Saari reply

[Alex Small]

>> No, sorry, there does not need to be a near-tie in order to have
>> cycles.
>
>
> MUST be approaching a tie, even if you do not like "near" as an
> adjective.
>   We know that while A>B and B>C are significant enough for both to
>   head
> for the winner's circle, C>A also MUST have significant backers or we
> could not be cyclic.

First a simplified example of cycle without near-tie, then discussion:

33% A>B>C
33% B>C>A
34$ C>A>B

Obviously these exact numbers will happen about as often as elections
where the crucial electoral votes come from a state whose governor is
related to one of the candidate--rare, unlikely, but ever discount it
because then it will happen.
Now to the real world:

If we stick to a world where most people view politics via a left-right
spectrum then you are right, cycles only occur in close elections.  But we
just saw in 2000 that close elections can happen, and when they do it's
best if everybody has already agreed in advance on what the rules are. 
Otherwise, some people might become very angry...
But, in a world where third parties fit into categories other than "Even
more liberal than the Democrats" or "Even more conservative than the
Republicans" (a world I'd like to inhabit some day) then situations which
are roughly similar to my simplified example can happen.
Imagine three candidates:  A liberal (in the usual, contemporary American
politics sense of the word), a conservative (same disclaimer), and a
candidate who's somewhere in the middle on domestic policy but has a very
different vision of foreign policy (a field where left-right isn't as
well-defined).
The liberals mostly place the third party candidate in second place
because they're mostly interested in domestic policy, and they agree more
with the third-party candidate.
The third-party people, being free-traders, tend to place the conservative
second because of the ostensibly market-oriented policies of
conservatives.
The conservatives decide they prefer the status quo, and place the liberal
in second place (better the devil you know than the devil you don't).
Three factions, each with plausible and respectable reasons for their
preferences, and together they form a cycle.  Not likely to happen as long
as we keep plurality, because all new ideas are filtered through a
two-party system.  But when extra parties become competitive it is
plausible that a third coalition could form that doesn't fit on a neat
spectrum.
If you disagree with my characterizations of the left and right, or of
foreign policy, well, that isn't really the issue.  The issue is whether
or not cycles require near-ties, and I'm arguing that with the injection
of a very new perspective cycles can occur without near ties.
> Without being certain, "random ballot" sounds like giving up my right
> to  express my desires.

I don't think anybody seriously advocates it.  If we wanted arbitrary
methods that forfeit freedom of choice we'd all be supporting the
Electoral College.  Random ballot is a hypothetical method used for
understanding theoretical problems.
Alex Small

-- 
The first thing we do, let's kill all the lawyers!

Of course, that's just my opinion.  I could be wrong.


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