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Voting matters - Issue 13, April 2001

Is STV transparent?

B A Wichmann


The problem with the issue of transparency is to decide what it means. Even then, to be useful, we need something which can be measured, at the very least in an informal sense. Is transparency just a matter of assurance? In which case this can be assisted by auditing, such as is used in the ISO 9000 quality management standard. I think not, since we surely accept that we need to trust those performing the election count. Even with a witnessed count, such as in public elections, we still need to trust those handling the ballot as any conjurer can testify. Even given that trust, we expect evidence that the count has been conducted according to the relevant rules.

Use of computers

Even if the election rules are such as to permit a manual count, it is quite likely that an STV count will be conducted using a computer. Hence we now have to question the validity and evidence for such a computer-based operation.

The public perception of computers is mixed. Few check the arithmetic in their bank statements - so surely we should accept such arithmetic when it can be checked by hand. On the other hand, the very complex calculations in weather forecasting cannot be checked, and we all know that the results are far from perfect. Fortunately, an STV count is nearer to a bank statement than to weather forecasting and hence public trust is not unreasonable.

An interesting analogy to trusting a computer-based count is that of safety-critical software which must be trusted. The recent problems in the railway industry, specifically passing a signal at red, is being tackled by the automatic train protection system which uses computers to stop the train. Indeed, on the Docklands Light Railway, the problem has been solved by having no drivers! In other words, we trust computers to be more reliable than people, at least when the situations are well-defined.

Nevertheless, there is something comforting about seeing piles of ballot papers building up against each candidate which is lost when machine counting takes place. For those witnessing a manual count, it is comforting because it is easier to place trust in people you can see. The experience in Florida is a warning that machine counting can be flawed unless sufficient controls are exercised.


It cannot be denied that the counting process of First Past The Post (FPTP) is simple. This, in itself, is a substantial aid to transparency. Hence the simpler the rules, the easier it is to demonstrate beyond reasonable doubt, that the rules have been applied. Indeed, transparency might be a euphemism for to understand rather than anything associated with verification and auditing.

All the different STV rules must be regarded as complex. The nature of the complexity is different in the hand-counting variety compared with the machine-based versions like Meek. If rules designed for manual counting are used, but implemented using a computer, then the issue of transparency is different - since one must be concerned with the correctness of the software.

Proponents of a specific rule are likely to claim it is simple - not unreasonable if they know it well. The fact is that we have no widely accepted measure of complexity and hence we cannot use complexity as a means of quantifying transparency.

Criteria for Transparency

The main approach is to demonstrate traceability from the ballot papers through to the election result. The actual papers themselves are of no concern (in this article) and hence it is assumed that they can be (or have been) transcribed without error. There is no doubt that FPTP is 100% transparent.

We now consider three examples of STV from the point of view of transparency.

ERS97, by hand

We are assuming that ERS97 is followed to the letter[2]. Hence we have a defined result sheet. Hence the question arises as to whether this information provides complete traceability. It does not since the following information is missing:
  1. The transfers at substages are merged and just the total transferred listed.
  2. The quota is listed only once, and hence if quota reduction takes place, one assumes that only the final quota is listed. Hence it will not be clear that quota reduction has taken place.
  3. When a tie-break is required, there is no indication as to how this should be recorded (if at all).
  4. In ERS97, a tie can be broken on the basis of (the first difference of) a substage result, but these results are not recorded on the result sheet.

Church of England, by computer

The Church of England regulations[3] do not specify in detail the form of the result sheet, but a pro-forma result sheet is provided by Church House. This is similar to the ERS97 result sheet and therefore does not list substages as above.

Items 2 and 4 of the previous case do not apply to the Church of England rules, and therefore the remaining issue is the manner for recording tie-breaks.

However, all the computer programs that conduct STV counts provide substantial detail on the actions performed - much greater than the typical result sheet. This includes the resolution of any tie-break. Hence one has a reasonable degree of transparency if the fullest form of computer output is available.

On the question of checking the computer software, the Church of England rules are relatively easy to program and the corresponding checking of the software is also manageable (at least without the facility of constraints which is not considered here).

Meek, by computer

The issues here are quite different from those with the two previous cases with hand-counting rules. The algorithm is defined[1], and hence the correctness of the software is relatively simple to address.

The problem is that at each stage, a computation is required which needs at least a Spreadsheet to handle with ease. Moreover, without any other information than the votes and keep values for each candidate at each stage, it is not possible (in general) to determine the preferences which gave the observed result. In other words, we have lost traceability to the actual ballot papers. (A similar situation arises with multiple exclusions with ERS97[2], but it is not so common.)

Other issues

Two questions a voter could reasonably ask need consideration:

What happened to my vote? In the case of hand-counting rules, a detailed knowledge of the rules is required as well as the result sheet. The rules are devised so that relatively few of the preferences given are used - this is deliberate to minimise the actual work involved in a count. Hence, in most cases, it is simple to trace the position of the paper amongst the piles of papers within the count. For the Church of England rules which does not allow multiple exclusions, it is more straightforward to trace your vote. It is even simpler with Meek[5], since at each stage, all the papers are re-considered. The formula using the keep values for each candidate gives the fraction of the paper going to each candidate. If issues of security could be resolved, a voter could interrogate the voting system to validate and trace his/her vote.

What if I changed my vote? This is similar to the last question except that if the change was sufficient to alter the decisions on election and elimination, then the subsequent stages would be in doubt. The uncertainty arises because preferences may then be inspected which were never examined before - and hence cannot be determined from the result sheet.

The Data Protection Acts of 1984 and 1999 imply that the candidates have some rights of access to the information about them contained in the preferential ballots. The 1984 Act is reasonably straightforward to follow and my view was that the candidate should be told, if a request is made, of the number of votes he/she attained in each preference position, assuming the data was held on a computer.

The 1999 Act is much more complex and very hard for anybody other than a trained lawyer to interpret. It does cover manual as well as computer counts. As I understand it, ERBS has never been asked for information under the Act nor has concluded what information should be disclosed.


The transparency of STV is nowhere near that of FPTP, regardless of the voting rules in use. Currently, it is not really possible for a voter to obtain the same level of understanding for an STV ballot as for FPTP. This is a serious loss, since in many cases, the impact of a single vote with STV could change the result and the voter should be aware of this. (Of course, this loss is more than compensated by the additional information STV uses.)

I conclude that the above should be rectified by two changes to current practice:

Preferences should be published if they contribute to the count.

This is not complete publication of the ballot papers. My own experience suggests that complete publication might allow some individual papers to be identified which would be contrary to the overriding need for a secret ballot. For the last remaining candidate, say, only the initial preference is inspected, and hence all that would be stated would be the total number of first preferences attained. Similarly, many papers differing in some preferences would be grouped together, since the differences were not used in the ballot.

It has been suggested to me that full publication would be possible for large elections in which the identification of a single paper would be more difficult. I have rejected this since it would imply an arbitrary decision as to when an election is large. Moreover, for large ballots, the published summary of the papers would be small compared with the total, and hence would not be an excessive requirement.

Full publication would also allow candidates to try other STV rules which would not necessarily encourage acceptance of the declared results. For some (small) elections, the summary proposed here for publication would be the complete data from the ballot papers. However, in this situation, it may well be possible to derive that information directly from the result sheet anyway, so formal publication could not be regarded as sacrificing ballot secrecy.

In the case of the Meek rules, the removal of the unseen preferences is undertaken as follows (where KV is the Keep Value of a candidate):

  1. Remove all preferences for withdrawn candidates
  2. For each eliminated candidate A, compute at the point of elimination, the set X of candidates having KV=1.0 (must be continuing or elected candidates). Remove all preferences for A that appear after any candidate within X (in each paper).
  3. For those candidates B for which KV=1.0 at the end of the count, eliminate all preferences after B. (Hence a first preference for B will have only a first preference.)
Similar logic can be produced to remove unseen preferences for the hand-counting rules.

Joe Otten made an interesting comment about a witnessed count. If you could not go in person, could you provide your own copy of a vote-count program to observe the count? I think not, since it would provide terrible problems if the results did not agree, and the returning officer could not be expected to ensure that the provided program only undertook appropriate actions. (David Hill[4] made a similar point that the data should be available for people to run their own program.)

Internet facilities should be available for voters to determine what happened to their vote.

This would be simple to provide and can be made secure by means of a Java applet that runs on the voter's computer.

Assuming that the used preferences are available in an electronic format, then anybody would be able to re-run the election count with suitable software. This is surely as transparent as possible. The Internet facility would allow voters to understand the impact of their vote without having to be an expert in the particular STV rules in use.


The author received very detailed comments on an earlier draft of this paper from: David Hill, Michael Hodge, Joe Otten, Steve Todd and Joe Wadsworth. I have tried to take these comments into account, while not necessarily accepting all of them.


  1. I D Hill, B A Wichmann and D R Woodall. Algorithm 123 - Single Transferable Vote by Meek's method. Computer Journal. Vol 30, pp277, 1987.
  2. R A Newland and F S Britton. How to conduct an election by the Single Transferable Vote. ERS 3rd Edition. 1997.
  3. Church of England, General Synod. Regulations for the conduct of elections by the method of the single transferable vote. GS1327. 1990 and 1998.
  4. I D Hill. Are better STV rules worthwhile? Voting matters 3, Page 8. December 1994.
  5. I D Hill. How was my vote used? Voting matters 7, Page 7. September 1996.

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