[E-voting] The VVAT Debate - Technical or Not ?

Dr J Pelan J.Pelan at gatsby.ucl.ac.uk
Mon Mar 8 16:38:45 GMT 2004

On Mon, 8 Mar 2004, Michael McMahon wrote:

> But, what is an acceptable chance? A 50% chance means checking 50% of
> constituencies, or ballots whatever. A 90% chance means checking 90%
> etc.

I'll try to give a quick answer here and perhaps a longer answer later if
time permits and demand requires it. I am not a statistician and have an
embarrassingly woeful recall for that subject.

If we take the example of an opinion poll, it seeks to determine the
opinion of a very large number of people by asking questions of
('sampling') a much smaller, more manageable number of people. This
smaller group must be selected randomly from the larger set, i.e. without
any bias, if they are to be truly representative.

There are two important factors to describe the accuracy of the poll - the
'margin of error' and the 'confidence level'. These are mathematical
functions of the sample size and the overall distribution (of opinions).
To put some figures to this and without going into any detail, a typical
opinion poll might sample 1000 people. The resulting margin of error is
+/- 3% (i.e.  1/sqrt(1000)) and by assuming a particular distribution type
we get a confidence level of 95%. This means that 95% of the time the poll
result will be within +/- 3% of the true result. 

The beauty of statistics is that this applies to any sufficiently large
population be it 1, 10 or 100 million people. So survey groups in the
Ireland, the UK and the USA can all limit their questions to one thousand
people and still have that +/- 3% result accuracy. Note that it is more
meaningful to talk about absolute sample sizes rather than sampling
'percentages' of whole populations, so checks wouldn't be of the nature of
'10%' but more by absolute numbers like 1000, 2000 and 10000.

By obtaining the opinions of a relatively small number of people we can
achieve a result that applies - on the balance of probability - to the
whole, sampled population and which may be accurate enough for our needs.  
A similar principle applies in checking the validity of electronic voting
records by comparision with a subset of the verified paper trail.

John P.

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