Addendum/Erratum:
The logic used above to argue for the
‘population’ to be taken as the constituency may be wrong. To explain, first look
at the table below, and then the corresponding plot, for 99% confidence level,
for the required sample size S for different rigging fractions(calculated using the hypergeometric distribution):
|
N
|
Fr = 0.5%
|
Fr =1%
|
Fr=5%
|
Fr=25%
|
|
104
|
875
|
448
|
90
|
16
|
|
105
|
915
|
457
|
90
|
16
|
|
106
|
919
|
458
|
91
|
16
|
|
107
|
921
|
458
|
91
|
16
|
As seen before, in the plot by
Shetty, as N increases, S saturates, and, in fact, is completely flat at the
highest rigging fraction (25%) – the easiest case to detect rigging. At the
lowest rigging fraction of 0.5%, the sample size is much larger, since it is
more difficult to detect low-level rigging.
The question discussed earlier was
whether the population should be restricted to the EVMs in the constituency or
should contain all the EVMs in India.
I re-read Shetty’s paper and realized
that he actually recommended that the population should be all the EVMs in each
State (not constituency, as I thought) – and the number of EVMs tested should
vary from State to State, being a larger fraction of the total number of EVMs
in smaller States (since saturation does not occur for small N).
I argued earlier that the
constituency level was the appropriate population to be considered because the
rigging fraction would vary from one constituency to the next, being low or
non-existent in safe constituencies and definitely occurring in
closely-contested ones. However, it is easy to detect high level rigging – it
requires very few EVMs to be tested. It is more difficult to detect low level
rigging – it requires more than an order of magnitude EVMs to be tested. But
since the SC has already recommended 5 EVMs per constituency, this amounts to
about 2,715 EVMs which will assure even low-level (0.5%) rigging is detected
with 99% confidence (see Table above, where only 920 are needed) – and will definitely
detect high-level rigging (a point that Shetty also makes).
Shetty makes a different argument: he
considers the work-load of testing n EVMs in a population vs the added work-load
of testing N-n EVMs as well, if even one EVM out of n EVMs is found to be rigged.
He argues that the population should not be considered as all the EVMs in
India, because if even one EVM anywhere in India is found to be rigged, all
EVMs all over India would have to be tested. As a compromise, trading off the
two types of work-load (n & N-n), he argues that each State should be considered
as an independent unit, so only one State would need all its VVPATs to be
checked. However, the decision that if India is the unit, and any one EVM is
found rigged, need not trigger the testing of all EVMs in India – it could be
restricted to the State in which the rigging was detected. This point, is,
however, debatable.
The conclusion seems to be that the
number of EVMs being tested is, in terms of statistics, sufficient at the 99%
level of confidence. If it can detect low-level rigging at 0.5% in some
constituencies, it can manage both high-level rigging, and a situation where
many constituencies are not rigged at all, while low-margin ones are rigged
(non-uniform rigging case). That means that the Expert Committee report must have used similar logic (although the exact numbers have not been released) considering all the EVMs in India as the 'population' - which Shetty also believes was the Committee's approach.
However, as pointed out earlier, this assumes that
the testing protocols are sufficient to detect all forms of rigging – and this
remains an area of doubt.
1. https://www.hindustantimes.com/analysis/can-v-vpat-slips-detect-rigged-electronic-voting-machines/story-obRW9ZR2EaajIj5gt1XxuO.html
Atanu Das 27th Apr.2018
2 2. K.Ashok Vardhan Shetty “Winning Voter
Confidence: Fixing India’s faulty VVPAT-based audit of EVMs“, The Hindu Centre
for Politics and Public Policy, Policy Watch Paper No.7, 2018
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