FPTP family theory, REDLOG shadowing

[Markus Schulze]

Dear Craig,

you wrote (14 Dec 1999):
> I now consider the participation axiom to be uninteresting.

But many other people consider the participation criterion
to be interesting. Even you said a few days ago that election
methods that violate this criterion were "too defective to be
used in practice." It is surprising that you -now that it has
been proven that Alternative Voting violates this criterion-
say that this criterion was "uninteresting."

******

You wrote (14 Dec 1999):
> At 06:33 15.12.99 , Markus Schulze wrote:
> > I don't remember that ever somebody said "that pairwise comparing
> > of two candidates had some mathematical importance." Those who support
> > Condorcet methods do this because their supported Condorcet method meets
> > monotonicity and is very difficult to manipulate by running additional
> > candidates. It never happened that anybody said that he prefers a
> > Condorcet method simply because it is a pairwise comparison method.
>
> Surely they hold a belief that if A beats B in a pairwise comparing
> then A ought beat B in the election.
>
> > Do you want to say that pairwise methods are eo ipso worse than
> > non-pairwise methods? If the answer is "Yes!": Does your criticism
> > of Condorcet methods also include those methods that on the one side
> > meet the Condorcet criterion but that on the other side do not depend
> > only on the matrix of pairwise comparisons (e.g. the Dodgson method)?
>
> It seems to me obvious that if A beats B in a pairwise comparing, there
> is no good reason why A should win before (or if) B does.

Nobody ever said that a Condorcet candidate was eo ipso better than
every other candidate. Those who support pairwise methods do this
because they think that SPC is less important than monotonicity or
the guarantee that their supported method is very difficult to manipulate
by running additional candidates. Nobody ever said that every pairwise
method was eo ipso better than every non-pairwise method. It seems to me
that you are fighting against somebody who isn't there.

******

You wrote (15 Dec 1999):
> That is is a contradiction and so the steps are a proof by contradiction
> that Demorep1's clone rule is just a corollary of (P1). (I've assumed
> I've understood the clone rule).

It is true that Alternative Voting meets SPC and clone criteria.
But that doesn't mean that SPC and clone criteria are the same.
For example: FPTP meets SPC and violates clone criteria; Tideman
violates SPC and meets clone criteria.

You should really browse through Blake Cretney's home page at
http://www.fortunecity.com/meltingpot/harrow/124

Markus Schulze