[EM] Condorcet divisor method proportional representation

[Kristofer Munsterhjelm]

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.