[EM] Condorcet divisor method proportional representation

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
> On Sun, Jul 3, 2011 at 2:33 AM, Kristofer Munsterhjelm
> <km_elmet at lavabit.com> wrote:
>> 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.
> 
> I disagree. In your example, clearly 55 prefer right to left, but only
> 45 prefer left to right.  And center is the clear winner overall.
> Thus, if only two will be elected, it should be center and right.

That's incompatible with the Droop proportionality criterion. The DPC 
says that if there are k seats, and a fraction greater than 1/(k+1) of 
the electorate all prefer a certain set of candidates to all others, 
then someone in that set should be elected.

(Actually, the more general sense is that if more than p/(k+1) of the 
electorate all prefer a set of q candidates to all others, then min(p, 
q) of these candidates should win.)

You could also consider a single-candidate variant of the majority 
criterion: If, in a single-winner case, more than 50% vote a certain 
candidate top, he should win. If, in a two-winner case, more than 33% 
vote a certain candidate top, he should win. If in an n-winner case, 
more than 1/(n+1) vote a certain candidate top, he should win. Such a 
criterion would mean that Left and Right have to be elected, because 
each is supported by more than 33%.

> Unless you really like hung partisan governments run by opposite
> extremists who care more about the next campaign than about governing
> - like we have now in the US Congress.  Any method that reduces to
> IRV, like STV does, is going to tend to elect extremists rather than
> majority preferred centrists, and thus contribute to bad governing
> practices IMO.

Unless I'm mistaken, the divisor method does not reduce to IRV in the 
single-winner case. Rather, it reduces to Ranked Pairs (wv).

> So, I say that the word "Condorcet" applied to that method is wrong.
> At least in the case of multi-winner elections -- as your example
> shows.

It is correct that this method doesn't meet the Condorcet criterion in 
the multiwinner case. In that sense, you are right. However, none of the 
other Condorcet-reducing multiwinner methods (CPO-STV, Schulze STV) do, 
either, except Schulze STV's proportional ordering, which passes it as a 
consequence of being house monotone.