Voting matters - Issue 7, September 1996

Meek style STV - a simple introduction

I D Hill

Until recently, David Hill was Chairman of the ERS Technical Committee

For its 1996 Council election, ERS used the Meek counting rules, instead of the Newland and Britton rules that are suitable for counting by hand. Now that there is sufficient availability of computers, I believe that ERS owes it to itself and to its members to use the best rules of which we are aware.

However many people seem to be muddled as to what this involves and some seem to be sadly misinformed. It is therefore desirable to have available a simple listing of what is the same and what is different in these systems.

It needs to be said clearly that there is no intention of abandoning STV. The system adopted (taking its name from B L Meek who first proposed it) retains all the essential features and aims of STV, but uses the power of modern computers to get a closer realisation of the voters' wishes, better meeting all the traditional STV virtues.

Some of the main changes were mentioned by Robert Newland in Comparative Electoral Systems, section 7.8(c). He wrote that these further refinements 'which would be likely rarely to change the result of an election but which greatly lengthen the count, are not recommended'. At the time, that was probably a reasonable judgement but information gained since then has shown it to be untrue that the result would rarely change, whereas lengthening the count is unimportant when counting is by computer where, either way, the counting time is trivial compared with the effort needed to input the data.

Meek style STV - what is the same?

• 1. Each voter votes by listing some or all of the candidates in order of preference.
• 2. Each voter is treated as having one vote, which is assigned initially to that voter's first-preference candidate.
• 3. A quota is calculated, as the minimum number of votes needed by a candidate to secure election.
• 4. If a candidate receives a quota of votes or more, then that candidate is elected, and any surplus votes (over the quota) are transferred to other candidates in accordance with the later preferences expressed by the relevant voters.
• 5. If, at any stage of the count, no surplus remains to be transferred, but not all seats are yet filled, then the candidate who currently has fewest votes is excluded. Votes assigned to that candidate are then transferred to other candidates in accordance with the later preferences of the relevant voters.

Meek style STV - what is different?

• 6. All surpluses are transferred simultaneously instead of in a particular order.
• 7. Surpluses are taken, in due proportion, from all relevant votes, not only from those most recently received.
• 8. To make that work properly it is necessary to give votes to already-elected candidates and not "leap frog" over them. This does not waste votes as the same number are transferred away again, but now in due proportion to all relevant votes.
• 9. Whenever a candidate is excluded, the count behaves as if that candidate had never existed (except that anyone previously excluded cannot be reinstated).
• 10. Whenever any votes become non-transferable, the quota is re-calculated, based on active votes only. This lower quota then applies not only for future election of candidates, but also to already-elected candidates giving them all new surpluses.
• 11. No candidate is ever elected without reaching the current quota.
• 12. For surpluses, every relevant vote goes to the voter's next choice, at fractional value. If there is no next choice, the fraction becomes non-transferable.
• 13. At an exclusion all the relevant votes are dealt with at once. There is no doing one little bit at a time.
• 14. The only disadvantage is that it is too tedious to do by hand, but has to be by computer.

Examples

1. A very simple, though artificial, example of the superiority of the Meek method is seen in 4 candidates for 3 seats. If there are only 5 voters and the votes are: 2 ABC, 2 ABD, 1 BC it is obvious to anyone, whether knowing anything of STV or not, that the right solution must be to elect A, B and C, as the Meek method does, yet traditional hand-counting rules elect A and B but declare the third seat to be a tie between C and D.
2. In a real election held recently, I shall call 4 of the candidates A, B, C and D of whom at the last stage, A and B had each been elected with a surplus, C had been excluded and D was still continuing, to be either the last elected or the runner-up. Four of the votes gave preferences as ABCD, ACBD, CABD and ABD. As C had been excluded, these became identical votes, each now having A as first preference, B as second and D as third. The Meek method would have treated them identically, but the rules actually in use gave D wildly different portions of these votes, as follows:

   Vote      Rules as used                Meek rules
        Portion of vote assigned to  Portion of vote assigned to
           A    B   C    D            A     B    C    D
   ABCD  0.72 0.28  -    -          0.471 0.285  -  0.244
   ACBD  0.72  -    -   0.28        0.471 0.285  -  0.244
   CABD   -    -    -   1.00        0.471 0.285  -  0.244
   ABD   0.72 0.28  -   -           0.471 0.285  -  0.244
   

   The variation between all of the vote going to D, and none of it doing so, is really startling.