[EM] Replies to Saumur

[Mike Ossipoff]

Lucien Saumur writes:
> 
> In an article, dfb at bbs.cruzio.com (Mike Ossipoff) writes:
> 
> >Earlier you said that it doesn't make any sense to speak of how
> >beaten a candidate is. That means that you're saying that it
> >doesn't make any sense to speak of how many people ranked
> >Clinton over Buchanan, to say that they want to defeat Buchanan,
> >and would prefer Clinton to him. I disagree, and I say that it
> >matters very much what a majority want, and it matters that
> >majority wishes are respected.
> 
>           Yes. It matters very much what a majority wants,
> but a majority, that produces a circular tie, has been

A majority that produces a circular tie? The majority who ranked Clinton
over Buchanan didn't produce a circular tie. That's the result of several
pairwise defeats, some perhaps by majority, some perhaps not.

> ambiguous in expressing its want. I interpret a circular

Oh no, the majority who said they would rather have Clinton than
Buchanan were quite unambiguious in expressing that.

> tie as meaning that the majority does not have a
> significant preference and I suppose that the majority

There isn't just 1 majority. There's no 1 set of people who are
_the_ majority.

> would not have expressed itself ambiguously if it had had
> the option of expressing equal preference.

The circular tie isn't necessarily, and probably isn't, the result
of voters not being allowed to vote equal preferences. The genuine
preferences of all the voters could be so as to naturally result in
a circular tie. Or there could be a circular tie caused by the _common_
practice of voting short rankings. Every rank-balloting election that
I've conducted or participated in had significant numbers of people voting
short rankings. When sufficient people don't rank the Condorcet winner,
they allow someone to beat him/her, and a circular tie results.

> 
>           The voters who produce a circular tie are like
> the car buyer who walk into a car dealership to buy a car.
> When asked if he wants to buy a red car, the buyer says
> that he prefer a blue car to a red  and when told that
> there is a blue car in stock for him, he says that he
> prefers a white car to a blue car. Finally, when he is then
> told that there is a white car in stock for him, he says
> that he prefers a red car to a white car.

No, not necessarily. As I said, truncation--the voting of a short
ranking, is quite common in rank-balloting elections, and can easily
cause a circular tie, even when there's a Condorcet winne (candidate
who'd beat each one of the others in separate 2-way races).

Additionally, though it would be well-deterred in Condorcet, 
order-reversal would be a viable profitable strategy in your
Random-Solution method, which solves circular ties by random
process.

Further, even if it's a _natural_ circular tie, not caused
by order-reversal or truncation--a circular tie that exists because
there isn't a Condorcet winner--if there's a full majority of all
the voters who've ranked Clinton over Buchanan, majority rule is
violated by electing Buchanan, unless every candidate has a similar
majority against him. So even in a natural circular tie, some of the
voters are saying something unmistakable, and something that 
shouldn't be ignored. Condorcet doesn't ignore it.


> 
>           The electoral officials, who would be confronted
> with a circular tie, would be faced with the same kind of
> problem as that poor car salesman. I do not think that such

Not if they have a good rule for solving circular ties.
I've proposed a good rule: Condorcet's method.

> a situation will happens very often, if ever, and that we
> should not be too concerned with the possibility that it
> will happen.

As I said, truncation will be quite common, and can easily cause
circular ties. Condorcet's method is the only circular tie solution
not using a 2nd balloting that doesn't have its results screwed up
by truncation. It's the only one in which the truncting voters can't
steal the election from the Condorcet winner, and the only one
in which that majority against Buchanan really ensures his defeat,
in spite of truncation by the Buchanan voters. 

With Condorcet, a candidate with a majority against him can't win
unless every candidate has a majority against him--something that won't
happen unless large-scale order-reversal occurs, or unless those
majorities really reflect voter sentiments, in which case, as you say,
it's a chaotic, ambiguous & indecisive situation. But even then it
makes sense to count how beaten the candidates are.

As I said, order-reversal is well-deterred in Condorcet's method,
and would be most unlikely on a scale sufficient to change the
election result in a public election using that method.



Mike

> 
> __________________________________________
>           aa447 at FreeNet.Carleton.CA
>           http://www.igs.net/~lsaumur/
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