David Hill is Chairman of the ERS Technical Committee.
In Voting matters issue 3, B A Wichmann reported that, using data sampled from real voting patterns, 'Meek violates mono-raise much more than ERS'. Is this something that Meek supporters should worry about?
We know: (1) that all electoral systems have to suffer from some anomaly or other; (2) that STV's anomaly is that it can fail on monotonicity i.e. a change of vote in a candidate's favour can cause that candidate's defeat; (3) that traditional rules do not even look at a voter's second or subsequent preferences if the first preference is elected later than the first count. So the way to make Meek run into an anomaly where traditional rules do not is to find a case where monotonicity trouble occurs among the preferences that such rules ignore.
Although the numbers of such violations reported are indeed considerably greater for Meek, it should be remembered that these arise from examining many thousands of pseudo-elections, and the proportions of occasions are small. For example, the greatest number of Meek violations found was 141 from a data set called R038, but that number comes from 12421 comparisons of one pseudo-election with another. Furthermore each of these pseudo-elections has only 20 voters, which is very few for electing to 5 places from 17 candidates. So the degree of trouble should not be exaggerated, but nevertheless 141 Meek violations were found and no ERS violations in comparisons derived from that particular data set.
It should be borne in mind that the method used to form these pseudo-elections from any given data set involved sampling each time from the same set of votes and thus there are many repetitions, of particular votes being used more than once. This makes it difficult to judge what the results would be from truly independent samples.
I have examined one case in detail to see what it shows and, to avoid all bias in choosing which case to examine, I decided to take the first one found in the data sets available to me. This involved 14 candidates (A - N) for 7 seats, and contained among its votes one for EJICDNG in that order of preference. Those elected are EFGHIJN by Meek rules, but if that one vote is changed to read EIJCDNG (all other votes being unchanged) which should be to I's advantage, those elected become CEFGHJN, and I has lost the seat to C.
The current ERS rules elect EFGHJCN with 25% probability, EFGHJAI with 58% probability and EFGHJCI with 17% probability, depending upon how two random choices come out. That they reach the same result, given the same random choices, irrespective of whether the one vote is as in the original data set or changed, is inevitable because the only vote changed is from EJICDNG to EIJCDNG. At the first count E has 3 votes where the quota is 3.13 and so is not yet elected. At the second count 2 votes starting GE are transferred to E each at value 0.55, to give E a total of 4.10 and a surplus of 0.97, but that surplus is redistributed solely from the 2 newly-received votes. Whether J or I comes next in the vote that is changed is never even looked at.
Using Meek rules with either set of votes GEFHJ are elected and BDKLM are excluded. At that point with the original votes A has 2.145 while C has 2.100, C is excluded, N and I elected and A left as runner-up. With the modified votes, A has 2.053 while C has 2.060, so A is excluded and nearly all A's votes pass to C. This results in C and N elected, I as runner-up. Either way it is a very close-run thing, but who is ahead, of A and C, happens to reverse and the result unfortunately causes the observed lack of monotonicity.
Should all this worry Meek supporters? I think no more than the fact that lack of monotonicity is an upsetting feature of all STV. We could get rid of that feature by abandoning STV altogether and refusing ever to look at preferences beyond the first, but we know that what is lost by so doing far exceeds what is gained. Similarly if we do not look at later preferences some of the time (even when they are relevant) then we can get rid of the feature some of the time, but again, what is lost by doing that far exceeds what is gained. In general, looking at voters' later preferences whenever they are relevant helps to meet those voters' wishes; that it is occasionally troublesome is a pity but cannot be helped. It remains true that the voter concerned could not possibly anticipate such an effect, so it cannot lead to tactical voting, and also that even if such votes were to arise in reality, the lack of monotonicity would never be noticed except by detailed research of the ballot papers such as is hardly ever performed.
In case anyone wishes to examine this data set further, here are the original votes in Wichmann-Hill format. For those not used to this:
14 7 means 14 candidates for 7 seats;
1 5 10 9 3 4 14 7 0 means a vote for candidates 5 10 9 3 4 14 7 in that order, the initial 1 meaning 1 vote and the 0 terminating it, and so on;
Following all the votes there is an extra 0 to terminate them all and then the names of candidates in the order of their reference numbers, and a title for the election.
To get the modified votes, change the first one to start 1 5 9 10 instead of 1 5 10 9, and change the title on the last line.
14 7 1 5 10 9 3 4 14 7 0 1 3 5 13 12 7 1 4 8 0 1 8 7 10 12 13 3 6 4 14 11 9 1 2 5 0 1 5 11 14 7 9 0 1 6 7 10 11 12 3 0 1 8 7 5 13 12 14 6 3 1 2 0 1 6 7 10 12 0 1 7 9 5 8 10 14 3 4 1 2 6 11 12 13 0 1 10 7 12 5 8 3 6 9 14 0 1 7 5 11 6 0 1 1 12 3 14 8 6 13 5 0 1 7 5 12 10 14 4 3 9 6 0 1 9 0 1 7 6 10 12 9 14 0 1 1 12 3 8 14 6 5 13 0 1 10 1 12 8 6 3 9 0 1 8 5 12 3 9 1 7 13 10 11 4 6 0 1 3 4 7 10 0 1 7 10 8 12 3 4 9 14 1 13 2 6 11 5 0 1 14 11 5 10 0 1 14 13 2 1 3 9 12 4 5 8 0 1 7 8 9 5 6 0 1 7 12 4 9 8 14 3 11 0 1 5 14 7 0 1 6 7 10 12 0 0 "A""B""C""D""E""F""G" "H""I""J""K""L""M""N" "Original"