[EM] Condorcet divisor method proportional representation

[Kathy Dopp]

On Sun, Jul 3, 2011 at 1:34 PM, Kristofer Munsterhjelm
<km_elmet at lavabit.com> wrote:

>>> 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.

In your example:
55: prefer Center to (Left or Right)
55: prefer Right to Left
45: prefer Left to Right

and you say that the Droop criteria says that Right and Left must be elected!

But by the rule you cite, then all three candidates must be elected,
and thus the Droop quota requires electing k+1 candidates, which
contradicts the statement of its own rule.

Thus, QED, the Droop criteria doesn't elect k seats, and so must be
abandoned, unless you are insisting on burying the 2nd choice
candidates of all voters - like STV and IRV do to some voters, while
considering the 2nd choice candidates of others.  Thus, it seems
logical, that only an IRV proponent, who insists on not looking at the
2nd choice votes of some voters would insist on using the Droop quota.
 I dare say, that to apply the Droop quota  in many instances requires
the unfair treatment of voters' votes (looking at only some voters 2nd
and later choices, but not others) in most cases, or it would tend to
elect more or less than the required number of seats otherwise. Hence,
the Droop quota, not in this example, but in many others with the same
number of voters and candidates, would require the unfair treatment of
voters' rank choice votes or if not, it would elect the wrong number
of seats.



>
> (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.)

Throwing p in the expression, seems to make little sense. You mean if
only p= 6/(k+1) = 2 voters prefers a set of 3 candidates to all
others, in the case of k=2, then min(2,3) = 2 of these candidates
should win!  That's a funny rule.

A more common sense rule IMO would be for k seats, elect the k
candidates who are preferred above the rest of the candidates by more
voters.

-- 

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051