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PR-Squared

Julian D. A. Wiseman

Abstract: PR-Squared is a new electoral system. It typically elects a majority government; it elects one local MP from each constituency each of whom is dependent on the local vote; yet still ensures that if two parties receive equal votes then they receive equal seats. Hence it has the advantages of first-past-the-post, and yet still has the 'fairness' of proportional representation.

Contents: PDF version, Publication History, Introduction, The 1997 election under PR-Squared, The Prime Minister's Requirements, Other Advantages, Criticisms

Publication history: This paper was sent to the The Independent Commission on the Voting System on 14th February 1998, and has been privately circulated since. The acrobat version is the original, the HTML versions contains minor alterations for simplicity of formatting. Usual disclaimer and copyright terms apply.


[ This paper has been superseded by PR-Squared: A New Description, effective September 2001.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

PR-Squared

Introduction

PR-Squared is a new electoral system. It typically elects a majority government; it elects one local MP from each constituency each of whom is dependent on the local vote; yet still ensures that if two parties receive equal votes then they receive equal seats. It works as follows:

As a first example, recall that in the 1983 election the three large parties split the vote in the proportion 44.5% to 28.9% to 26.6%. Seats would have been allocated in proportion to the squares of these numbers: 1980.25, 835.21 and 707.56. Scaling the ratio of the squares so that they total 650 seats gives 365.4, 154.1 and 130.5. These would be rounded for an actual seat allocation of 365, 154 and 131: a majority of 80 for the largest party.

The following table shows the 1997 election in greater detail:

PartyVotesVotes SquaredUnrounded seatsActual seats
Labour12,917,988166,874bn388.65389
Conservative9,600,94092,178bn214.68215
Liberal Democrat4,724,62622,322bn51.9952
Referendum Party811,679659bn1.531
Scottish National Party617,260381bn0.891
Labour Co-operative599,423359bn0.841
Ulster Unionist Party258,34967bn0.160
S. D. & L. P.192,06037bn0.090
Plaid Cymru161,03026bn0.060
Sinn Fein126,92116bn0.040
D. U. P.107,34812bn0.030
UK Independence Party106,00111bn0.030
otherssmallsmallsmall0
(Assumes that the vote totals were as 1st May '97, assumes that the three largest parties would have fielded candidates in every constituency, and that the Speaker was an independent.)

And who would have won which seat? As a randomly-chosen example, in Sedgefield the Labour Party candidate received 33526 votes, against 8383 for the (second-placed) Conservative Party candidate. This would have been sufficient to ensure that the "happiness-maximisation" allocated this seat to the Labour candidate in this constituency; and if in this constituency fewer than 23804 of those who voted Labour had stayed a-bed that day, then this seat would still have been held by the same candidate.

This electoral system satisfies the requirements specified in the Commission's terms of reference:

The Economist thought that the Prime Minister's list of requirements was "a bit like ... having your cake and eating it too". But it can be done, and PR-Squared is how.

There are five other advantages that should be mentioned here.

Criticisms

Five criticisms have been levied at PR-Squared, and because I might not have the chance to reply to any criticisms in person, I shall briefly reply to them here.

In summary, PR-Squared is an electoral system in which voting is simple, in which voters choose a local MP, which gives stable government, but which treats equally parties with dispersed and parties with concentrated support. It may not be perfect, but it is materially less imperfect than any other electoral system.

Julian D. A. Wiseman, 14th February 1998

[Also available is a worked example of the happiness maximisation calculation, some technical notes relating to PR-Squared, and a description of PR-Squared in the context of New Zealand.]


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