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*Julian D. A. Wiseman*

**Abstract:** This short paper contains various technical notes relating to PR-Squared, and to simulating PR-Squared. It is assumed that readers are already very familiar with PR-Squared (or with PR-Squared in the context of New Zealand), and are fully conversant with the worked example of the calculations.

**Contents: **
Publication History,
Simulating PR-Squared using results from a First-Past-The-Post election,
Bye-Elections,
On the death of a candidate.

**Publication history:** Only here. Usual disclaimer and copyright terms apply.

**[ This paper has been superseded by PR-Squared: A New Description, effective September 2001. ]**

This short paper contains various technical notes relating to PR-Squared, and to simulating PR-Squared. It is assumed that readers are already very familiar with PR-Squared (or with PR-Squared in the context of New Zealand), and are fully conversant with the worked example of the calculations.

**Simulating PR-Squared using results from a First-Past-The-Post election**

Under First-Past-The-Post, what would happen if, in a particular constituency during a general election, no candidates stood? There ought to be a rule, even if only for completeness. Of course, in practice, the parties' incentive is such that no rule is needed. Parties want seats, and will stand in any in which they have a reasonable chance of winning.

Likewise, in PR-Squared, what if, in a particular constituency, no seat-winning party put forward a candidate? (Ie., what if, in a particular constituency, all the candidates come from local parties?) There ought to be a rule, but in practice, the parties' incentive is such that this rule will never be needed. Parties want votes, and any party with a chance of winning seats anywhere will want every vote it can get in every constituency.

However, this question is relevant when one tries to map First-Past-The-Post results onto PR-Squared. Under FPTP, the Conservatives, Labour, and the Liberal-Democrats gain little by standing in Northern Ireland. And historically, they haven't. But under PR-Squared, every vote is useful, irrespective of its geographic origin. So the big three parties will want to field candidates in every constituency, and this rule will be redundant.

So how does one map First-Past-The-Post results onto a PR-Squared election? Ideally, one would employ a tame psephologist, who would be able to say how people would have voted had PR-Squared been in place, simultaneously assuming that the parties had responded to the incentives that PR-Squared would have given them. That is a big task, and inevitably the results would be controversial.

The following is more realistic. Parties have put forward candidates in constituencies. For each party, for each constituency where that party did not put forward a candidate, assume that the party did put forward a candidate (a 'deemed null candidate'), but that this candidate received zero votes. This assumption allows one to use FPTP results to crudely simulate what would have happened under PR-Squared.

As a legalistic detail, an actual implementation of PR-Squared would state that seats won by a deemed null candidate would remain empty. But it should be emphasised that this is a petty detail, included only for theoretical completeness. The major parties' incentive to stand in every seat is so strong that this symptom of FPTP (there being seats contested only by local parties) would not be repeated under PR-Squared. Rephrased, mapping First-Past-The-Post voting behaviour to PR-Squared is counter-factual, even if it is sometimes illustrative.

**Bye-Elections**

Because First-Past-The-Post handles each constituency in isolation, it handles a bye-election very elegantly.

The situation is less clean under PR-squared. There are two obvious possibilities.

The first possibility is that bye-elections don't happen. Empty seats would remain empty until the next general election.

The second possibility is that a FPTP-style bye-election is held.

This second possibility requires great care. PR-Squared gives parties an incentive to negotiate coalitions before an election, and to court votes without regard to geography; it gives candidates an incentive to encourage both the local and the national votes; and gives voters an incentive to vote for a party with a realistic chance of forming a government.

Care must be taken to ensure that the rules about bye-elections do not create any unwanted incentives.

In the UK, at least one heavily-armed terrorist and racketeering organisation has a political front. Such support as it has is geographically narrow, and under First-Past-The-Post it wins only the constituencies of Belfast West and Ulster Mid. (American readers, rightly appalled, are reminded that in 1994 Washington DC re-elected Marion Barry as Mayor.)

Under PR-Squared, it is highly unlikely that these seats would be won by the terrorists' front organisation. But they would win a bye-election. This gives the terrorists an incentive to 'cause' a bye-election. This is not an idle concern: during their so-called 'cease-fire' the terrorists still continued to attempt assassinations. In the past, the 'preferred' method of killing politicians has been the car-bomb: this is not an incentive that an electoral system should be creating.

So death by murder should not cause a bye-election. But if resignations cause a bye-election, then the terrorists will have an incentive to kill the MP's children one at a time, until the MP 'gets the message' and resigns. This is not an idle concern: in the past the terrorists have placed a bomb in a trashcan outside a McDonalds (apparently a shopping mall constitutes a 'commercial target'). Hence it should be assumed that if killing an MP's children is useful to the terrorists, it will be done. This is not an incentive that an electoral system should be creating.

These are, alas, unsavoury incentives to consider, but this unsavouriness actually makes it all the more important that they be considered carefully.

So, if there are to be bye-elections, they should be triggered only by the death from natural causes of a sitting MP, and should be conducted under the current FPTP rules.

[This is an apposite place to remark on a factual error in the original description of PR-Squared. It said that, in the US, "seats vacated by resignation or death remain vacant until the next general election". This is incorrect: they are filled by appointment.]

**On the death of a candidate **

What should happen if a candidate dies, or is otherwise disqualified, between the closing of nominations and the polling date? To withdraw the candidate from the poll denies voters the opportunity to vote for that party. This seems unfair.

The natural course is to allow the dead candidate to remain a candidate: for electoral purposes the candidate will be deemed to have died immediately after the election. If the dead candidate is elected, the bye-election rules come into force.

*Julian D. A. Wiseman, March 2000*

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