More ruminations on this topic:
Suppose that a voter ranks six candidates as follows in a three seat
multiwinner race:
A1>B1>B2>A2>A3>B3 .
Which of the following two outcomes would this voter be most likely to
prefer?
(1) The A team {A1,A2,A3} wins.
(2) The B team {B1,B2,B3} wins.
Note that the B team median, B2, is preferred over the A team median,
A2, but the average rank of the A team is ahead of the average rank of
the B team, i.e. the A team's Borda Count his higher than the B team's.
The voter's favorite is an A, and the last ranked candidate is a B.
Of course, the answer would depend on the utilities as well as upon the
order of the candidates.
However, in the face of unknown utilities, our best guide to the highest
average utility subset is the subset with the greatest Borda Count. So I
would have to guess that this voter would prefer the A team over the B
team, if the ranking is sincere.
On the other hand, the Condorcet spirit seems to dictate the choice of the
higher median subset, since the one with the higher median has more
pairwise wins (relative to the ballot).
Shall we use a hybrid method?
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