[EM] General PR question (from Andy Jennings in 2011)

[Kathy Dopp]

Hi Kris,  Thanks for your questions.

On Wed, Oct 1, 2014 at 2:33 PM, Kristofer Munsterhjelm <km_elmet at t-
>
>
> What do you think of methods like Schulze STV that use a Condorcet-like
> setup to consider all candidate combinations and thus avoid the path
> dependence of the eliminations?

They sound good to me if they avoid the path dependence of
eliminations and  give Condorcet winners.


>
> How about this?
>
> 51: ABCD
> 49: EFGH
>
> Four to elect.
>
> Consider first a proportional outcome, ABEF. This would give:
>
> 51: ABCD 2/4
> 49: EFGH 2/4
>
> = 50.

Using the method I suggested for summing voters' representation, for
ABEF you would get

51/2 + 49/2 so, yes, 50.

>
> Then consider the extremely majoritarian outcome ABCD:
>
> 51: ABCD 4/4
> 49: EFGH 0
>
> = 51, so this has a greater score. But that's not proportional!

Yikes.  You're right!  The method I suggested does *not* work for
proportionality. Toby's method of minimizing the variance works better
I'm sure.  I would like to find something simpler, though, if
possible.

>
> PAV (proportional approval voting) is an example of such a rule: it gives a
> voter 1 point for the first candidate both on the council and the voter's
> approval ballot, 1/2 additional points for the second, 1/3 for the third and
> so on (reducing to D'Hondt in a party list situation). Then it chooses
> winners so that the sum of points is maximized. There's also birational
> voting, which is similar but with a different penalty function; if I recall
> correctly, birational did better than PAV according to my tests (
> https://www.mail-archive.com/election-methods@lists.electorama.com/msg05937.html
> ).
>
> It would be an interesting mathematical puzzle to determine such a penalty
> function so that various desirable properties are satisfied.

Yes. I like that method also.

Thanks for this.



-- 

Kathy Dopp
Town of Colonie, NY 12304
 "A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas
Jefferson

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

View my working papers on my SSRN:
http://ssrn.com/author=1451051