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By a
resolution of the Council in August 2002, the elections for Council are
counted by the Single Transferable Vote system. One of the properties of
this system is that if any group of candidates gets a sufficient share
of the votes (1/(m+1), where m is the number of candidates
to be elected) then one of this group is bound to be elected. Therefore
it is hoped that this method will lead to a more diverse Council than
the result of the present election, and furthermore that individual
members, other than those chosen by the nominating committee, will feel
able to stand with a real chance of being elected.
There are many descriptions of the STV system (see, for example,
www.votingsolutions.com)
but the basic principle is that voters rank the candidates in order of
preference. In order to be elected a candidate must achieve the quota
of N/(m+1), where N is the total number of
votes cast. Excess votes over the quota are appropriately downweighted
and allocated to the next preference of voters. If no candidate reaches
the quota, the candidate with the least number of votes is eliminated
and their votes transferred to next preferences.
Voters in IMS council elections are asked to rank the candidates 1, 2,
3, ..., r until they have no further preference between candidates.
Thus 1 is a voter’s first preference, 2 is their next choice, and so on.
There is no disadvantage to higher candidates in expressing a full list of
preferences; later preferences are only used when the fate of candidates
given higher preferences has been decided one way or the other. A vote is
reckoned as spoiled if the preferences are not numbered consecutively
starting at 1. Apart from the candidates not numbered at all, no ties are
allowed among the numbered preferences. The fact that voters may not
express a full list of preferences is allowed for by reducing the quota as
necessary during the later stages of the count.
The votes should be entered into a spreadsheet, with the first row of
the spreadsheet containing the names of the candidates and each subsequent
row the votes cast, with blank preferences being replaced by zeroes. It is
advisable to number the ballots before entering them and to enter the full
data twice. This will allow a check for errors and will also allow a
reference back to the original vote if necessary. Of course it is
preferable for votes to be cast electronically, so that the spreadsheet
can be creted automatically.
Once the votes are all recorded in the spreadsheet, they should be
exported as a tab delimited text file, called, for the sake of argument,
votes.s. The count is carried out by the
S-PLUS program stv, included as an appendix to this document. The program
needs to be supplied with a filename x
giving the tab-delimited file, for instance
votes.s, in which the data are stored, together with an argument
mcan=the number of candidates to be
elected. Invoking the program stv with
these arguments will then check the validity of the ballots, eliminate any
which are spoiled, and carry out the various stages of the count. The
argument oldcount (not recommended) allows
for a demonstration of what would have happened with the old method of
counting the votes. On the other hand the argument
verbose displays the various stages at
which candidates are elected or eliminated, and shows how the first
preference votes are redistributed at each stage.
At the end of the process, the program yields a list of the successful
candidates in the order in which they were elected. The order may be
useful, for instance, when an extra member of Council has to be elected to
fill a casual vacancy, in which case the last candidate to be elected
would be in this position. However, usually it is not appropriate to
publish the list in this order.
The method resolves ties deterministically; if a candidate is to be
elected, the last named member of a tie is chosen. On the other hand, if
there is a tie for elimination, it is the first named who is eliminated.
These choices are aimed at compensating in a small way for the tendency of
candidates higher up the ballot paper to get more votes.
The program should run fairly fast and should be user-friendly. Any
comments or corrections will be gratefully received. (see
the stv program)
Bernard Silverman,
b.w.silverman@bristol.ac.uk
August 3, 2002
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