[EM] thoughts on the pairwise matrix

[Paul Kislanko]

> -----Original Message-----
> From: Andrew Myers [mailto:andru at cs.cornell.edu] 
> Sent: Tuesday, November 29, 2005 2:11 PM
> To: Paul Kislanko
> Cc: election-methods at electorama.com
> Subject: Re: [EM] thoughts on the pairwise matrix
> 
> On Mon, Nov 28, 2005 at 06:41:34PM -0600, Paul Kislanko wrote:
> > I don't have to support my argument, since I am asking for 
> those who claim
> > Condorcet methods are "better" to support the claim that 
> those methods are
> > "like" Nx(N-1)/2 different elections. They are not, unless 
> I get to make
> > Nx(N-1)/2 choices, which I don't get to do.
> 
> It seems we could easily generalize most Condorcet methods to 
> allow the voter
> to specify an NxN matrix instead of a sorted list. This would 
> provide the same
> information as the C(N,2) elections, with the added ability 
> for a user to
> provide an arbitrary preference graph that
> 
>  - violates transitivity
>  - does not connect every pair of nodes,
>  - or contains cycles.
> 
> Violations of transitivity and acylicity seem of dubious 
> value to me, but they
> could be accommodated.  So I'd claim that ranked ballots are 
> just as good as
> the hypothetical C(N,2) elections, if you can say that two 
> candidates are
> equally preferred on your ballot.

Nice, but support your claim with some kind of proof. Otherwise, it is just
a "belief", and I am not required to adopt it.