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Voting matters - Issue 14, December 2001

Do the differences matter?

Brian Wichmann


In preparing material for a CD-ROM which contains ballot data[1], I have revised and extended the data which makes it feasible to undertake meaningful comparisons between the different STV counting rules.

It is naturally regrettable that the counting rules do indeed produce different results, that is, elect different candidates. This is to be expected, especially when comparing the Meek algorithm with the hand counting rules. Approximations must be made to provide a feasible manual process, so if it is required that a witnessed count be undertaken (and hence the moving of ballot papers between piles for each candidate) then a manual counting rule is required.

Unfortunately, real election data is hard to collect due to the confidentiality that usually applies to such data. However, a computer program has been written to produce such data anonymously by a random process which would not invalidate statistical tests on the anonymous data. This has resulted in a few more data sets from which a comparison can be made. The two counting algorithms being compared here are Meek[2] and ERS 97[3].

Data selection and comparison

The total election data contains many examples used to test counting software which is not representative of real ballot data. However, 188 ballot sets have been identified as appropriate in three classes, as follows: When a count is conducted, if a random choice has to be made, it is hard to conclude that a real difference has occurred. In fact, 29 of the above elections produced a different result, but in 10 of these a random choice was made and hence we ignore these. We are therefore left with 19 differences out of 188 elections, ie 10.1% different. (I could have omitted those for electing one person, but I did not. These are mainly the third class above in which no difference was observed.)

In the table, the last entry records the number of seats whose occupancy changed and, in brackets, the number of votes less than the quota which the Meek algorithm recorded against the candidate which ERS97 elected (expressed as a percentage of the total number of votes). Hence for M005, the last remaining candidate which the Meek algorithm did not eliminate was the one elected by ERS97 and had 6358.85 votes against a quota of 6517.76 (6517.76-6358.85=158.91 votes = 0.57% of 27,757). The star indicates that the remaining candidate in the Meek count was not the one elected by ERS97 and hence the two counts diverged at an earlier point - not just the last stage. Of course, in the one case in which two seats differed, it is not possible to provide a simple numerical difference.

It can be seen from the table that the differences are significant and large in some cases. In five cases (M070, R004, R005, R046 and R048) the differences are small and perhaps could be regarded as acceptable. The total number of seats in these 19 elections is 106 with 20 differences and hence a discrepancy in those elected of 18.8%, or 2.1% difference if all the elections are considered.

The difference in the handling of non-transferables between the two algorithms is a matter of controversy. To indicate whether the number of non-transferables is a factor, the difference that the two algorithms give in the number of non-transferables is expressed as a percentage of the total votes. In the case of R046, ERS97 has a very much lower number of non-transferables which surely has a key effect on the result. However, in general, the pattern is not so clear.

It could be that the method of constructing the Mddd data (first class above) produces results which would not be typical of real elections. However, the table clearly shows that the Rddd (real elections, second class) examples show similar differences.


I conclude that unless it is essential to have a manual, witnessed count, the Meek rules should be used for STV counting. The approximations introduced to enable a manual count produces too many differences for the hand counting rules to be used otherwise.

Any of the data upon which this paper is based can be provided to interested parties.


  1. See Editorial, Voting matters, Issue 13. April 2001
  2. I D Hill, B A Wichmann and D R Woodall. Algorithm 123 - Single Transferable Vote by Meek's method. Computer Journal. Vol 30, pp277-281, 1987.
  3. R A Newland and F S Britton. How to conduct an election by the Single Transferable Vote. ERS 3rd Edition. 1997.

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