[EM] Cloneproof SSD

[MIKE OSSIPOFF]

>
>Not all solutions guarantee that the strong version of clone
>independence is met.

>Tideman suggests for his "Ranked Pairs" method that all n! ways to
>drop one pairwise defeat after the other should be checked. And I
>believe that this is the unique way to guarantee that Tideman's
>method meets the strong version of clone independence.

Is that true for Cloneproof SSD, the Schwartz set equivalent of
BeatpathWinner? Does Cloneproof SSD need the n! procedure to maintain
strong clone independence? Would be the "drop all of the equally
weakest defeats" solution violate that criterion?

Having to try every possible dropping order would overtax the patience
of most people, in an explanation, compromising Cloneproof SSD's
natural motivation advantage. But in public elections, we needn't
worry about clone independence, since clone problems of SSD require
pair-ties, which will be quite rare in public elections.
For public elections, I'd just propose ordinary SSD.

But organizations may be put off from Cloneproof SSD if it requires
equal defeats to be dealt with by trying every dropping order, when
used in small committees.

Small committee votes, and all the tie situations that can happen
there--that hasn't been my area of interest, but now I'm trying to find
out some of these facts about Cloneproof SSD, BeatpathWinner, &
Tideman.

>Of course, Random Candidate is simpler than Random Ballot.
>But when you use Random Candidate, then the strong version of
>clone independence is violated.

I'd been considering a case where 2 candidates are pair-tied. But
now that you mention it, if a clone set that's pair-tied with
a candidate has pair-ties among the clones, then the bigger the
clone set is, the better its chances in the Random Candidate
solution. The bigger the cloneset, the more ways there can be pair-ties
in it, with no unique top candidate, and the better it stands to do, with 
Random Candidate.

>
>******
>
>You wrote (17 Jan 2001):
> > But most of the details are crucial only in small committees. And
> > final ties for winner are provided for in existing electoral law.
> > Defeats tied for weakest, that could require a special rule, unless
> > the "draw lots" law is construed to apply to all ties, even ties
> > for weakest defeat, in the middle of the count.
> >
> > Anyway, I acknowledge that BeatpathWinner may have fewer details
> > to deal with. That makes it appealing for a committee that would
> > appreciate BeatpathWinner, but it doesn't seem to outweigh SSD's
> > greater overall plausibility for people who are completely new to
> > voting systems.
>
>Again: When one only wants to explain this method, then there is no
>need to concentrate on only one heuristic. Only when one wants to
>write the laws of a given organization, one has to concentrate on
>only one heuristic.
>
>Example: Suppose that you have used the Schwartz set heuristic to
>motivate this method. Suppose that someone asked you to explain
>whether this method meets monotonicity. Would you consider it to
>be inconsequent to use the beat path heuristic to explain this?

That would be the easier way to show that. I just meant that I think
that the Schwartz set approach works better for introducing people
to the method. And if an organization's official rules mention only
the beatpath version, then, to show that the method has precedent in
that organization, I've got to convince someone that Cloneproof SSD
and BeatpathWinner are equivalent. But if those official rules also
list the Schwartz set definition too, then my task is much easier.

My main question now is: Does Cloneproof SSD have to try all possible
dropping orders when it encounters several equally weakest defeats,
in order to meet the strong Clone Criterion? Would simultaneous dropping
of all those equally weakest defeats violate that criterion, with
Cloneproof SSD?

Mike Ossipoff

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