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(Extract from a de Borda Institute discussion document, dated 5 September 2000, presented to Mr. George Howarth, MP)

The rules for PR-STV elections have been written and re-written on a number of occasions. For example, one of the first advocates, Mr. Hare, proposed his own quota, whereas these days, we are more acquainted with the one named after Mr. Droop. In general, however, we regard PR-STV as reasonably fair and, for a divided society, its benefits need little emphasis.

That is not to say, however, that the present rules are perfect; indeed, in one particular respect, they are erroneous, and hence this paper, for every society should try to improve its democratic structures as and when necessary, so as to ensure they are always as fair as possible. The error in the current rules relates to the fact that, in certain instances, the transfer value of a vote will be altered, and this appears to offend the very principle of proportionality upon which the system is supposedly based. We hope the following example will help to explain our argument: imagine, if you will, an election in which four of the candidates are A, B, C and D, and in which A has a surplus in the first count.

The value of A's transferable votes depends upon A's surplus divided by A's total vote. If, for example, her total vote is 10000 while the quota is 9000, she will have a surplus of 1000 votes, and each second preference will therefore have a transfer value of 0.1. If, then, 5000 of A's first preference voters give their second preference to B, he gets a transfer of 5000 x 0.1 = 500. If at the same time C gets 3000 of her second preferences, C gets a transfer of 300; and if D gets 2000, D gets 200. All of that is in accordance with the rules, and all thus far is both logical and fair.

In Principle

In Practice

1st count

2nd count

2nd count

A

10,000

- 1000

- 1000

B

+ 500

+ 500

C

+ 300

+ 300

D

+ 200

+ 200

Non-transferables

-

-

But what happens when, while 5000 of A's first preference voters give their second preferences to B and 3000 give theirs to C, the other 2000 voters express no second preferences at all? In this case, according to the rules, with only 80% of the votes transferable, the value of the transfer vote is adjusted. From a human rights point of view, there can be no justification for this adjustment whatsoever!

What happens is as follows: the value of the transfer vote is increased from 0.1 to 0.125, so B now gets a transfer of 5000 x 0.125 = 625 votes, while C gets a transfer of 3000 x 0.125 = 375 votes. In effect, therefore, those people who cast no second preferences are 'assumed' (in a mathematical sense) to have cast second preferences, in exactly the same proportion as those who did do so, and, as a consequence, in this particular example, there appear to be no non-transferable votes at all.

In Principle

In Practice

1st count

2nd count

2nd count

A

10,000

- 1000

- 1000

B

+ 500

+ 625

C

+ 300

+ 375

D

-

-

Non-transferables

200

-

The rules add a proviso to state that no candidate can receive a transfer greater than the original number of second preferences cast in his/her favour. In the example given, B receives 625 which is far less than the total of 5000 of A's second preferences cast in his favour, so it is deemed (by the rules) to be acceptable. 625, however, is still more than the fair figure of 500 and, as is well known, such relatively small mathematical differences can easily make all the political difference between success and failure!

We would now like to take the example one stage further, to see what can happen when B's theoretical transfer is greater than the number of A's second preferences cast in his favour. Imagine only 500 voters of A's 10000 first preference voters cast their second preferences for B, only 300 voters for C, and that all the remaining 9200 votes are, in theory, non-transferable. Such a situation could quite easily occur at the latter stages of many PR-STV counts. In principle, from a human rights point of view, the transfer value should still be 0.1, so B should now get a transfer of 500 x 0.1 = 50 votes, C should get a transfer of 30 votes, and all the other votes should be non-transferable, both in name and in fact.

What happens, however, is that the transfer value is again increased, but those two transfers, which would be 625 and 375 but for the above-mentioned proviso, are thus reduced to 500 and 300 respectively. These transfers of 500 and 300 are still greater than what they should be, namely, 50 and 30. Furthermore, in this third example, there will now be a non-transferable total, namely, 200; if the rules were fair, though, this last total would be 920.

In Principle

In Practice

1st count

2nd count

2nd count

A

10,000

- 1000

- 1000

B

+ 50

+ 500

C

+ 30

+ 300

D

-

-

Non-transferables

920

200

In principle, a vote's transfer value should depend only on the size of the surplus in relation to the size of the total vote. As the above examples indicate, transfer values in practice depend on the number of further preferences cast, and the value of Citizen Y's second preference for Candidate F, say, increases if Citizen Z, instead of giving a second preference to candidate G, say, decides to express no second preference at all. That cannot be correct; the effect of Citizen Y's second preference should not be so subject to the deeds of Citizen Z.

There is, after all, only one principle involved; it should not therefore be necessary to have two procedures and one proviso, one compact rule should suffice. Accordingly, the change we suggest would be a simplification.

The above paper was presented to Mr. George Howarth MP and, at his request, a delegation from the de Borda Institute then visited Mr. Denis Stanley, the new Chief Electoral Officer, in December, 2000. Despite the above arguments, however, the government has stated – 28th March 2001 – that it does not intend to consider any changes.

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