[EM] PR-Squared, SMP, and related matters

Wiseman, Julian julian.wiseman at csfb.com
Wed Jul 28 02:10:00 PDT 1999

Blake Cretney has written a good commentary on PR-Squared
(http://www.jdawiseman.com/papers/electsys.html). In particular, I agree
that supporters of SMP haven't reconciled the local and the national
plurality requirements: this realisation was one of the inspirations of

Blake Cretney's last point is most interesting. Three parties A B C, in
which A supports some particular policy opposed by B and C. They split the
vote 42:35:23. The people have voted 42:58 against the policy, yet A has the
majority required to implement it (squares are 1764 1225 529, giving A a
minimal majority of 1764:1754 = 50.14%:49.86%). This seems like an
objection, but isn't. 

There are two possibilities. Either B and C disagree about other policies,
or they don't. 

If B and C disagree, then the people are choosing between portfolios of
policies. If there are 10 yes/no policies, and many fewer than 2^10 parties,
it is highly likely that some majority policies will not be favoured by the
winning part / coalition. Inevitable in representative democracy. 

But what if B and C agree on all or most policies. Then PR-Squared provides
a massive incentive to form the inevitable coalition before the election,
where it will be visible to voters, rather than after. It gives them a
massive incentive to resolve their few remaining policy desputes before the
election, rather than after, so that voters can see the choices. B & C
should get on with it NOW, and if their coalition is deemed plausible by the
voters, to win by a storming 42:58 => 34.4%:65.6% majority. So much mroe
democratic than have B and C sit down, post election, to negotiate egos
versus polciies. 

> -----Original Message-----
> From:	Blake Cretney [SMTP:bcretney at postmark.net]
> Sent:	Wednesday, July 28, 1999 1:42 AM
> To:	election-methods-list at eskimo.com
> Subject:	RE: [EM] U.K. Voting Systems, 3rd edition
> Wiseman, Julian 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
> You seem to view "Majoritarian systems" as distinct from PR systems. 
> How do you define "majoritarian" to come to this conclusion?
> > negotiating table; and simple systems are widely understood and provide
> a
> > clear link from constituent to representative. Whilst I don't believe
> 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). 
> Does anyone know of any recent studies of Gerrymandering?
> Regarding PR-squared, I think that it is superior to SMP.  In SMP, it
> makes sense for government to concentrate programs on close-race
> constituencies (or regions of the country).  If seat allocation
> depends only on total vote, there is no reason to do this.  Although,
> it still makes sense to use government spending to help cabinet
> ministers get re-elected, this is done at the expense of back-benchers
> of the same party.  Similarly, PR-squared eliminates Gerrymandering as
> a way to increase total seats.
> Another advantage SMP has over plurality is that it does not give
> some voters more power by virtue of living in smaller constituencies. 
> However, people who live in small constituencies will not view this as
> an advantage, and attack the method based on this.  Worse yet, smaller
> constituencies will have lower margins of victory, and as a result
> will be more likely to be represented by other than their plurality
> winner, creating hostility towards the method.
> PR-squared is much more prone to minority governments than SMP.  A
> vote of 40% to 35% to 25% would likely result in a landslide win for
> the 40% in SMP, but in PR-square it causes a minority goverment.
> Plurality-squared has the advantage that a party cannot win more
> seats with fewer votes.  I don't see this as an important gain,
> however.  I don't place much meaning in a party's ability to gain a
> plurality of the vote, so I am not concerned if the actual winner gets
> a few percentage below the plurality winner?
> You'll have a hard time persuading non-PR advocates to back your
> method.  I suspect that most do not view SMP as having any need of
> reform.  There are people who have basic pluralitarian views, but are
> concerned that sometimes in SMP the plurality party does not win. 
> However, they will likely be just as outraged when a plurality winner
> does not win in an individual constituency.
> The primary reason that I prefer PR methods to either of these
> plurality methods is that they seem more likely to create a government
> which represents the public will.
> Of course, a pluralitarian would respond that in SMP, the government
> is chosen solely on the basis of the votes of the population, so
> clearly the government is the choice of the voters.
> But consider the hypothetical method called Second Past the Post. 
> This is the same as First Past the Post, except that in every seat the
> candidate who comes in second wins.  I think few people would see the
> result of such an election as "the will of the voters", and yet the
> election result would depend entirely on the votes.  However, I would
> say that the result reflects the peculiarity of the electoral method
> rather than the will of the voters.
> I hope this demonstrates that saying that an election result depends
> entirely on the voters, and that it gives the choice of the voters is
> not the same thing at all.  So, if an SMP government does represent
> the choice of the voters, there must be some other justification than
> that it is the direct result of voter choices.
> Often it is suggested that the best way of determining the choice of
> the electorate as a whole is the decision of the majority.  Since you
> affectionately refer to SMP as majoritarian, I suspect you would agree
> with this.
> We would therefore think that a system that was truly representing
> the will of the people would tend to impliment policies which
> represent the majority of the population.  Of course, any system which
> is representative rather than direct will filter majority decisions
> somewhat.  To what extent this should occur is an unrelated issue. 
> For simplicity, I am going to assume that voters vote for parties
> based on their policies, and that parties then attempt to carry them
> out.
> Now consider an election is held on an issue important to the
> electorate.  Assume a vote that goes as follows:
> Percentage  Square  Party   Stand on Policy    
> 42          1764    A       For
> 32          1024    B       Against
> 26           676    C       Against
> 58% voted against the policy, 42% for it.  However, the policy will
> be implimented because the square of the votes gives a majority to A. 
> Perhaps you have some reason for believing cases like this will be
> rare.  I suspect, however, that if you have more than two strong
> parties, they will be the norm, and the decisions of government will
> have little relation to majority will, but rather to the peculiarities
> of the voting method.
> ---
> Blake Cretney

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