[EM] thoughts on the pairwise matrix

Paul Kislanko kislanko at airmail.net
Tue Nov 29 10:14:12 PST 2005

> I apologize if my comments came off as an attack.  I am just 
> trying to 
> understand your complaint, and unfortunately I still don't.  If you 
> don't want to address the question, then from my point of view, your 
> complaint doesn't make sense and I just have to consider it "proven" 
> not valid and move on.  (likewise, it's your right to not care if I 
> or others dismiss your complaint)

Jobst and I made the point awhile back that a mapping of ranked ballots to
pairwise preferences isn't necessarily exact. People say constructing a
pairwise matrix is "like" N x (N-1)/2 different 2-alternative elections, but
it is not. Ballots that are an exact reflection of preference would allow me
to make all N x (N-1)/2 choices. 

The argument is made that a "rational" person would construct a ranked
ballot so that that is the case, with which I disagree. The reason is that
when I must consider ALL ALTERNATIVES AT ONCE, I have to balance all of the
issues, too. When I am allowed to consider the alternatives 2 at a time, I
need only choose between the issues upon which they disagree.

The best example I can think of is "ranking foods I like". Because I list
ice cream over brussells sprouts over brocolli in that list does not mean
that given a choice between the two vegetables that I'd choose the sports.

Now, any ranked ballot method will require me to make those compromises. My
mathematical objection is to cycle-breaking rules that pretend to use my
preferences when they are really making identifiable inferences/assumptions.
I just think those should explicitly be listed.

I DO prefer ranked ballots, and philosophically like Condorcet methods. I
just think there may be extensions that are more desirable the ones that
have been studied to death. 

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