[EM] Weighted voting systems for proportional representation

[Kathy Dopp]

On Sat, Jul 23, 2011 at 9:33 AM, Kristofer Munsterhjelm
<km_elmet at lavabit.com> wrote:
> 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.

I was reading what you wrote *literally* when you said: "Any given
slate has a score equal to the sum of, over all ballots, the
 *highest* rated candidate on that ballot that is also in the given slate."

You also said "Tiebreaks are leximax (sum of, over all ballots, the
second highest rated candidate, etc)." Taken *literally* this means
that the votes of the 2nd highest candidate is only considered for
breaking ties among slates.

The English language is so ambiguous. Your system would have to make
it clear to voters that ranking a candidate on the ballot *at all* is
likely to help that candidate win - even if ranked last.

 I probably would *not* support a system that counted ballots in a way
that is not precinct summable.


>
>> 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.
>
>



-- 

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