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Voting matters - Issue 11, April 2000

The problem of surpluses when the quota is reduced

Colin Rosenstiel

Normally a candidate elected with a quota receives ballot papers at the stage at which their votes first exceed the quota. Since the changes to the rules made in 1997 it is now possible for a candidate to be elected with a surplus at a stage where they receive no ballot papers. If the quota is reduced at the same stage from a larger number than the candidate's current vote to a figure below that vote they can be declared elected with a surplus. It has of course been possible for a candidate to be elected without a surplus at a stage where they receive no ballot papers since the introduction of the second edition of the rules in 1976.

The candidate's surplus does not then arise from papers received at that stage, the rule heretofore. However the principle remains that their surplus is derived only from the last-received parcel of papers, their first preferences if no papers have been received since then. The rules in detail say:

5.3 Transfer of a surplus

5.3.1 If a surplus arises at the first stage, select for examination all the papers which the candidate has received.

5.3.2 If a surplus arises at a later stage, because of the transfer of another surplus or the exclusion of a candidate or candidates, select only the last received batch of papers, which gave rise to the surplus.

Any difficulty in interpreting this wording is because of the possibility of different interpretations of the term 'arises'. The candidate declared elected due to the quota being reduced may not have received any papers at the stage in question. I would therefore maintain that only perversity could lead to the conclusion that the word 'arises' could refer to any other stage than the one at which the papers were received and that the most recently received parcel of papers should be the ones used to transfer the surplus as has always been the case.

It is also possible for the papers forming a surplus to be worth less than the value of the surplus. This is again not new, in terms of transferable papers, and is to be treated in the same way - no paper may be transferred at a higher value than it had when received by the candidate with the surplus.

In his article Dr Hill gives a number of examples which he claims there are difficulties over interpretation of the rules quoted above. He doesn't explain what the difficulties are. If the precise wording above is not applicable (which I argue above is not the case anyway) what rules does he imagine are to be followed?

There is also a problem about the importance of this supposed difficulty. The figure of 12% of cases is mentioned by Dr Wichmann, though without supporting evidence. His original claim was for 25% of cases but it turns out that half were AV elections where no surplus can ever be transferred!

Bear in mind that the disputed cases require (a) a reduced quota (b) a surplus arising at a stage where the elected candidate receives no papers (c) that surplus to be transferred. Since the rule came in I have counted many elections. I have records of 27 actual counts, all STV for between 2 and 50 places. Just three had examples of quota reduction. In addition, I conducted some elections to order party lists by repeated STV counting for reducing numbers of places. Ignoring the AV examples with no surpluses these included a further 52 counts with 6 reduced quota cases.

In no cases did a surplus arise at a stage where a candidate received no votes, let alone such a surplus requiring to be transferred. In one case a surplus of 12 arose at a stage when the candidate elected had received just 9 votes. Only 4 papers were transferable anyway.

I have data but not results from another collection of party list ordering elections amounting to another 80 counts but I haven't had time to count them all myself. No problems of this nature were reported while the counts were conducted. In the party list ordering case I did conduct, reduced quotas only occurred in counts for 2 or 3 places, or in one case 4.

In this other set it would appear that the proportion with reduced quotas will be rather lower. In the sample counts I have conducted, the number of non-transferable papers is so low that quotas are not reduced. The 80 counts will include a total of 14 for 2 or 3 places.

In summary, reduced quota real elections are unusual and any possible ambiguity in the rules not encountered at all so far.


  1. I D Hill. Quota reduction in hand-counting STV rules. Voting matters. Issue 11. p9.
  2. B A Wichmann. Checking two STV programs. Voting matters. Issue 11. pp6-8.

Brian Wichmann responds

Colin Rosenstiel correctly quotes my article which on reflection might be confusing. The 25% refers to those elections in which, logically, quota reduction takes place. The 12% refers to those elections in which subsequent transfers take place. Nobody knows what fraction of the 12% are truly 'ambiguous' in the sense raised by David Hill. All the above percentages are from an analysis of 'real' elections from the new data base. I would regard any significant percentage as quite unacceptable, since surely STV should be no less certain that First Past The Post. To avoid any problems, I would suggest that the Council of the ERS formally accepts a small wording change proposed by Colin Rosenstiel in a letter to David Hill dated 8th November 1998.

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