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ISSN 1745-6231 Voting matters To advance the understanding of preferential voting systems published by The McDougall Trust Issue 24 October 2007 Contents Editorial . i 1 I D Hill: STV in Northern Ireland 1 2 Jonathan Lundell and I D Hill: Notes on the Droop quota 3 3 H R Droop: On Methods of Electing Representatives 7 4 E Stensholt: Review — Elections in split societies 47 About the McDougall Trust (reg. charity no. 212151) The McDougall Trust is a charitable trust formed in 1948. The charity’s purposes as stated in its governing scheme of 1959 are to advance knowledge of and encourage the study of and research into: • political or economic science and functions of government and the services pro- vided to the community by public and voluntary organisations; and • methods of election of and the selection and government of representative organ- isations whether national, civic, commercial, industrial or social. The Trust’s work includes the maintenance and development of the Lakeman Library for Electoral Studies, a unique research resource, the production and publication of Representation: The Journal of Representative Democracy, and, of course, this pub- lication Voting matters, that examines the technical issues of the single transferable vote and related electoral systems. For further information on the Trust, please contact: The Secretary, McDougall Trust, 6 Chancel Street, London SE1 0UX, UK. Telephone: +44 (0)20 7620 1080 Facsimile: +44 (0)20 7928 1528 Email: [email protected] Web: www.mcdougall.org.uk For further information on this publication, please contact B A Wichmann, the Editor at the above address or by email at: [email protected] Review The McDougall Trustees recently asked a senior academic to undertake a review of Voting matters, partly due to some comments on the Internet. You may have noticed a difference to the front sheet since the subtitle has been changed from the previous text: for the technical issues of STV. This change reflects the actual content which is not restricted to STV. An issue which arose from the review was a criticism of the paper by Allard in Issue 5 which gives a low figure for the number of STV elections which are non-monotonic. It is perhaps not obvious that an election can fail to be monotonic in two distinct ways. Given an election for three seats and six candidates in which A, B and C are elected and X, Y and Z fail to be elected, then increased support for C could result in C not being elected; or alternatively, reduced support for X could result in X being elected. It seems clear that a more robust estimate for the occurrence of a non-monotonic election is needed. An academic has agreed to investigate this. It would also be interesting to know if the actual STV counting rule had an impact on this issue. CONTENTS Editorial correct in general. For instance, if a Meek count excludes candidates A, B and C (in that order), then There are 4 papers in this issue, all of which are rerunning the count without A will get the same re- comments or reviews of other work: sult, and also without A and B, or A, B and C. How- ever, a different result may be obtained by excluding • I D Hill: STV in Northern Ireland and B (without A), or by excluding A and C without B, proportional representation etc. With a conventional count, if the first stage ex- This paper makes two suggestions for increas- cludes a candidate, then rerunning the count without ing the degree of proportionality for elections. that candidate does not necessarily obtain the same Changing the number of seats per constituency result. would require a legislative change, but is con- Readers are no doubt familiar with the problems ceptually simple. Using the eligible votes to that were encountered with the Scottish elections determine the split is more radical, but why this spring. However, the STV elections went off not? What do readers think of this? smoothly. The Glasgow election area provided com- plete details of the voting profiles on the Internet, al- • Jonathan Lundell and I D Hill: Notes on the though it was the only area to do so. This provides Droop quota a very significant addition to the STV data available The Droop quota is a key issue of STV. Note for academic study. that the authors place great emphasis on DPC The site www.votingmatters.org.uk is (see the paper for details). This criterion could now working on the Internet, but bookmarks to the be regarded as critical for STV, yet some count- old site should be changed to the new one, since the ing methods fail this test, at least in marginal old site will be removed eventually. situations. • H R Droop: On Methods of Electing Represen- Readers are reminded that views expressed in tatives Voting matters by contributors do not neces- sarily reflect those of the McDougall Trust or In preparing the previous paper, it was clear its trustees. that the original paper of Droop was not widely available. Hence it was decided to reprint it, with the approval of the original publisher (al- though long out of copyright). Although long by modern standards, it raises very many is- sues, the majority of which are still outstanding today. Thanks to the two previous authors and David Farrell in assisting with this reprinting. • E Stensholt: Review — Elections in split soci- eties This is a review of a book edited by Peter Emer- son. The topic of the book is voting systems based upon Borda scores. Such systems are clearly related to STV in many respects and hence a comparison is surely of interest. In or- der to present the review, a scheme for illustrat- ing voting profiles is used. Note that the review and the book take into account the political po- sition of a divided society in Northern Ireland. The Editor must correct a statement made in the last editorial which stated: In electoral terms, Meek has the advantage that the intervention of a no-hope candidate cannot change the choice of the elected candidates — a failing of all the rules used for current hand-counting STV methods. This is not Voting matters, Issue 24 i STV in Northern Ireland and proportional representation I.D. Hill Even access to the complete voting pattern would [email protected] not necessarily tell us what would have happened because, for one thing, the list of candidates might have been different if the number of seats were changed. 2 A further possibility 1 How many seats per constituency? It could be argued, however, that it would be even better to use the number of valid votes, instead of the If STV is to give proportional representation, so far eligible electorate, thus making high turnout an ad- as can be done within the limits of practicality, it vantage. Table 2 shows what this would have done. is necessary that the number of seats for each con- Compared with Table 1, East Antrim, Lagan Valley stituency should depend on the eligible electorate. and North Down would each have lost a seat as a In the present rules for Northern Ireland this is not result of poor turnout, while Fermanagh & South done, but it is laid down that there shall be 6 seats for Tyrone, Mid Ulster and Newry & Armagh would each constituency, and the degree of proportionality each have gained one for good turnout. must suffer somewhat in consequence. This would be perfectly possible. Each con- A reasonably good job appears to have been done stituency could make its count of first preferences in trying to equalise electorates to go with the equal without knowing how many seats it would get, and numbers of seats, but the result is far from perfect. report to a central point the total number of valid Table 1 shows the electorate sizes, as given by the votes. As soon as all such reports were in, the central Electoral Office for Northern Ireland, in March 2007 point would tell each constituency its number of and how many seats each should have had for the seats and its quota, and the count could continue. Assembly election if allocation had been made by One slight disadvantage might be if voters hesi- the Sainte-Lague¨ rule. The difference from 6 seats tated to vote in case an extra seat were gained that everywhere is not huge, and it may not have made they suspect might go to a disliked party, but that any substantial political difference to the outcome, is probably not very likely to deter voters. It would but there is no denying that it could have done, and certainly make party workers very cross if they put any distortion may get worse over the years if no a lot of effort into getting a high turnout but, as a action is taken to correct it. result, gained an extra seat that went to a different What any such political difference would have party. been we cannot tell without access to the votes. This idea is in no way comparable to the “over- We can speculate about it, of course, but it is nec- hang” votes in the German electoral system. That essary to bear in mind that, in STV, the last seat is merely to allow for a slight difficulty in the sys- in a multi-member constituency is nearly always tem and it lessens proportionality by increasing the marginal, and may turn out quite differently from total number of seats in certain cases, whereas the the majority shown by the constituency.
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