[EM] RP(wv) to protect any Condorcet Winner

[Stephane Rouillon]

Eric Gorr a écrit :

> Care to provide the details? I would be interested.
> ...
> >However, I have designed a RP(winning votes) method on an extended
> >graph that I think can protect even a weak Condorcet Winner. This
> >method like any Condorcet Ranking
> >can be generalized to produce weights as an output so to be used in
> >a PR multiple-winners method.
> >
> >I hope it helps,
> >S. Rouillon

The problem as described by Mr. Ossipoff several times is the following.

Some Condorcet winner can lose their election because some voters
can unsincerely truncate their preferences to ameliorate the outcome
of the election in their eye.

For three candidates I had built a core family of cases where it can happen
even with winning votes. Adam and Alex produced several more cases
for margin and relative margin, even cases where a strong Condorcet winner
can loose after the strategical truncation occurs. Here follows my cases for
winning votes:

> Objet:
>         [EM] Request for Ranked Pair strategy holes (margin, rm & wv)
>    Date:
>         Wed, 10 Sep 2003 01:24:33 -0400
> ...
> In the past, several people sent me some examples where
> a week condorcet winner could get his victory stolen
> by some strategical truncation behavior...
>
> I was able to generate a family of problems to do so
> even with Ranked Pair (winning votes) at the time:
>
> 11+2X votes:
> --------------
> 2+X : A
> 2 : A > B > C
> 2 : B > A > C
> 1+X : B > C > A
> 4: C
>
> A is the Condorcet winner.
> The two B > A > C voters can get B elected by truncation, voting only B.
>
> Adam and Alex had the same kind of example, even more obvious for
> margin (and relative margin). Could anyone send me some again?
>
> Thanks,
> Stephane.
>
To cope with the problem, I introduce an additional virtual candidate (Z). This
candidate is the mean (average) replacement candidate. When we say we do not
approve some candidate, it means we would prefer elect this replacement
candidate.  For single-winner election, it seems useless. However:
1) for multiple-winners election it allows to use single-member ridings and to
identify when voters would prefer any ggod loser of another riding instead
of any of the candidates they are offered in their own riding;
2) even for single-winner election, it does not lead to the same.

So, using universal ballot notation I already agreed with Forest:
2+X : A
2 : A > B > C
2 : B > A > C
1+X : B > C > A
4: C

becomes:
2+X : A > Z > B ? C
2 : A > B > C > Z
2 : B > A > C > Z
1+X : B > C > A > Z
4: C > Z > A ? B

When applied using winning votes, the winner is now different (C), but does not
fit the will of the truncators... I am pretty sure it works for any three
candidates
(or less) scenario but I haven't yet proved it for more candidates.
Who can give me any counter-example?

Steph.
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