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# Voting matters - Issue 2, September 1994

## Two STV Elections

#### B A Wichmann

Brian Wichmann is the Editor of Voting matters, and is a Visiting Professor in Computing at The Open University.

I believe two STV elections may be of interest to the readers of Voting matters, due to the implications of the results on the properties that an ideal STV algorithm should (perhaps) have.

The first election is the Eurovision Song contest for 1992 which is an interesting election to analyse since the votes are publicly available, in spite of the voters not knowing of the other votes. Each country votes for the songs of other countries by awarding 12, 10, 8, 7, 6, 5, 4, 3, 2 and 1 points, which can be transcribed into STV preferences.

The points system gave for those over 100: Ireland (155), UK (139), Malta (123), and Italy (111). Since the points total is given after each country has voted, the commentator (Terry Wogan) reported that Ireland was unbeatable by the UK before the last few countries voted. An analysis of the votes by other means is quite different.

The ERS hand counting rules declare the UK as the winner, as does the Meek STV algorithm. However, more countries preferred Ireland to the UK than the contrary (by 12 to 11, rather close). Indeed, by the Condorcet rules, Ireland would be the winner, since Ireland is preferred to any other country by a majority. The reason that the ERS rules elect the UK is that Ireland is eliminated earlier, leaving the last contest between Malta and the UK, which the UK wins. The Meek algorithm is similar, but with Italy being the last to be eliminated.

One STV algorithm due to Tideman considers all possible pairs of results. In the case of a single seat, Tideman will elect a Condorcet winner (assuming there is one) and hence chooses Ireland in this case. One is therefore left to wonder if an 'ideal' STV algorithm should always elect a Condorcet winner, assuming there is one.

The second election is one for which I acted as returning officer for a rather unusual 'election' at my place of work.

The research institute at which I work has had a library for a group of about 60 scientists for at least 30 years. As the research has changed over the years, new journals have been ordered. However, except in obvious cases, it has not been clear which journals should be cancelled - especially since a complete 'run' of a journal will be lost. I therefore proposed that an STV election be run to determine which journals should be cancelled and which new ones to order.

The management agreed to this proposal and hence I ran the election as follows: A list was obtained of the (about) 200 journals, which were assigned a code. The scientists were asked to place up to 40 journals in preferential order, being given about a month to place their ballot.

Quite a bit of effort is necessary to fill in the ballot paper. Nobody attempted more than the 40 preferences, the average being about 20. About half of those eligible voted, which I thought was quite reasonable, since quite a few would have no direct use for the library.

The ballot revealed that 4 journals were in the library but not on the list provided. Eight journals were written in by electors which were not in the library.

The analysis of the results proved very interesting. With 31 people voting for a total of 198 journals, the quota is a lot less than 1. This implies that about the first six preferences would be selected for any reasonable number of journals. However, there was not a fixed number of 'seats', and hence I had to decide what threshold to set. Due to the difficulty for the electors, I did not interpret the ballot papers according the usual ERS rules. In one case in which one preference was unclear, I omitted that preference but did not ignore subsequent preferences. In two other cases in which a journal was selected twice, I merely ignored the second choice.

An initial analysis showed that 27 Journals did not appear in any position on the ballot papers. This gave an instant selection of journals to cancel. I ran the ballot with the option to cancel 10 and 20 further journals.

I have several STV algorithms available on my home computer which I used to compute the result. I had decided in advance that I would use the Meek algorithm for the election, but the other versions could be used to see what difference it made.

The first problem was that the programs I had, required a trivial modification to handle as many as 200 'candidates'. After having made that modification, it was found that the programs would not work on my PC because the full results over-filled my floppy discs! A further modification was needed to output only the final table and a summary of the eliminations and elections.

The three versions of STV were:

1. The Meek algorithm, as published in the Computer Journal (1987, Vol 30, p277)
2. The ERS hand-counting rules (as programmed by David Hill)
3. The Tideman algorithm, as approximated by my program.
The ERS results were quite unacceptable which shows that the hand-counting rules do not seem to have been used upon such an election. The problem is that if the election is run with the same number of seats as those selected in any preference, the algorithm does not select just those selected by the electors! This problem can be expected of any algorithm that does not see subsequent preferences.

The other two algorithms produced virtually identical results. With the reduction to 20 fewer journals than those selected, one difference was found between Meek and Tideman. A manual inspection of the results with the two journals in question, showed no clear distinction.

After producing the result, I computed for each of the 31 ballots, the way in which the final stage of the ballot had divided up the vote. This information was given to each elector. It created further interest in the STV algorithm. Those who had given more preferences had, in general, a lower non-transferable loss. However, the variations were very large. For instance, a person would gave the largest number of preferences (36) had a small loss, while a person would gave 15 preferences had no non-transferable loss.

I conclude from this election that STV can be used for such selections, but that the ERS hand-counting rules are not appropriate. Also, any STV algorithm approved by ERS in future should not suffer from this noted defect. Namely, if only N candidates are represented in the preferences and N is the number of seats, then the algorithm should elect those N. This requirement does not seem to lead to additional problems. It appears that the STV algorithms which recompute the quota can satisfy this requirement, since in the particular circumstances the entire ballot papers are then processed.

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