Kathy Dopp wrote:
I do not like this system and believe it is improper to call it
"Condorcet". It seems to have all the same flaws as IRV - hiding the
lower choice votes of voters, except if the voter voted for some of
the less popular candidates. Thus, I can see there may be lots of
cases when it eliminates the Condorcet winner.
Do you mean that it fails to elect the Condorcet winner in some
singlewinner elections, or in multiwinner ones? If it's the latter, then
there's a perfectly good reason for that.
Let me pull an old example again:
45: Left > Center > Right
45: Right > Center > Left
10: Center > Right > Left
If there's one seat, Center is the CW; but if you want to elect two, it
seems most fair to elect Left and Right. If Center is elected, the wing
corresponding to the other winning candidate will have greater power.
As for singlewinner, I think that reduces to ordinary Condorcet, though
I might be wrong. Note that
for each hopeful candidate C that is the topmost hopeful candidate on
at least one ballot is determined from PC = VC/(SC+1) where VC is the
total number of ballots where C is the topmost hopeful candidate and SC
is the sum of the seat values of ballots where C is the topmost hopeful
candidate.
In a singlewinner setting, there's only one round for each set, and in
that round, everybody's SC is zero. So if you have an AB primary, then A
gets points equal to the number of times it is ranked above B, and B
gets points vice versa. Say that A is ranked ahead of B on more ballots
than B is ranked ahead of A. Then A > B with magnitude according to PO
(I think?), which is handled properly by the Ranked Pairs-like resolver
at the end.
So unless I made a mistake, I think that in the singlewinner case, the
pairwise defeat data handed to the Ranked Pairs part would be just like
the pairwise defeat data used in Ranked Pairs itself. If that is true,
then that means the method reduces to Ranked Pairs, which is Condorcet,
and thus the method always elects the CW in the singlewinner case when
there is one.
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