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Voting matters - Issue 11, April 2000

Tie-Breaking in STV

Earl Kitchener

It is a fundamental principle of STV that later preferences should not affect the fate of earlier ones; this encourages sincere voting, but means that some arbitrary or random choice must be made to break ties, which can give unreasonable results.

An extreme case can arise where there is one seat and the electors are the same as the candidates; for example, if a partnership is electing a senior partner. Each candidate may put himself first, and all, except candidate A, put A second. Under most present rules, one candidate then has to be excluded at random, and it may be A. There is no way of getting over this unreasonable result without looking at later preferences, and the system of Borda scores is probably as good as any; with N candidates, N-1 points are allotted to a first preference, N-2 to a second, and so on. If it were desired to increase the importance of early preferences, the interval between values could be increased for early preferences. Ties in this system would be very rare, and it could be used to break ties in the normal STV counting.

In the above example no candidate or voter could reasonably object to the result, but in a real election, reported by Hill, with four candidates for one place, the voting was:

    A B C  1
    B A D  1
    A C D B 1
    B C A  1
The quota is two, which both A and B have. Under the proposed system A, with nine, beats B's eight. The second voter may complain that his second preference, for A, enabled A to beat his first preference. If the second voter had known in advance how the others were going to vote, he would not have put A second; but it is not unusual in small STV elections for a voter to find that if he had known the other voters' intentions he would have voted differently. He has got his second preference in, so has not much to complain about. In view of the uncertainty of voting intentions it is doubtful whether the proposed rule would lead to insincere voting, and it would avoid the possibility of A being unreasonably excluded in the first example. It has the virtue of satisfying Woodall's "No support" property, that no candidate who is not listed by any voter should be elected unless every candidate who receives some support is elected.

Hill has described a Sequential STV system which deals in a more general way with the problem of premature exclusion of a candidate with few first preferences, but many other early ones; Hill does not recommend it, because of the breach of the rule against looking at later preferences. The present proposal, being confined to tie-breaking, might be less likely to lead to insincere voting, which is the main (and perhaps the only) objection to looking at later preferences.


  1. I D Hill, ERS Document TC 95/13, September 1995.
  2. D R Woodall, Properties of Preferential Election Rules. Voting matters, Issue 3 (1994), p10
  3. l D Hill, Sequential STV. Voting matters, Issue 2 (1994), pp5-7

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