[EM] MMPO and Raynaud

[Gervase Lam]

> Date: Sun, 22 Apr 2007 06:42:06 -0400
> From: "Tim Hull"
> Subject: Re: [EM] Student government - what voting system to
> 	recommend?

> Votes are as follows
> 
> 48% - Democrat/Pro Wrestler/Republican
> 5% - Pro Wrestler/Democrat/Republican
> 47% - Republican/Pro Wrestler/Democrat
> 
> The pro wrestler beats the Democrat, 52-48, and the Republican 53-47, and
> thus wins. Under IRV, the Democrat would have won.  The only system other
> than IRV that I know of that doesn't suffer this issue is Range/Approval...

I thought I would give Raynaud(Pairwise Opposition Loser) a go on this
example.

The pairwise opposition scores are:

Democrat<Pro Wrestler 52%, Democrat<Republican 47%
Republican<Democrat 53%, Republican<Pro Wrestler 53%
Pro Wrestler<Democrat 48%, Pro Wrestler<Republican 47%

The Republican has the worst highest pairwise opposition score of 53%.
Therefore, the Republican is dropped.  This leaves the Pro Wrestler and
Democrat.  The Pro Wrestler wins as it has a better pairwise opposition
score than the Democrat.

Interestingly, the Pro Wrestler is also the winner under MMPO, unless I
have got things wrong.

Thanks,
Gervase.