[EM] Cloneproof SSD

[MIKE OSSIPOFF]

SSD (Schwartz Sequenial Dropping) can be made cloneproof, even in small 
committees, by changing its stopping rule.

First, here's the definition of SSD:

Drop the weakest defeat that is among the current Schwartz set.
Repeat till there's an unbeaten candidate.

[end of definition]

Let me define the Schwartz set:

1. An unbeaten set is a set of candidates none of whom are beaten by
   anyone outside the set.
2. An innermost unbeaten set is an unbeaten set that doesn't contain
   a smaller unbeaten set.
3. The Schwartz set is the set of candidates who are in innermost
   unbeaten sets.

[end of definition]


This is effectively free of clone problems in public elections, because
SSD can only have that problem when there are pairwise ties, as can happen 
in a small committee election. Even
then there are reasons to believe that the possible effect of clones
won't create a real strategy incentive. But, for small committees,
SSD can be modified so as to avoid the problem altogether:

Drop the weakest defeat that's among the Schwartz set. Repeat till
there are no cycles in the Schwartz set. Whoever is unbeaten at that
time wins.

[end of definition]

This avoids the problem of a clone set being cheated out of its
opportunity to be in a randomly-solved tie, due to cyclic defeats
among the clone set.


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.

Mike Ossipoff





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