CR pairwise

[Rob LeGrand]

Roy wrote:
> IMO, this gives too much weight to rankings and not enough to
> ratings. The collapsing strategy uses ratings, but it is only used to
> resolve cycles. I don't think that, given the information on a CR
> ballot, the Condorcet criterion should apply.
>
> Consider (sincere ratings):
>
> Voters   rate A   rate B   rate C
> 20       100      50       0
> 10       50       0        100
> 70       90       100      0
>
> B is clearly the Condorcet winner, but choosing A brings the rest of
> the voters into the represented group, without badly compromising the
> preferences of the majority. When you know the strength of a
> preference, you can do better than when you only know that a
> preference exists.

Yes, I know it's tempting to use the information more precisely, and if we
could count on voters' being sincere, it would be better.  But again, we want
to encourage sincerity.  Electing A in this example will encourage your 70
B-1st voters to rate A lower.  Any time you don't elect a voted Condorcet
winner, you create serious strategy problems.  If you use the rankings first
and use the ratings only to break ties, you're less prone to those problems. 
Dodgson and Borda are inferior to Minmax, Ranked Pairs and Schulze for the same
kind of reason.

Electing a Condorcet winner from CR ballots, and the CR winner if there is no
Condorcet winner, would be very similar to Black.  If the ratings were very
fine-grained, I might vote something like 1000, 999, 998, 3, 2, 1, 0.  But if
the ratings were coarser, I'd probably vote like approval.  I'm not sure this
is an improvement over plain CR.  But using ratings only to resolve pairwise
cycles might work better.  On the other hand, why not ignore ratings completely
after using them to generate rankings?  Voters would have much less reason to
be insincere then, and you could see who "should" have won.  :)

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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