[EM] thoughts on the pairwise matrix

Paul Kislanko kislanko at airmail.net
Tue Nov 29 10:32:29 PST 2005


> -----Original Message-----
> From: Dave Ketchum [mailto:davek at clarityconnect.com] 
> Sent: Monday, November 28, 2005 10:33 PM
> To: Paul Kislanko
> Cc: 'rob brown'; election-methods at electorama.com
> Subject: Re: [EM] thoughts on the pairwise matrix
> This one seems to identify the problem we have been stumbling 
> over, though 
> not doing much for a fix:
> We have a method called Condorcet with its way of expressing ranking, 
> producing an array of intermediate results, and determining a winner.
> You prefer a method that starts with different voting.  Rather than 
> throwing sand in our gears, you would be more productive if 
> you gave your 
> method a name, such as "PaulK", and initiated discussion as 
> to its merits.

I do believe I've tried that, and been dismissed as being "irrational", and
of course, "not an expert." However, I can try again.

My suggestion was to axiomitize the study of EMs sort of the way Turing did
for computing about the same time Arrow was doing his work. Divide "election
method" into two different things, a method for collecting votes and a
method for counting them. An "ideal" collection method for
Condorcet-counting might not be the ranked ballot. But a generalized
collection method that can support Approval, Condorcet, or anything else is
entirely possible. 

> On Mon, 28 Nov 2005 16:44:09 -0600 Paul Kislanko wrote:
> > 
> > I think the only pairwise-matrix that is defensible is one 
> constructed 
> > by ballots. If the Ballot says "Choose one, choose both, 
> choose neither" 
> > for each pair of alternatives then there's a clear path 
> from voters' 
> > choices to the resulting PM. Otherwise, it's a matter of 
> how the ballots 
> > were processed to get the PM.
> > 
> What weakens that paragraph is that the Condorcet matrix 
> produced from 
> Condorcet Ballots is as correct for the Condorcet method as 
> your array is 
> for your method.

I actually have no method. But "Condorcet ballots" is an ambiguous term as
used in the reply to me. I actualy suggested that there BE a well-defined CB
such that for each pair of choices I vote "A, B, Either, or Neither". Then
the matrix can be guaranteed to reflect the voters' pairwise preferences,
instead of having to infer them (under different rules depending upon
whether equal rankings and/or truncation is allowed).

Mind, this is a theoretical consideration, not yet a practical one. Sort of
like using the Universal Turing Machine to proove a program's correctness.

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