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# Voting matters - Issue 10, March 1999

## The Handsomely Supported Candidate Ploy

#### C H E Warren

Hugh Warren is a retired mathematician

There is an electorate of 1400, who have to elect candidates to fill 6 seats, so clearly the quota is 200. The electorate is made up of 418 members of the Labour Party and 982 members of the Conservative Party. Labour should, therefore, get 2 seats, and the Conservatives 4.

The Conservatives put up 5 candidates - L, A, B, Z and Y. Candidate L is the Party Leader, and is handsomely supported because of his ability to hold the party together, despite its Europhile and Europhobe wings. Candidates A, B are on the Europhile wing, and Candidates Z, Y on the Europhobe wing. If all the Conservatives voted sincerely their voting pattern would be as follows:

```503 LAB
479 LZY
```
Whether the count is done by Newland & Britton, Meek or Warren, 4 Conservatives would be elected - L, A, Z and B. Not surprisingly the Europhiles get one more seat than the Europhobes because they are the slightly larger faction. 182 Conservative votes would be 'wasted', as would 18 Labour votes, thereby making up a quota of 200 votes in total which are perforce 'wasted' in any STV election.

However, the Europhobe Conservatives adopt the Handsomely Supported Candidate Ploy. Above everything else they want to see their leader, Candidate L, elected. But they argue that their support of 479 voters should be enough to ensure that Candidate L is elected if they insincerely give him their second preference only, even if those Europhiles are even more insincere and don't give Candidate L a preference at all!

In practice the Europhiles vote sincerely, so the voting pattern turns out to be:

```503 LAB
479 ZLY
```
If the count is done by Newland & Britton or Meek, the Europhobes' ploy pays off, because the 4 Conservatives elected are L, A, Z, Y. So, by their ploy, the Europhobes have 'captured' the fourth Conservative seat for the Europhobes.

Of course one can not guarantee that one will always gain an advantage by adopting the ploy, but it is always worth trying on, for one can not lose provided it is done prudently, as in the example here, by not relegating a handsomely supported candidate to a preference where one has not the support to get him elected no matter what other voters do.

The Handsomely Supported Candidate Ploy, if practised by a group, can lead to a discernible gain, as just demonstrated. However, the principle, that one can gain an advantage by not giving one's first preference to a handsomely supported candidate, holds even for voters voting individually.

Consider an election for nine seats by 100 voters, so the quota is 10, in which the voting pattern is as follows:

```39 H...
19 M...
41 ....
1 HM...
```
H is clearly a handsomely supported candidate, and M a moderately supported candidate. These two candidates do not figure in the voting pattern other than in the places shown.

If the count is done by Meek the individual voter HM... will have 0.37025 of a vote to pass on to his third preference after H and M have retained just the votes necessary to attain the quota.

However, if the individual voter decides not to give his first preference to the handsomely supported candidate H, who would be his sincere first preference, but instead to vote MH..., then he finds that he has 0.37342 of a vote to pass on to his third preference.

It is the principle that is salient from this example - that one can get more out of one's single vote by not giving one's first preference to a handsomely supported candidate.

### References

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