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Voting matters - Issue 10, May 1998

Producing a Party List using STV

C Rosenstiel

Colin Rosenstiel is a member of the Council of ERS and the author of a computer program for STV.

With some of the current proposals for electoral reform, parties will be required to produce a list from whom candidates will be elected in order from the top. STV can be used to construct the ordered list, given a preferential ballot of all party members.

The conventional use of STV to elect n members gives members of equal status, since the order in which STV elects does not necessarily determine the strength of their support. Repeated use of STV elections can be used to determine an order as follows:

Given a total list of 10 (say), then the first step is to determine those on the list (without an ordering) by running an STV election with all the candidates and 10 seats to fill. The next step is to run an STV election for 9 seats with 10 candidates being those previously elected (using the same ballot papers). The eliminated candidate is then placed last on the list. Next, an STV election if run with the remaining 9 candidates with 8 seats to determine the next lowest candidate, and so on.

This process might sound tedious, since so many STV elections are run, but if a computer is used, it is straightforward. Note that the above process will not work in reverse, i.e. selecting the top candidate first. The reason for this is that when electing two candidates, it can happen that neither of those elected is the previously selected 'top' candidate.

Two elections were taken in which there was more than ten candidates to which we have applied the algorithm above to order the top 10 candidates. The results obtained was as follows:

                     Election 1      Election 2
This algorithm    :  ABCDEFGHIJ      ABCDEFGHIJ
Order of election :  CABDEFGHJI      CBAFEHDGIJ
As expected, it can be seen that the order of election does not give the same result as successive elimination. Hence this algorithm is recommended in producing party lists.

Editorial comment

It has been suggested to me that if the Meek method is used, then just one election would suffice (to determine the order of the 10 candidates). Their order can be found from the retention factor in the final table of the election results - the smallest retention factor implying the strongest candidate since that candidate required the smallest proportion of the votes retained to get the quota. These values do give a measure of their relative support, unlike the order of election. In the elections above the Meek result were:
                     Election 1      Election 2
Meek 'keep' factor:  ABCDEFGJHI      ABCEFDHGIJ
This would appear to indicate that the methods of ordering of the candidates produce a similar result. In practice, both methods would need to use a computer and hence there seems to be little to choose between them.
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