# [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

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

--
davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

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