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# Voting matters - Issue 11, April 2000

## Incorporating X-voting into Preference voting by STV

#### C H E Warren

Hugh Warren is a retired mathematician.

### 1. Introduction

One of the thing said by many people, particularly by those who have used the X-voting system for many years, and by journalists, is that preference voting by STV is difficult to understand. However much advocates of preference voting by STV may find this view unjustified, and itself difficult to understand, they must accept that it is a view that is expressed, and no doubt genuinely held by a lot of people.

The purpose of this paper is to make the point that, instead of trying to win over the X-voting enthusiasts to the STV way of voting, consideration should be given to allowing the X-voting enthusiasts into the preference voting by STV system.

### 2. The Basic Idea

The basic idea is that, in addition to those who wish to vote in the STV way by showing preferences 1, 2, 3, .. in the recognized way, those who wish to vote by putting an X against the candidates they wish to see elected should be allowed to do so, provided of course that they do not put an X against more candidates than the number to be elected.

### 3. Interpretation of the Ballot Paper

With some ballot papers marked in the STV way by preferences 1, 2, 3,.. and some marked by an X against a number of candidates, the way in which it is suggested that the two may be accommodated is to treat the X votes as equal preference for a first preference candidate.

The allowing of equal preferences in the STV system is a matter which has been talked about in the past, but usually ruled out on the grounds that it would make an already complicated system more complicated. However, to allow equality of preference to be exercised on the first preference only should not lead to seriously greater complexity.

### 4. The count

The count is not of course a matter with which the voters have to concern themselves, provided that they can be assured that it is being done in a fair way.

If there are, say, 10 candidates to be elected, then at the first stage of the count, each candidate will have a number of votes of value 1 from the preference votes, and a number of votes of value 0.1 from the X-votes.

From this point onwards the count can proceed just as if it were a regular STV count, except that, of course, when surpluses have to be transferred, it will only be the preference votes for which the amount retained will be reduced, thereby allowing some of the vote to be transferred to the next preference.

### 5. Conclusion

The advocates of preference voting by STV have been trying for over 100 years to beat the advocates of X-voting. There is an adage which says If you can't beat them, join them. What is proposed here is not so much a case of joining them as incorporating them.

It is possible that, in the course of time, the X-voters will see that their interests could be better served by going across to preference voting, but the proposal is not to try and force STV on them.

### Editorial Comment

The above proposal effectively merges the voting methods of First Past The Post and STV, so that the user can choose which method to employ. However, given that an STV-style count is to be undertaken, it seems logical to make an extension to Warren's proposal as follows: Allow the voter to place any number of X's on the ballot paper. Each X counts as a first-preference value of 1/n, where n is the number of X's. With this proposal, an election for a single candidate in which the voter judges two candidates as of equal merit and no others of interest, two X's can be used, counting as 0.5 for each. More significantly, in my own experience for some elections, one can have, say, 6 seats to fill, but one has knowledge of only, say, 3 candidates. Under conventional X-voting (and Warren's proposal) one could place 3 X's and lose half of ones voting power. Under this suggestion, 1/3 of a vote would go to each candidate and there would be no loss of voting power.

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