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A Criticism of the Jenkins Report

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, Author, The Commission’s Evidence, PR-Squared, The Commission Was Misled, Conclusions, Footnote On Monotonicity.

Publication history: Privately circulated only — no formal publication. Usual disclaimer and copyright terms apply.


In late October The Rt Hon Lord Jenkins of Hillhead OM delivered to the Home Secretary The Report Of The Independent Commission On The Voting System; he having been invited to chair this Commission in December 1997. The Commission’s terms of reference requested “an alternative to the present system”, with the obligation to “observe the requirement for broad proportionality, the need for stable government, an extension of voter choice and the maintenance of a link between MPs and geographical constituencies”.

The Report is an interesting and detailed comparison of a number of voting systems. However, the Report is not — and does not pretend to be — a complete treatment of voting systems. Several voting systems are omitted or compared incompletely. Most obviously, the Commission’s Report does not fully examine the merits and demerits of the current system, because the terms of reference specify “an alternative”. But one particular omission fatally wounds the Report: a new voting system called PR-Squared is not discussed, despite that fact that it well satisfies the four simultaneous equations in the second paragraph of the terms of reference. This criticism explains why the omission so greatly undermines the worth of the Commission’s conclusions, and attempts to identify the reason for the omission.

The author

Before discussing the omitted system, and the reasons for its omission, the reader is asked to allow a few words about the author of this criticism. The author is also “independent”, in the sense of not being a member of or employed by a political party, nor having ever stood for any form of public office. (In this sense more ‘independent’ than some of the members of the “independent Commission”.) However, the author has devised a new voting system, which has all the merits of the current system, yet still has the fairness of Proportional Representation. Those who suggest “he would say that, wouldn’t he” are referred both to ¶24 of the Report, and also to the description of PR-Squared [since superseded by PR-Squared: A New Description]. The author is British, and is employed as a researcher in financial markets.

The Commission’s evidence

The Commission’s Report comes in two volumes. The first, containing much excellently crafted language, gives the Commission’s conclusions. The second volume, published on CD-ROM, is described as containing “items of key evidence”. It actually contains submissions from political parties / fora, submissions and correspondence from Members of Parliament, submissions from academics, from representative / campaigning groups and from commentators, listed in that order in the table of contents. Those of a cynical disposition will notice that political parties come before MPs, and also that, although the majority of the “over 1500 written submissions” were from the public, the public is entirely unrepresented in the Commission’s compendium of evidence.

Amongst the unrepresented evidence is a description of PR-Squared dated 14th February 1998, that was sent by the author of this criticism. That description is attached as an appendix to this criticism. Perhaps some readers of this criticism will not like PR-Squared, but nonetheless all should concede that it has a distinctive set of advantages, and hence that, at a minimum, it (and its obvious variants) should have been considered, and that any rejection of it or them should have been fully justified.


PR-Squared is a new electoral system, designed for the UK’s House of Commons. It has two novel features: vote squaring; and a seat assignment mechanism called “happiness maximisation“. The Commission considered neither PR-Squared as a whole, nor its two novel features.

PR-Squared 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 numbers of votes then they receive equal numbers of seats. In brief, it works as follows:

As an 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, with the opposition seats split much more equitably than under FPTP .

Again making the counter-factual assumption that voting habits would be unchanged under PR-Squared, then 1997’s Labour landslide would have resulted in a majority of 119. In 1992 the Conservative majority would have been about 50; in 1987 of almost 64; in 1983 80; in 1979 of 66 seats; and in October 1974 Labour would have had 308 of the 635 seats.

So under PR-Squared: equal votes mean equal seats (“broad proportionality”); there is usually a majority (“stable”) government; votes cast in ‘safe’ seats have exactly as much effect on the national result as votes cast in marginal seats (“voter choice”); and yet all MPs are constituency MPs (“maintenance of a link”). Further, PR-Squared is monotonic*, though this property is so obvious that I neglected to mention it in the original description.

PR-Squared and its advantages are discussed in more detail in the appendix.

There is a natural variant of PR-Squared that might well have appealed to the Commission, which works as follows. Pure Proportional Representation with a cutoff would be used regionally (each region containing about a dozen constituencies). Within each region, seats would be assigned to parties using happiness maximisation. (Although note that this author would favour a more majoritarian system than this variant.)

The Commission was misled

The Commission did not consider PR-Squared and its variants because the Commission was misled. From volume 2 of the report it is possible to identify how this happened.

Professor David Butler writes “I was asked by the Jenkins Commission to consult a few academic students of elections to see if they could reach consensus on some technical questions about systems of proportional representation” (page 1 of acdmcs01.pdf). Amongst the most important questions asked (of the Butler Group or indeed of anybody) by the Jenkins Commission was:

E.1. Are there systems other than AMS, AV/SV, and STV that the Commission should be considering

Rephrased: “what are the choices”. The academics replied:

1. The Commission might want to consider a national list system, if only to reject it.

2. The Commission might want to put forward a ‘tailor-made’ system and not confine itself to ‘off-the-peg’ models. For example, it could pursue an open party list system with about five members per constituency. The broad proportionality of such a system is evident in the work of Dunleavy et al. {Dunleavy et al. 1997].

3. The Commission might wish to refer to parallel systems (as in Russia) if only to dismiss them.

4. The Commission might want to consider versions of AMS using open lists to elect top-up MPs.

It is now apposite to admit mea culpa. Because I am not a professional academic, PR-Squared has not been published in any academic journal. Naïvely, I wrote directly to the Commission, not realising that the list of candidate systems would be constructed away from Clive House.

But the academics’ error was not a once-off:

E.6. Are there systems which discourage a multiplicity of parties?

the reply once again missing the existence PR-Squared:

The lower the threshold the more the parties. FPTP is probably the most discouraging, but it can allow in small parties with strongly localised support to secure disproportionate representation.

On page 7 of acdmcs07.pdf Professor Ron Johnston and David Rossiter reach the punchy conclusion:

… with any electoral system based on constituencies, you cannot get away from the effect of geography

a conclusion which suffers from the one drawback of being completely wrong. Under PR-Squared every MP is a constituency MP from a single-member constituency, yet redrawing the boundaries would have no effect whatsoever on the number of seats won by each party. (So, under PR-Squared, boundary commissions would be entirely depoliticised, and constituencies could be more ‘natural’ and less like the “artificial creation” referred to by Gareth Thomas MP in mp-24.pdf.) Anyway, my fault for never having written to Professor Johnston and Mr Rossiter.

Drs David Farrell and Michael Gallagher (page 7, acdmcs06.pdf) sent the Commission a useful summary table:

  Broad Proportionality Stable government Extension voter choice Maintenance of geographical link
FPTP - +? - ++
Double ballot - +? + ++
Open list in large constituencies ++ 0 ++ -
Open list in small constituencies + 0 ++ ++
Closed list in large constituencies ++ 0 - -
Closed list in small constituencies + 0 - +
AMS ++ 0 + ++
PR-STV + 0 +++ ++

Unfortunately, the table missed a row:

PR-Squared + ++ + ++

PR-Squared may not be perfect, but it compares very favourably to all the other systems mentioned. (Admittedly, this is when PR-Squared is scored by its designer. Please do read the full description sent to the Commission [since superseded by PR-Squared: A New Description], and then score it yourself. It will still do well. Alternatively, score PR-Squared in the context of the table on page 4 of Martin Linton’s mp-14.pdf — it will still do well.)


The Commission was misled about the choices open to it.

The Commission’s recommendation must therefore be considered as its opinion of the best amongst those that it considered.

PR-Squared is a viable alternative with much to commend it. Because its existence was not drawn to the attention of the Commission, it went unconsidered. In the opinion of this author it should have been the Commission’s recommendation, but there can be no doubt that it should have been considered.

Julian D. A. Wiseman, 15th November 1998

* The Conservative Party’s submission to the Commission gives an example of non-monotonicity in ¶3.3.13 on page 14 of ppf-02.pdf (in volume 2 of the Report). As a simpler example, consider a election held under SV or AV or double-ballot, in which there are 3 candidates (colour-coded R, Y and B) and 17 voters. Voters’ true preferences are as follows: 8 voters favour R; 3 favour Y with R as second preference; 2 Y then B; and 4 B then Y. If all vote ‘honestly’ then the first preferences for R:Y:B split 8:5:4, B is eliminated, its second preferences go to Y which wins 9 versus 8. But if 2 of the voters who favour R instead put B as first choice and R as second, then first preferences split 6:5:6, Y is eliminated and R wins 9 versus 8. So putting R higher rather than lower in the preference list would be to R’s detriment. In contrast, in ¶s 4.20 and 4.21 of cmmnt01.pdf Peter Kellner emphasises that this type of tactical voting requires “precise knowledge of the initial support of all three candidates”. But in contrast to this contrast, Kellner’s addendum rightly argues that voters will have enough information to unfairly disrupt the top-up allocations.

The PDF version includes, as an appendix, the full description that was sent to the Commission (which has been superseded by PR-Squared and the 2015 General Election).

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