[EM] Cloneproof SSD

[Markus Schulze]

Dear Mike,

you wrote (15 Jan 2001):
> It's known that, in public elections, where there are no pairwise
> ties or equal defeats, SSD chooses the same winner as BeatpathWinner
> (aka "Schulze's method"). In small committee elections where
> pairwise ties can happen, Cloneproof SSD appears to meet every
> criterion that BeatpathWinner meets. Can anyone name a way in
> which BeatpathWinner is better than Cloneproof SSD? That latter
> method has the natural & obvious motivation & justification that
> BeatpathWinner completely lacks. Sure, BeatpathWinner can be
> justified in terms of criteria, and they're really what's important.
> But the public would expect the count rule itself to make sense,
> to have obvious motivation & jusification. Aside from criteria,
> BeatpathWinner's only obvious motivation is that it's an
> implementation of Cloneproof SSD.

Could you please post an example where these two heuristics
lead to different winners?

If these two heuristics always lead to the same winners then I would
like to ask: Why should we concentrate on only one of these two
heuristics?

I always considered it to be advantageous when there is more than one
heuristic for a given method so that it is possible to explain some
properties with the one heuristic and other properties with the other
heuristic. Actually I don't even see why we should differ between
the Schwartz set heuristic for the Schulze method and the beat path
heuristic for the Schulze method:
http://www.egroups.com/message/election-methods-list/2291

Example 1: In so far as the Schwartz set heuristic is an iterative
heuristic while the beat path heuristic is not an iterative
heuristic, it is more simple to explain the fact that the
Schulze method meets monotonicity when one uses the beat path
heuristic than when one uses the Schwartz set heuristic.
Example 2: In so far as the runtime of the Schwartz set
heuristic is O(NumberOfCandidates^5) while the runtime of
the beat path heuristic is O(NumberOfCandidates^3), one
would implement the beat path heuristic even when one used
the Schwartz set heuristic for the Schulze method to explain
this method.

Markus Schulze