[EM] simple question (I think)

Paul Kislanko kislanko at airmail.net
Wed Nov 16 17:08:28 PST 2005

> -----Original Message-----
> From: election-methods-bounces at electorama.com 
> [mailto:election-methods-bounces at electorama.com] On Behalf Of 
> Scott Ritchie
> Sent: Wednesday, November 16, 2005 6:49 PM
> To: rob brown
> Cc: election-methods at electorama.com
> Subject: Re: [EM] simple question (I think)
> On Wed, 2005-11-16 at 16:27 -0800, rob brown wrote:
> > Hmmm, ok.
> > 
> > Obviously though, if A has 8 pairwise wins, B has 7, and 
> everyone else
> > has less.....A will be the winner no matter what, right?  Regardless
> > of how close A's wins are and how large B's majorities are?
> This is only guaranteed if there are 9 candidates, in which case A is
> the condorcet winner.  Otherwise both A, B, and another could 
> end up in
> the Smith set.

But the original condition was that there was NO condorcet winner, so there
must be more than nine candidates. 

In fact, this points out that the condition for D to win (the original
"simple question") is that D must be in the Smith set. Presumably all of the
alternatives that have more pairwise wins than D are. 

So the conditions that D win are:

1. {A B C D} pairwise beat everybody else, forming a Smith set
2. The method that selects the winner puts strength of support above number
of pairwise wins

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