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Voting matters - Issue 11, April 2000

Quota reduction in hand-counting STV rules

I D Hill

The 1997 ERS rules for STV include a rule for reducing the quota if some votes become non-transferable before anyone has been deemed elected. In general, such a rule is to be welcomed, as the smaller the quota can legitimately be made the better.

However, in attempting to implement this rule in my STV computer program I ran into difficulties of interpretation. It may be that the circumstances that cause such difficulty would rarely arise in practice, but that is irrelevant. Rules, and programs derived from them, have to work in all circumstances. I wished to know whether the difficulties were real, or whether I was being over-fussy in imagining them, so I consulted a number of people, chosen as being knowledgeable in STV, and asked for their views on what the rules required with each of four examples. Their replies were sufficiently varied as to show that there is a real problem.

The rules in question are:

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.

With minor changes of wording those two rules are as in the previous edition, but we now also have:

5.4.8 If any papers have become non-transferable before any candidate has been deemed elected, recalculate the quota as in paragraph 5.1.6, ignoring the non-transferable vote.

The first three examples were as shown below. The fourth was somewhat different as it did not do what was intended and it is better here to show the intended case instead of the unintended one.

Election 1  Election 2  Election 3   Election 4

 17 AB..     14 AB..     17 AB..      12 AB..
 11 BC..     11 BC..     11 BC..      11 BC..
 10 CD..     10 CD..     10 CD..      10 CD..
 10 DA..     10 DA..      9 DA..      10 DA..
  6 E(plump)  6 E(plump)  6 E(plump)   6 E(plump)
              3 EAC..     1 EAC..      5 FAD..
In each of these there are 2 seats to be filled and 54 votes. In each case the initial quota is 54/3 = 18. In each case 6 votes become non-transferable before any candidate is deemed elected, so the quota is reduced to 48/3 = 16. In each case candidate A now has over a quota of votes. How do the rules require A's surplus to be dealt with?

As a result of the exercise, it seems clear to me that trying to implement these rules would not be sensible until they have been amended for, even in the simplest cases, elections 1 and 2, it is not absolutely clear where A's surplus should go, since it cannot really be said that the papers concerned 'gave rise to the surplus'. In election 3 there was much disagreement about how much goes to C and how much (if any) to B. If experts disagree, to the extent that was observed, on what the rules mean, what hope is there for an ordinary returning officer?

In election 4 the 'gave rise to the surplus' wording is even more far-fetched than in the other cases, and my own view is that this case is not catered for in the rules.

I am grateful for an additional case that was suggested to me later by one of those whom I had consulted:

        Election 5

        14 AB..
        11 BC..
        10 CD..
        10 DA..
         3 E (plump)
         6 EAC..
I would probably have got this one wrong, as my first reaction on seeing it was 'No problem here', because A has already got more than the original quota by the time it is known that any votes have become non-transferable, so quota reduction would not apply, but not so. Although exceeding the quota, A is not actually deemed elected (para 5.4.9) until after the quota reduction has been made (para 5.4.8).

My own view is that, in principle, the right way to do such quota reduction is to re-start the election after the reduction, with the equivalent of a new Stage 1, treating all excluded candidates as if withdrawn, but the wording of the current rules does not seem to support that. For the moment what is wanted is the publication of a clarifying amendment to the rules, so that users can know how to proceed. This issue can be resolved only by a properly authorised statement from the ERS Council.


  1. R A Newland and F S Britton. How to conduct an election by the Single Transferable Vote. ERS 3rd Edition. 1997.

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