[EM] RE : MMPO and Raynaud

[Kevin Venzke]

Gervase,

--- Gervase Lam <gervase.lam at group.force9.co.uk> a écrit :
> > Here's an extreme situation of this:
> > 
> > 1000 A
> > 1 A=C
> > 1 B=C
> > 1000 B
> > 
> > C wins.
> 
> Apart from may be disallowing equal rankings but still allowing
> truncation (as mentioned in previous posts), another way I thought of to
> alleviate this problem

This doesn't really alleviate the problem. You just change those two
ballots then to strictly prefer C over A and B. I guess the example is
written normally (by me) with equal rankings because 1. it shows the
problem exists even on approval ballots, and 2. it leaves C without any
strict first preferences.

> is the following:
> 
> (1) Like MMPO, get the highest pairwise opposition scores of each
> candidate.
> 
> (2) Drop the candidate with the greatest such score, together with the
> candidate's pairwise results.
> 
> (3) Repeat step (2) until one candidate remains.

This is exactly the definition I understand of Raynaud(WV). Because the
highest opposition score among all candidates is going to be a winning
score (unless it's a tie).

> Changing the example slightly:
> 
> 1000 A 
> 2 A=C
> 1 B=C
> 1000 B
> 
> The pairwise opposition scores are:
> 
> A<B 1001 A<C 1
> B<A 1002 B<C 2
> C<A 1000 C<B 1000
> 
> When the method is used, B is dropped because its highest pairwise
> opposition score is the greatest compared with the other candidates'
> highest pairwise opposition scores.  With A and C left, A wins because
> it has a better pairwise opposition score than C.  Using MMPO, C would
> still win in the example.

Unfortunately Raynaud's properties aren't very good. It loses both 
LNHarm and FBC relative to MMPO. You may as well use Schulze if you're
going to do that.

> I suppose this is Raynaud(Pairwise Opposition Loser), which is very
> similar to Raynaud(Gross Loser).  If none of the voters submit ballots
> with equal rankings, Raynaud(Pairwise Opposition Loser) and Raynaud
> (Gross Loser) are the same.

True, but otherwise I don't think it is very similar to Raynaud(GL).

> I think Raynaud(Pairwise Opposition Loser) satisfies the Plurality
> Criterion in a similar way to Raynaud(Gross Loser).

I'm afraid not:

49 A
24 B
27 C>B

A is eliminated and then C beats B, contrary to Plurality.

The reason Raynaud(GL) satisfies Plurality is because it eliminates
based on votes cast in favor of a candidate, which is what the Plurality
criterion is concerned with. Raynaud(PO) or (WV) only regards votes
cast *against* candidates.

Kevin Venzke


      
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