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# Voting matters - Issue 3, December 1994

## The comparative steadiness test of electoral methods

#### I D Hill

David Hill is a regular contributor to Voting matters.

In comparing one electoral method with another it is useful to examine their comparative steadiness. It should be noted that it is only a comparative test and does not give a "goodness" score for any individual method on its own but only for one method relative to another. Nor does the fact that any method comes out as the better of the two by this test indicate that it is necessarily better in any other way.

To use it, first run each method for the same number of seats and the same given set of votes and see whether they both elect the same candidates. If they do, this test is not applicable. Otherwise, see whether there is one or more candidate whom neither method elects. If there is no such candidate, again the test is not applicable. In particular, the test can never be applicable if the number of candidates is only 1 greater than the number of seats, but the fact that it is often not applicable does not destroy its value in those cases where it does apply.

If the test is applicable, then treat all candidates who failed to be elected by either method as withdrawn, and re-run each method. If each method continues to elect the same candidates as before, then there is nothing to choose between them on this test for this particular set of votes. If, however, one method makes no change in whom it elects while the other makes a change, then the no-change method gains a point in comparison with the other.

For example, if there are 5 candidates for 3 seats, and the votes are:

```        51 ABC
44 ABD
5 EABD
```
the current ERS rules will elect A, B and D whereas the Meek rules will elect A, B and C. They agree that E is not elected, so the comparative steadiness test treats E as having withdrawn and re-runs the election. Now the Meek rules still elect A, B and C, but the ERS rules switch to electing A, B and C too. Meek therefore shows greater steadiness for this particular set of votes.

While such artificial elections are important as illustrations, what most matters is which rules are steadier for real elections. Taking the 57 real elections that I have available, I find the test to be applicable for only 10 of them. In 4 of those, these two systems are both steady, neither changing its result when the relevant candidates are withdrawn. In the other 6, however, the Meek system remains steady but the ERS system changes. By this test, the Meek system seems to be superior, so far as the evidence goes, though a few more results in the same direction would help to make more certain that the difference is not just a chance effect.

It should be noted, of course, that discovering a lack of steadiness must not be used to change the result of a real election, which must always be in accordance with the rules as laid down for that election. The test is only for research purposes, not to interfere with a result.

Editorial Note: It is possible to apply the steadiness test even when an election gives the same result. This can be done by selecting random ballot papers from the election in the manner of the mini-elections in the previous paper. With the 100 mini-elections from the real election R006, 17 of these elect different candidates so that the steadiness test can be applied. Of these 17, none were steady for the ERS rules, while 13 were steady according to Meek. One mini-election could not be considered since a random choice was made. For the remaining 3 mini-elections, neither were steady, and in one case, the removal of the no-hope candidates causes the two algorithms to interchange the results!

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