[EM] MMPO and Raynaud

[Gervase Lam]

> Date: Thu, 21 Dec 2006 18:36:06 +0100 (CET)
> From: Kevin Venzke
> Subject: Re: [EM] Election methods in student government...

> --- Tim Hull a ?crit?:
> > Regarding the single winner methods, it seems that IRV or MMPO may be the
> > way to go there if one wants to maintain later-no-harm.

> 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 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.

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.

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.

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

For a brief description of various Raynaud methods, see the following:

<http://wiki.electorama.com/wiki/Raynaud>

Thanks,
Gervase.