[EM] thoughts on the pairwise matrix

Dave Ketchum davek at clarityconnect.com
Mon Nov 28 20:33:12 PST 2005

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.

On Mon, 28 Nov 2005 16:44:09 -0600 Paul Kislanko wrote:

> I'll try again to make clear what I mean by not being convinced that 
> methods that use the PM to count votes can accurately reflect voters' 
> preferences.
> The basic claim is that the pairwise matrix accurately reflects pairwise 
> preferences by the voters. I do not believe this claim, because it it is 
> not based upon collecting votes via ballots that collect that kind of 
> information.
> The "is it raw data or an intermediate value?" question is critical.
> A process that translates a ranked ballot into the pairwise matrix form 
> is normally what is used to construct the intermediate value. But I 
> (along with Jobst Heitzig) have argued that if you want the voters' 
> pairwise preferences, the BALLOTS have to be in that format.
> If you ask me to rank 5 alternatives, I might vote A>B>C>D>E. But if you 
> ask me to pick one of A and C, I might chose C. To ASSUME that my ranked 
> ballot reflects my pairwise votes has not been (and probably can't be) 
> justified.

What can be picked out of that statement is that that voter is not sure as 
to liking A>C better than C>A.

> Academics suggest that voting C>A in a two-way race but A>C in a 
> five-way race is not rational. All I offer in response to that is "PROVE 
> that the PM reflects the voters preferences". (Hint: Arrow got a Nobel 
> prize for proving they can't do that).
> 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.

> ------------------------------------------------------------------------

  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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