[EM] Problems of PR-squared/ cubed/ etc systems

Tom Round T.Round at mailbox.gu.edu.au
Tue Jul 13 22:27:48 PDT 1999

The "third way" (excuse pun) option of combining a party-list system of
voting with -

[a]	a distribution of seats that's proportional to the cube (or square, or
some other specified power) of each party's vote tally, and/or

[b]	candidates voted for, and elected, one per party list in each district,

- has been proposed before. I think it was Arend Lijphart in the early
1980s who quoted Dutch proposals to cube each party list's vote tally
before allocating seats. And the method used for the Danish Folketing seeks
to ensure as far as possible that each candidate elected from a party list
has his/her "own" local constituency.

Political scientists from David Butler onwards have noted the "cube rule"
effect of simple plurality voting, which explains why normally the party
with most votes, if facing a divided opposition, will win an absolute
majority of seats unless its vote is very low and the second and
third-placed parties are both fairly close to it (eg, UK 1974). Thus the
attraction of schemes that will institutionalise this result consistently,
without the risk that the plurality party will win fewer seats than the
runner up (as also occurred in 1974).

My main objection to PR-cubed is that the result would depend so very
heavily on coalition deals (formal or informal) negotiated by the party
leadership long before election day. Thus, if the votes go Red 45%, Blue
35%, Green 20%, and these parties run separate lists, the seats will be
divided in the proportions 91,125 to 42,875 to 8,000, ie Red 64.17%, Blue
30.19%, Green 5.6%.

But if before the election Blue and Green agree to run a joint list, they
will have a combined 55% of the vote and this will mean the seats are now
divided in the proportion 91,125 to 166,375, so the seats will now go
35.38% to Red, 64.61% to the Blue/ Green alliance. Thus, without a single
voter changing his/her voting preference, Red has been reduced from 2/3 to
1/3 of the seats (given voting patterns not all that different from, say,
the 1983, 1987 and 1992 UK House of Commons elections). The result would be
similar, although more moderate, if the vote totals were squared instead of

It matters not that the electoral rules might _say_, on paper, that
explicit "joinder" or apparentement of lists, European-style, is not
allowed. So great are the incentives for Blue and Green to unite and turn
electoral annihilation into a landslide for them that they could still no
doubt easily agree on a single joint list (doing so would yield them so
many extra seats that they could easily afford to be magnanimous to each
other). Unlike simple plurality, PR-cubed would not even require the party
leaders to persuade their local party branches, activists and candidates to
agree to stand down before they could make an electoral pact stick.

Both plurality and PR-cubed, however, share the defect that the voters have
no control over these coalitions or pacts -- ironically, exactly the same
accusation that plurality's defenders throw at PR systems. Mirroring the
anti-PR charge that PR encourages coalitions negotiated in smoke-filled
rooms after the votes are cast (which means voters can't cast a free and
informed vote to ratify them) is the brute fact that any system which
swings seats so violently back and forth (depending on whether 55% of votes
go to one party or two) will conversely encourage coalitions negotiated in
smoke-filled rooms before the votes are cast, which means voters can't cast
a free and informed vote to ratify them either. It is a fallacy to boast,
as many do, that plurality systems discourage coalitions. All they do is
discourage coalitions which offer voters a choice of candidates or parties.
All PR systems at least do the latter. [I expound on this in more length in
"A Matter of Preference?", available at
http://www.cs.mu.oz.au/~lee/prsa/tround/ -- my opinion on this matter has
not changed since 1992.]

Single Transferable Vote PR systems, which I support, have the further
advantage that they mean the final, "marginal" seat in each electorate is
almost always decided by inter-party preference flows while the earlier
seats are almost all won by parties on their own votes. Thus, STV-PR both
(a) encourages party leaders to negotiate their coalition deal before
election day -- otherwise their supporters' preferences will "leak" and
they may lose crucial seats they could otherwise have won. But it also (b)
allows voters to decide whether or not to reject that advice.

I would also respectfully query whether, as Julian says, single-member
plurality "has served two countries well for centuries". Firstly, if the
second country is the USA, I would suggest that the plurality system works
in the USA almost the opposite to the UK -- primary elections, fixed terms,
a separate presidential executive, and party-block ballots for multiple
offices have produced a very loose, undisciplined US party system behind
the nominal Republican/ Democrat divide. Secondly, plurality was used in
multi-seat electorates -- even for national elections -- in both USA and UK
until only about a century ago.

Deliberate gerrymandering by politicians can be avoided if you use a
boundary commission, but even with impartial drawing single-member
boundaries can still produce weird results (eg, giving victory to the
runner-up party in two of the last four Australian House of Reps elections).

I cannot comment on Julian's assessment of PM Blair's motivations for
supporting the change, except to note that almost all politicians support
particular systems for reasons of party advantage, so the motivation game
is little help in deciding which system gives voters the best deal.

Round's law for predicting a party's choice of preferred electoral system:
"1. Every party will advocate whichever electoral system will give it the
most seats for its expected number of votes in the foreseeable future. 2.
Corollary: It will therefore advocate the system that gives it the most
seats for its expected share of votes, excluding any system that has a bias
so blatant and hard to justify that ordinary voters will lose faith in that
party and thus give it fewer seats -- due to loss of votes -- than it gains
due to the workings of a favourable electoral method." Works every time!

At 10:14 AM 7/5/99 +0100, you wrote:
>Just for the record, many people (myself included) do not believe that
>single-member plurality is "ANTI-DEMOCRATIC", whether whispered or shouted.
>Majoritarian systems prevent power being passed from the ballot box to the
>negotiating table; and simple systems are widely understood and provide a
>clear link from constituent to representative. Whilst I don't believe SMP is
>optimal (my preference can be found via
>http://www.jdawiseman.com/papers/electsys.html), SMP is far from pessimal,
>and has served two countries well for centuries. Gerrymandering can be
>avoided by depoliticising boundary commissions (as in the UK); and elections
>can be made fairer by capping campaign spending (perhaps a more complicated
>constitutional change).

>If the UK switches, it is for domestic political reasons entailing a split
>in the Labour Party and an alliance of the right of that with the Liberal
>Democrats. Any Prime Minister who spends the taxpayers' cash on supporting
>his side of a referendum campaign (in a word, cheating) has motivations
>other than democracy itself. (And as for his attempt to impose a Hindenburg
>solution on Northern Ireland by allowing a private army to take power,
>please don't ask how that is pro-democratic.)

>> -----Original Message-----
>> From:	DEMOREP1 at aol.com [SMTP:DEMOREP1 at aol.com]
>> Sent:	Monday, July 05, 1999 12:57 AM
>> To:	FairVote at compuserve.com; ban at igc.apc.org;
>> elections-reform at igc.apc.org; civic-values at civic.net;
>> canada-votes at egroups.com; election-methods-list at eskimo.com
>> Subject:	[EM] U.K. Voting Systems, 3rd edition

>> The below Research Paper pdf file shows how primitive (i.e. in the
>> political
>> barbarian Dark Ages) the ANTI-DEMOCRATIC plurality- single member district

>> gerrymander system is for electing legislative bodies in Canada, India,
>> U.K.
>> and the USA and any other similar areas.
>> -------
>> http://www.parliament.uk/commons/lib/research/rp98/rp98.htm
>> has a link to----
>> -------------
>> [U.K. House of Commons Library]

>> 14 DECEMBER 1998

>> Voting Systems - The Government's Proposals (3rd revised edition)

>> [Summary]

>> This Paper seeks to draw together the Government's proposals for new
>> systems
>> of voting for the European Parliament, the Scottish Parliament, the Welsh
>> National Assembly, the new Northern Ireland Assembly and the Greater
>> London
>> Authority. It discusses common themes related to those elections. It also
>> summarises the proposals of the Jenkins Commission which has recommended
>> an
>> alternative system to First Past the Post so that a referendum can be held

>> during the lifetime of this Parliament on a new voting system for the
>> House
>> of Commons. Finally the possibility of a new voting system for local
>> government is briefly discussed. This Paper replaces Research Paper 98/80.

>> More detailed consideration of voting systems is given in Research Paper
>> 98/112 Voting Systems: The Jenkins Report. This Paper is designed so that
>> each section can be used separately as a guide to the voting procedures of

>> the relevant institution, and so there is an unavoidable element of
>> repetition.

>> Oonagh Gay
>> Bryn Morgan

>> --- Summary of main points

>> The Government introduced Bills in the 1997-8 Session to create new
>> voting
>> systems for the European Parliament, the National Assembly for Wales and
>> the
>> Scottish Parliament. There are some common themes which are explored
>> briefly
>> in the introduction to this Paper. A closed list system is intended for
>> the
>> European Parliament and for the additional member aspect of the Additional

>> Member System (AMS) proposed for the National Assembly and the Scottish
>> Parliament. In effect electors vote for a party rather than an individual
>> candidate. Greater attention focuses on party candidate selection
>> procedures,
>> and all the major parties have been reviewing their systems for the new
>> types
>> of elections expected in 1999. The role of MEPs, and members of the
>> National
>> Assembly for Wales, and the Scottish Parliament may undergo review
>> following
>> the introduction of party lists. In addition legislation to create the new

>> Northern Ireland Assembly has meant that another form of PR, the Single
>> Transferable Vote, is being used for a devolved assembly in that province.
>> At
>> Second Reading of the European Parliamentary Election Bill, the Home
>> Secretary promised to review the possibility of an open list system on the

>> Belgian model, but a final decision was announced before Commons Report
>> stage
>> that the closed list system would be used. 84 MEPs will be elected under a

>> Regional List System. Scotland and Wales will form one single electoral
>> system each, and England will be divided into nine regions, each with
>> between
>> 4-11 MEPs. Single Transferable Vote (STV) for Northern Ireland is
>> preserved.
>> The Bill was finally lost after the Commons and Lords could not agree on
>> closed and open lists. A new Bill has been introduced, which is identical
>> to
>> the 1997-8 one and which is discussed in Research Paper 98/102 The
>> European
>> Parliamentary Elections Bill The Additional Member System is planned for
>> elections to the National Assembly for Wales and the Scottish Assembly.
>> The
>> elector has two votes, one for a constituency MP and one for an additional

>> member selected from party lists for a electoral region. In Wales there
>> will
>> be 40 constituency members and 20 additional members. In Scotland there
>> will
>> be 73 constituency members and 56 additional members. At present closed
>> lists
>> will operate for the Additional Member aspect and the Government has no
>> plans
>> to introduce open lists. In Northern Ireland 108 Members, 6 for each
>> Parliamentary constituency, have been elected using STV. The Greater
>> London
>> Authority Bill is expected to have its second reading on 14 and 15
>> December
>> 1998. It will introduce an AMS system for the elections of Assembly
>> members
>> and Supplementary Vote (SV) will be used for the election of a Mayor for
>> London. Elections are expected in May 2000. The Government promised in its

>> manifesto for the 1997 election that it would set up an independent
>> commission to recommend an appropriate proportional voting system to First

>> Past the Post (FPTP) for the House of Commons. A referendum would then be
>> held to allow voters a choice between the two systems. An independent
>> commission under Lord Jenkins was announced in December 1997, and reported
>> in
>> October 1998. It proposed a version of AMS, using the Alternative Vote in
>> the
>> constituency element and with 15-20 per cent of the seats elected on an
>> open
>> list system, to be known as Top-up Members. It is not yet clear when the
>> referendum will be held. Further detail on the Jenkins report is given in
>> Research Paper 98/112 Voting Systems: The Jenkins Report.

>> Related Library Research Papers include:

>> 98/118 The Greater London Authority Bill: Electoral and Constitutional
>> 11.12.98
>> Aspects Bill 7 of 1998-99
>> 98/115 The Greater London Authority Bill [Bill 7 of 1998-9] 11.12.98
>> 98/112 Voting Systems: The Jenkins Report 09.12.98
>> 98/102 The European Parliamentary Elections Bill [Bill 4 of 1998-9]
>> 01.12.98
>> 98/76 The Northern Ireland Bill: Implementing the Belfast Agreement
>> 20.07.98
>> [Bill No 229]
>> 98/62 The Registration of Political Parties Bill [Bill 188 of 1997-8]
>> 01.06.98
>> 98/57 Northern Ireland: Political Developments since 1972 11.05.98
>> 98/1 The Scotland Bill: Devolution and Scotland's Parliament 07.01.98
>> 97/129 The Government of Wales Bill: Devolution and the National 04.12.97
>> Assembly
>> 97/120 The European Parliamentary Elections Bill [Bill 65 of 1997-98]
>> 19.11.97
>> 97/114 The Greater London Authority (Referendum) Bill 06.11.97
>> [Bill 61 of 1997-98]
>> ----
>> The below 1999 reports continue the above-- at

>> http://www.parliament.uk/commons/lib/research/rp99/rp99.htm

>> 99/64 Elections to the European Parliament - June 1999 18. 06. 99

>> 99/57 European Parliament Elections - 1979 to 1994 02. 06. 99

>> 99/54 Institutional Reform in the European Union 20. 05. 99

>> 99/52 The Local Elections of 6 May 1999 11. 05. 99

>> 99/51 Welsh Assembly Elections: 6 May 1999 11. 05. 99

>> 99/50 Scottish Parliament Elections: 6 May 1999 11. 05. 99

>> 99/46 Local Elections - Proposals for Reform 28. 04. 99

>> 99/7 The House of Lords Bill: Lords reform and wider constitutional reform

>> [Bill 34 of 1998-99] 28. 01. 99

>> 99/6 The House of Lords Bill : Options for "Stage Two" [Bill 34 of
>> 1998-99]
>> 28. 01. 99

>> 99/5 The House of Lords Bill :"Stage One" Issues [Bill 34 of 1998-99]28.
>> 01.
>> 99

Tom Round
BA (Hons), LL.B (Qld)
[1] Research Officer, Key Centre for Law, Ethics, Justice and Governance
(incorporating the National Institute for Law, Ethics and Public Affairs), and
[2] Associate Lecturer, School of Criminology and Criminal Justice,
Griffith University, Queensland [Australia] 4111
Ph:	[1] 07 3875 3817 or [2]  07 3875 6671 or [3] 07 3875 5957
Fax:	[1] 07 3875 6634 or [2] 07 3875 5608
E-mail: 	T.Round at mailbox.gu.edu.au
Web:	http://www.gu.edu.au/school/ccj/

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