Tideman vs. Schulze

[Mike Ositoff]

This is in reply to Norm's letter. You asked what intuitive
justification there is for Schulze's method. If we can get
rid of the cycle by ignoring the weakest defeat, the problem
is solved. It's no longer a cyclic beat-path, but is now a
linear one, and the person at the top of it wins over the person
at the bottom of it, not because he beats him (he doesn't), but
because he wins over him via a beat-path. (and of course because
he's now unbeaten; you could put it either way).

So one way of looking at the problem of a cycle is that they
all have beat-paths to eachother. Otherwise it would just be
a linear beat-path with one candidate at the top.
So it's difficult to say whether A or B is more qualified to win,
when they both have beat-paths to eachother. So which is a
stronger beat-path? That seems a natural & intuitive question.

Sure, the public preferences are intransitive, but which part
of that intransitive chain of preferences, between A & B, is
more strongly-felt by the public, meaning felt by more people,
all along that chain of preferences? That obvious question leads
right to Schulze's method.

***

You asked if there's a way in which Tideman is inferior to
Smith//Condorcet. Yes, and the question about what that
inferiority is will be answered when I answer your other question
about Tideman's worse violation in subcycle situations that are
more common than the subcycle situations where Tideman brings
improvement.

Give me a day to post that answer. I noticed that problem of Tideman
when I first returned to this list, some time ago, and should
have posted it here at the time, but didn't, because there didn't
seem enough interest in Tideman to justify posting about it. 
As I said, when I post that, it will answer both of the questions
that I mentioned in the previous paragraph.

***

Mike Ossipoff