[EM] Weighted voting systems for proportional representation

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
>> From: Kristofer Munsterhjelm <km_elmet at lavabit.com>

>> I don't think that passes DPC (since Borda doesn't pass Majority), but
>> it passes the weaker "force proportionality" criterion (in that an 1/n
>> faction can, by strategy, force their representative to be the one they
>> want). So it is at least better than SNTV, except for the whole bit
>> about not being summable :-)
> 
> It *is* a summable method because it would simply require reporting
> and summing the sum from each precinct for every ballot's (1) 1st
> choice candidate, (2) 2nd choice candidate, and so forth.

Is it? I may be wrong, but consider these alternate scenario snippets:

Scenario A:

1: X: 2, Y: 1, rest 0
1: A: 2, B: 1, rest 0

Scenario B:

1: X: 2, B: 1, rest 0
1: A: 2, Y: 1, rest 0

Say the current slate is {X,Y}. Then in the first scenario, you want to 
add two points to the score from the first voter's ballot, and none from 
the second ballot; but in the second scenario, you want to add two 
points from the first ballot and one from the second.

Yet the per-candidate sums give X two points and Y one in both 
scenarios. Even if you count the vote ranked style, you get:

First scenario: first place: one X and one A, second place: one Y and one B.
Second scenario: first place: one X and one A, second place: one B and 
one Y.

> On first glance, I like this method, including the leximax tie-breaker
> for possible slates which garner the same number of 1st choice votes
> (I assume this can be continued if some slates garner the same # of
> 1st and 2nd choice votes to examine the 3rd choice candidates) which
> seems very fair.

That is indeed what I meant by the ", etc". I think truncated ballots 
would count as if the person voted the minimum rating possible for the 
candidates in question, so if you were counting 2nd choice votes and 
someone bullet-voted, that just means he counts as if he voted the other 
slate members zero.

It would also be possible to use mean instead of sum score, in which 
case one just wouldn't add to either the numerator or denominator when 
encountering a truncated ballot -- or you could use Warren's soft quorum.