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Voting matters - Issue 7, September 1996

STV and Equality of Preference

C H E Warren

The Single Transferable Vote is a preferential voting system, in which the voter has to list the candidates in the order in which he prefers them.

One of the questions which is asked is whether a voter should be permitted to express an equality of preference between two candidates whom the voter assesses as equal in his judgement. My view is that the expression of equality of preference should be permitted in principle, although of course it would complicate both the voting and the subsequent count.

If a voter does express an equality of preference between two candidates A and B, then it is assumed that this is tantamount to his expressing two half-votes with non-equal preferences, one half-vote for A followed by B, and the other half-vote for B followed by A, but the half-votes otherwise identical.

However, Bernard Black is concerned that, if equality of preference is permitted, a voter may see neither of his equal preferences elected, whereas if the voter had given one of his two a clear preference then at least he would have got that one elected.

The following example of an election for 3 seats from 6 candidates by 30 voters, for which the quota is 7.5, exemplifies Black's concern. 29 of the voters vote as follows:

      1 AB
      1 BA
      9 CAB
      1 CEF
      9 DBA
      1 DEF
      3 EF
      4 F
The thirtieth voter is undecided between A and B. If this thirtieth voter votes AB, or votes BA or expresses an equality of preference between A and B, then the votes after the surpluses of C and D have been transferred are:
       AB         BA         ½AB + ½BA
       A  4.25    A  3.25    A  3.75
       B  3.25    B  4.25    B  3.75
       C  7.5     C  7.5     C  7.5
       D  7.5     D  7.5     D  7.5
       E  3.5     E  3.5     E  3.5
       F  4       F  4       F  4
We see that if the voter gives a clear preference for either A or B, then that one gets elected, because the other one is now eliminated and his votes then transferred to the preferred one. However, if the voter expresses equality of preference, then E is now eliminated, and E's votes then transferred to F who is elected, so that neither A nor B is elected. Hence Black's concern is justified.

The main benefit that is likely to arise from permitting equality of preference, as Douglas Woodall has said, is not for voters who are undecided between their top preferences, but for voters who want to put certain candidates as their bottom preferences, below a whole lot of candidates whom they do not know much about, but for whom being able to give equality of preference would be ideal.

David Hill has shown, in an unpublished paper, that, in a real election, this middle group of candidates whom the voter does not know much about is more likely to be of relevance with Meek counting than with Warren counting, because with Warren counting the count does not extend down to this middle group of candidates.


  1. B L Meek, A new approach to the Single Transferable Vote, reproduced in Voting matters, Issue 1, pp 1-10, March 1994.
  2. C H E Warren. Counting in STV Elections. Voting matters, Issue 1, pp12-13. March 1994.

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