[EM] Re: Borda-Elimination

[Rob LeGrand]

Kevin Venzke wrote:
> Thank you.  That makes me wonder if Borda-Elimination can be rephrased in
> a manner which makes it look more like a Condorcet method.  It impresses
> me that there's no need for a cycle-breaker.

Note that neither Baldwin (one-at-a-time Borda-elimination) nor Nanson
(below-average Borda-elimination) is clone-independent.  Baldwin is
nonmontonic; anyone know whether Nanson is monotonic?  I rather doubt it.

Anyway, not all Condorcet-completion methods use cycle-breakers.  Although
Cloneproof SSD breaks cycles in its procedure, its equivalent Schulze's
Method does not.  Schulze simply compares strengths of beatpaths, among
which there are never "cycles".  You can think of Schulze neatly resolving
cycles, but only in the sense that any Condorcet method must.

By the way, Steve Eppley used to argue for Tideman over Schulze by pointing
out that Tideman's winner tends to beat Schulze's winner pairwise when they
differ.  Recent simulations have shown that Baldwin and Nanson are two of
the very best methods in this regard; in fact, the only method I've found
that beats them is Arrow-Raynaud (Minmax-elimination), which generally
gives very poor social utility compared to other Condorcet methods.  I
don't find this pairwise-beat measure at all important, though.

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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