[EM] thoughts on the pairwise matrix

[Dave Ketchum]

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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