CONSTITUTION

The voting system shall allow the voter to place the candidates in preference order, either by numbering candidates continuously from 1 until they cease to hold a preference between further candidates, by writing the names of candidates in order until they cease to hold a preference, or by some other method analagous to these.

The voting system must allow voters to express any preference order between candidates, and to cease expressing a preference at any point, including allowing the submission of a spoilt or blank ballot paper. It should, as much as possible, make all preferences equally easy to choose.

Ties should not be expressed, nor should any preference be given to a candidate not standing in the election. Re-Open Nominations should, if available as an option in the election, be treated in a manner equivalent to a candidate.

These rules solely describe the theoretical conduct of a count. No attempt is made to suggest practical considerations of the forms and papers needed to keep track of the various stages of the count. Such judgements and preparations are the responsibility of the Senior Returning Officer. The rules explicitly do not give guidance on how the Senior Returning Officer should and should not prevent and/or detect electoral malpractice.

At all stages of the count, numerical calculations should be kept to the maximum possible level of precision. Use of a standard scientific or graphical calculator will allow at least 8 significant figures, which should be adequate for most cases. Where votes are close or expected to be so, it may be advisable to use a higher number. How far to go in pursuit of higher levels of precision is at the Senior Returning Officer's discretion. At least 2 decimal places should be used at all times.

Terms such as "ballot paper" and "paper" are used throughout this document for convenience; these may refer to a vote cast, for example electronically, for which no physical paper exists.

1. Sort the votes by First Preference, including one sorted part for votes that do not have a valid First Preference (referred to as spoilt/blank). Record the total number of votes that have a Valid Preference - this number is the Total Active Vote.

2. Calculate the Quota, to be the total number of votes with a validly expressed first preference, divided by one more than the number of positions to be filled.

3. If any candidate has a greater number of votes to the Quota, they are elected. If enough candidates are elected in the first round to fill all available positions, the count ends, otherwise, further rounds are necessary.

If the previous round did not elect sufficient candidates to fill all available positions, then the Surplus of candidates already elected shall be transferred. If no candidate has a Surplus then instead a candidate will be eliminated, and his/her votes transferred.

Where multiple candidates have a Surplus to transfer, transfer the Surpluses in size order, beginning with the largest. This may lead to Surplus transfer occuring in an order other than the order of election of candidates. If two candidates have Surpluses of equal size, then transfer first the candidate with the higher first round vote, or if this is equal, the higher second round vote, and so on. If votes at all rounds are equal, determine the surplus to transfer first by a random method.

Where there are no Surplus transfers to be made, eliminate the candidates currently with the lowest number of votes. If two candidates have equal numbers of votes (elimination), eliminate the candidate with the lower first round vote (lower second round vote if this is also equal, and so forth). If it remains impossible to distinguish between two (or indeed more) candidates in this way, the the candidate to be eliminated shall be selected randomly.

Whichever route is taken, Quota should first be recalculated - it is the Total Active Vote divided by one plus the number of remaining unfilled positions.

1. Begin by working out all Transfer Paths through which the vote papers currently with that candidate could have reached them. In the second round, there will always only be one Transfer Path - that of the candidate. In later rounds, multiple paths may become possible, occuring when the votes of someone elected or eliminated in a round after the first are transferred.

2. Locate the votes associated with each Transfer Path and find the next Valid Preference on these papers. Sort these votes within their Transfer Path into the destinations (including untransferable if there is no next Valid Preference), and record in a table the number of ballot papers from each Transfer Path going to each destination.

3. For each Transfer Path, calculate the Current Value of papers in that Transfer Path by multiplying together the Transfer Values of the candidates in the Transfer Path. Record in a table the number of votes (equal to the number of ballot papers multiplied by the Current Value of those papers) for each Transfer Path and destination.

4. Calculate the total number of Effective Papers to be transferred by summing the numbers in the votes table for all Transfer Paths and all destinations except spoilt/blank.

5. Divide the Surplus for the candidate by this number (Surplus / total transferable vote). If the result is greater than 1, round it down to 1. This number becomes the Transfer Value for this candidate.

6. Sum the number of Effective Papers transferring to each destination (except spoilt/blank, as these papers effectively stay with the current candidate) and multiply each by the Transfer Value for this candidate to get the number of votes transferred. Add this number on to the current vote total for each destination.

7. If any further candidates have now achieved Quota then they are also elected, and their surplus may be transferred in later rounds. Reduce the record of the Total Active Vote by the Quota.

8. If the Transfer Value for the candidate would have been greater than 1, had it not been rounded down, then subtract 1 from the value it would have been, and multiply this by the number of Effective Papers for all Transfer Paths and all destinations including spoilt/blank. Subtract this number from the Total Active Vote as well.

6. Sum the number of Effective Papers transferring to each destination (including spoilt/blank) to get the number of votes transferred. Add this number on to the current vote total for each destination.

If at any stage, the number of places remaining is equal to or more than the number of candidates remaining, all remaining candidates are elected. This should not, however, take place, if Re-Open Nominations is being used and has not been eliminated at a previous stage.

The number of papers `given' to spoilt/blank will only rise either upon the elimination of a candidate, or if a surplus transfer value would be more than one.

In the event of a re-count being necessary for any reason, random determinations shall not be carried out in the event of ties. Instead, the candidate eliminated or Surplus transferred shall be the same as in the original count. This rule may be suspended at the discretion of the Senior Returning Officer if the reason for the recount involved the validity of a random determination or determinations.

Re-open nominations (RON) shall be treated as a candidate with respect to votes being transferred to them, and votes being transferred away from them if they are eliminated. If, however, RON achieves Quota, then one position is filled by `RON'. In the case of a single-post election, the position shall therefore be declared unfilled.

In the case of a multiple-place election in which further positions remain to be filled, a further candidate, known as "RON 2" shall be created, and RON's Surplus shall be transferred to this candidate immediately by the following method:

If RON 2 now has more votes than Quota, repeat the above procedure to transfer RON 2's surplus to a new candidate, "RON 3", and so on. This will give a Transfer Value for RON 2 as well, and RON 2 takes a second position. Otherwise continue the count.

RON 2 (or 3+) continues to pick up transfers from other candidates. If any further RON candidate achieves Quota, repeat the above procedure.

RON 2 can of course be eliminated, which can lead to complicated Transfer Paths. It must be recorded which RON any votes transferred to, as it is possible for votes to transfer to RON 2 in rounds between RON being elected and RON 2 being eliminated.

If at any stage in the count, the difference between two candidates or options is smaller than 1% of the total vote (or less than 10 votes), and were the current vote totals of the two candidates to be reversed, the action taken on the next stage would be different (e.g. a different candidate would be eliminated or a different surplus would be transferred next), then a recount shall automatically take place.

Any discrepancies between a recount and the initial count shall be explained to the satisfaction of the Senior Returning Officer (and if necessary, further recounts held) before any announcement of the result. This shall be done even if the count and the recount elected the same candidates.

If, in the election, not all positions are available to all candidates - for example, if at least one female and one male, or at least one postgraduate student must be elected, this procedure should be used:

1. Before the start of each round, including the first, and after declaring any candidate elected, see whether, to satisfy constraints, any candidate must be elected at this stage. For example, if at least one female was required to be elected, and only one female candidate remained, that female candidate would be declared elected.

Note: unless RON has been eliminated, no candidate may be elected in this way. If RON is the only candidate who can fill a particular place, the place should be declared unfilled and RON should not be declared elected to it.

Candidates elected in this way do not have a surplus, so their surplus is not transferred. Reduce the Total Active Vote by the number of votes already assigned to the candidate(s) declared elected.

2. See if any candidates must be eliminated. For example, if the only places remaining were male-only, any remaining female candidates would be eliminated.

Re-Open Nominations is eligible for every place, so should never be eliminated at this stage. Votes assigned to candidates eliminated in this way shall be redistributed immediately.

Note that this procedure may occur in the middle of a round if candidates are elected, so if multiple candidates exceed quota simultaneously it is vital to declare them elected in order of highest surplus, rather than arbitrarily.

If any constraints are non-exclusive, this becomes extremely complicated† - for example, if there are three places remaining, and you still need to elect two female and two postgraduate students, and only one female postgraduate is left in the election, then she must be elected (assuming RON has already been eliminated). It is also possible for RON to be elected on this basis, leaving open places only fillable by female postgraduate social scientists, or even by candidates with attributes which, while theoretically possible, are in fact held by no-one - for example, for a minorities committee you might end up requiring a black, female, lesbian or bisexual, mature postgraduate with a disability (having just elected six young straight white able-bodied male undergraduates).

If constraints are used, they will inevitably either have no effect, or lead to the election of candidates with fewer votes than those eliminated. As the number and complexity of the constraints increases, the probability increases that the candidates elected will be vastly different from those the electorate wanted. The authors of this document do not recommend the use of constraints.

Current Value:
The remaining unused value of a paper - equal to 1 multiplied by all the transfer values of each step on its transfer path. If the paper then transfers to someone else it will transfer at a value equal to its current value (in the case of a candidate being eliminated) and its current value multiplied by the transfer value of that candidate (in the case of a surplus being transferred)

Effective Paper:
The number of votes involved in a specific action - for example, if there are 3 votes at a value of 1, and 2 votes at a value of 0.8 being transferred from one candidate to another, this is 4.6 effective papers.

First Preference:
The highest valid preference on the paper - the number one (1), or, if the only mark on the paper, a cross, tick, the word yes; a candidate's name written in the space allocated for specifying the first preference; or equivalent marking. The Senior Returning Officer may rule at his/her discretion that another marking or markings is/are a clearly expressed first preference. A paper has no first preference if the number zero appears on the paper, or if there is more than one cross, etc on the paper.

Quota:
The number of votes that a candidate needs to be elected. The Total Active Vote divided by the number of positions remaining to be elected.

Total Active Vote:
The number of votes still available to influence the vote. Equal to the initial total valid vote minus all votes or parts of votes remaining with a candidate who has been elected, and minus all votes deemed to be spoilt/blank/untransferable when transferring the votes of a candidate to be eliminated.

Transfer Path:
The route by which the remaining part of a ballot paper (i.e. the part not allocated to a candidate or candidates who have been elected) has reached the person currently assigned to. Usually expressed as a list of candidates.

Transfer Value:
The multiplier to current value given by a transfer path including a candidate is the transfer value of that candidate.

Valid Preference:
A clear statement of preference. For preferences other than the first preference, this must be a number from 2 onwards (the word "TWO" or another unambiguous numeric identifier is appropriate), a name written in the space indicating a preference from 2 onwards, or the equivalent for the voting system in use. A number that follows a break in the sequence (e.g. 1,2,4) or a name after a gap is left is not a valid preference, and a duplicated number or name is not a valid preference either on its first appearance or on subsequent appearances. It is possible for a paper to have some valid preferences and some non-valid preferences. A paper that has no valid preferences remaining is called spoilt/blank/untransferable.

This system is based upon the Single Transferable Vote system as proposed by the Electoral Reform Society in 1997. The system of transfering of surpluses has been modified in a manner similar to Meek's 1969 ruleset, in accordance with established practice at Durham Students' Union. The system for election of the Re-open Nominations candidate is taken from the election regulations of the National Union of Students. The system for dealing with constraints is based on the system used by the General Synod of the Church of England.

The authors are also indebted to the various former Senior Returning Officers of Durham Students' Union for observations and suggestions on the Single Transferable Vote System over the years.

† The authors believe that, for certain combinations of constraints, preferences and candidates, it may be impossible to achieve a result. However, we have yet to find an example of this. We expect that the first time someone tries an appropriate set of constraints, the electorate will delight in casting preferences to suit.