wishes to tamper with the outcome of the national elections would need to tamper say 1% or more of the EVMs in the country.

Of course, if we see a mismatch between EVM count and VVPAT count, it could be due to mechanical defects or may have been tampered with. 

Let us denote by θ the proportion of EVMs that are defective (mechanical defects or have been tampered with and manipulated). We need to explore if it is possible for a fraudster to tamper EVMs in θ = 0.25% (or more) of the booths.  Of course, the fraudster could (and would) choose the booths so as to minimise probability of detection. So, we should explore the probability that indeed θ = 0.25% or more EVMs are defective and yet a random sample of five booths from each of the assembly segments does not detect any tampering.  How likely or unlikely is this?

We consider
          Null Hypothesis H₀: θ ≥ 0.25% and Alternate Hypothesis H₁: θ = 0 and take the level of significance of the test to be very very low: 0.000000001.

Let T denote the total number of mismatches between VVPAT count and EVM count observed in the chosen sample. What is needed is to obtain an upper bound of the probability that T=0 but more than 0.25% EVMs are tampered. 

Denoting the total number of EVMs, EVMs in the i^th  assembly segment as n_i and out of these a_i  are tampered, the probability that no mismatch is found in a random sample of size five can be obtained and then the product over all assembly segments yields P(T=0).

Let us denote by δ the maximum of all such P(T=0).

It can be seen that P(T =0|H₀) ≤ 3.201×10⁻¹¹ .

Thus, the Null hypothesis is rejected with a very high degree of confidence, which is the ‘Statistical proof that EVMs are tamper proof’. 

One issue with EVMs is that the candidates and parties can find out the total number of votes each candidate got in each booth. The EC has worked on eliminating this and given a solution called the Totaliser. It is a separate device where on the counting day, one can connect (one by one) 7 EVMs and the data (candidate wise total votes) will be transmitted to the device, and it will only display the total votes in these 7 EVMs. Hope that the focus shifts from EVMs to Totaliser after the 2024 elections.

The writer is Professor Emeritus, Chennai Mathematical Institute. He can be at rlk@cmi.ac.in and rkarandikar@gmail.com.