[EM] Weighted voting systems for proportional representation

[Kathy Dopp]

On Sun, Jul 24, 2011 at 4:53 AM, Kristofer Munsterhjelm
<km_elmet at lavabit.com> wrote:

>
> Ah, yes. This leads me back to an older thought that perhaps the criterion
> of summability should be refined for multiwinner methods by turning it into
> two criteria. These criteria would be:
>
> - Weak summability: If the number of seats is fixed, one can find the winner
> of the method according to precinct sums, where the amount of data required
> for these sums grows as a polynomial with respect to the number of
> candidates, and as a polylogarithmic function with respect to the number of
> voters.
>
> - Strong summability: Same as weak, but without the number of seats being
> fixed or known in advance.
>
> To my knowledge, Schulze STV is weakly summable, as is this method, because
> if you fix S, N choose S is bounded by a polynomial.
>
> When people here talk about summability for multiwinner methods, they
> usually mean strong summability, though. This is like SNTV or party list. If
> you have the Plurality counts for SNTV, it doesn't matter how many seats you
> want, you can just read off the n first Plurality winners. Similarly, for
> party list, you can just run the Sainte-Laguë method n times for n seats
> with the same input data.
>
> Do you think weak summability is sufficient to audit multiwinner methods?
>
>

Your definitions do not differentiate between the enormous difference
between the difficulty of summing STV vs. the far more summable voting
method you were proposing!  That is an enormous difference -
regardless of whether the number of seats is known in advance or not.
I was only considering contests where the # of seats are known in my
remarks.  Thus, I do not think that your definitions are sufficient
for evaluating methods.


-- 

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