# [EM] pairwise, fairness, and information content

James Gilmour jgilmour at globalnet.co.uk
Fri Aug 16 15:06:19 PDT 2002

```Maybe there's something I'm missing here, but I just cannot see "the issue" with 'two candidates, one winner' elections.
I'll freely admit most of the maths, the complex equations and the formal logic statements (to say nothing of the jargon) go
straight over my head, but just what is the problem?

Whether you mark your ballot paper "X" and blank, or "1" and "2", or use weighted preferences, eg "0.8" and "0.2", or use weighted
preferences expressed on any scale of the voter's choice provided you normalise the gross values (all = 1.0) before summing, surely
the outcome is simple, clear and always the same, except when a tie occurs.  If I am wrong in this simple-minded view, please,
somebody, present a simple arithmetical example to show how and why I am wrong.

I also fail to see the relevance of this boundary condition, ie "two candidates, one winner", to the resolution of the real issues
that do arise as soon as you move away from this extreme, eg  move to "three candidates, one winner".  So why is "two candidates,
one winner" being discussed in the context of the more general (and more common) problem?

While I think the maths of "two candidates, one winner" is extremely simply no matter how you choose to do the maths, I do recognise
there can be a major problem in terms of "representation" in all "two candidate, one winner" elections.  If candidate A has the
support (however expressed) of 49 voters and candidate B has the support of 51 voters, you have a clear winner, but half of that
electorate is left without representation.  This tension is much worse if the result is very close in a much larger electorate, eg A
10,000,001 votes to B 10,000,000 votes, but the issue is still the same.

This is an unresolvable problem.  In any "one winner" election, the best you can do is to guarantee representation to half of the
voters.  That is why "one winner" elections present the greatest challenge to electoral science.

"Three (or more) candidates, one winner" elections present a number of different problems, but still the best you can do is to
guarantee representation to only half of those who voted.  Of course, your method of voting and counting may do much worse than
that.  And there will be different outcomes, depending on the methods you use.  And there will be debate about which outcome "best"
reflects the "wishes" of the voters. And there will be debate about how those "wishes" are to be assessed and how "best" is to be
defined.

Most of the discussion here is about "one winner" elections, because these are seen as the priority for reform in the USA, but there
are occasional references to "multi-winner" elections.  Another set of issues is added when we move to "three candidate, two winner"
elections, and to more general multi-winner elections.

Leaving aside the maths, there seem to be two quite different approaches to determining what kind of outcome "best" reflects the
"wishes" of the voters in multi-winner elections.  Those who believe in representative democracy want to see all significant
viewpoints represented, ie maximise the diversity of those elected, to reflect all the significant diversities among those who
voted.  (Let's leave aside for now the determination of "significant".)  But there are others in this debate who appear to come from
a "social choice" background, where the objective is not to ensure the representation of all significant diversity, but to achieve
"consensus" representation in those who are elected.  These two approaches are fundamentally incompatible because their desired
outcomes are diametrically opposed.

I detect a social choice origin in some of the criticisms of voting systems made here and on other US-based websites, but these
critics rarely admit their true intent.  The concepts of social choice MAY have some relevance to "one winner" elections, but the
situation seems quite diffferent for multi-winner elections to councils and boards that are being elected to represent the
communities they serve.

James Gilmour

FAIRSHARE - Scotland's Campaign for Local Democracy

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