Hugh Warren is a retired aeronautical engineer, past member of the ERS Council and a present member of its Technical Committee.
Counts have been done in many ways, and in some peculiar ways by some well-meaning, but unversed, enthusiasts for STV. One of the commonest methods of conducting the count, and indeed the method that the Electoral Reform Society uses, is that given by Newland and Britton. Their paper tells one how to conduct a count by their method, but not why they make many of the arbitrary decisions that they do. Woodall has suggested that they are made for expediency - to simplify the count - and he goes on to propose another method, which he advocates whenever computer counting is used. As Woodall points out, his method would be prohibitively long with human counting. As Woodall also states, a differently worded but an exactly equivalent method to his had been proposed by Meek in 1969.,
The object of this paper is, first, to consider some of the principles that are felt to be important in deciding upon a method for conducting the count, and then to go on and propose a method that meets these principles.
The second principle concerns the transference of a voter's vote to the preferences later than his first preference. The voter needs to be assured that his later preferences will in no way upset the voter's earlier preferences. Equally a voter's later preferences should not be considered unless, in regard to each earlier preference candidate, either the voter has borne an equal share with other voters who have voted for that candidate in giving him the necessary quota, or that earlier preference candidate has been eliminated. The way in which Newland and Britton conduct a count does not meet this principle.
The third principle concerns the elimination of candidates. Unfortunately no-one appears to have proposed a principle in this regard. So what is usually done is that, when no candidate has a surplus above the quota, in order to allow the count to continue, the candidate whose vote is least is eliminated.
The candidate whose vote at the end of the first stage is least is eliminated. This means that, wherever his name appears on a ballot paper, it is 'passed over', and, in effect, all the later preferences are 'moved up one'. Elimination of a candidate will usually cause the votes for some other candidates to exceed the quota. The amount to be retained by each candidate is then reduced to such lower value as will give each candidate just the necessary quota. Voters who have voted for these candidates with reduced amount retained will then find that they have more vote remaining for transference to later preferences. Proceeding in this way, at the end of each stage of the count, some candidates will have just the quota, whereas the remainder will have varying amounts of vote less than the quota.
Eventually the number of non-eliminated candidates will be reduced to one more than the number to be elected. When the amounts to be retained are now recalculated so as to reduce each candidate's vote to the necessary quota, all candidates will have just the quota, so the one candidate who has an amount retained of just 1 is the one eliminated. The remaining candidates are deemed elected.
If at any stage a ballot paper does not contain sufficient preferences for transference to be made, then the balance of vote is ascribed 'non-transferable', and the quota is recalculated excluding the non-transferable vote.
The main question that the proposed method of conducting the count poses is: how does one decide upon the amount to be retained by each candidate at each stage? From what has been said, the amounts retained have to be such that, when the count is made, each candidate to whom an amount to be retained of less than 1 has been assigned achieves just a quota. The problem of finding the amounts retained, and the associated quota, is a mathematical one which is relatively straightforward, even if protracted, but which a computer can help to solve. Here we are concerned only with the principle, not with precisely how the task be done. However, it is not necessary for everyone to know how to assign the amounts retained. As Woodall has exemplarily pointed out, it is only necessary for anyone to be able to check that the assigned amounts retained do in fact achieve the desired result.