[EM] VoteFair representation ranking recommended for Czech Green Party

[Raph Frank]

On Fri, Apr 30, 2010 at 8:22 PM,  <VoteFair at solutionscreative.com> wrote:
>> I would appreciate if Votefair ranking would have some mathematical
>> description and at least well described and discussed in some
>> peer-reviewed paper.
>
> If you replace the word "paper" with the word "article," there is a widely
> peer-reviewed, published description of the Condorcet-Kemeny method.  (Below
> I'll get to the issue of VoteFair representation ranking.)  It's in
> Wikipedia under the name "Kemeny-Young method."  The description is
> rigorous, which is what I presume you mean by "mathematical."

Can you put on a clear description of the method (single seat and PR
version) on your website and ideally link it from the front page.

For example:

"Q:  In VoteFair ranking, how are all the votes combined into one
overall sequence?

A:  The best way to see how the calculations are done is to try it! "

This is totally not true (at least for me).  You are asking someone to
reverse engineer your method.  Just explain how it works (it could
just be a link).

It is hard for us to comment if you don't describe the method completely.

Anyway, based on what I can determine by searching for info about the
method, is this an accurate description?

Single seat Votefair is equivalent to the Condorcet-Kemeny system.

VoteFair representation ranking works like reweighted range voting.

You use a single seat method and then elect candidates in rounds and
deweight ballots after each step.

The process is:

1) Voters cast a ranked ballot

2) All ballots start with a weighting of 1

3) Determine the Vote Fair winner (W).  This candidate is considered elected.

4) For next step, ignore all ballots which rank W first choice

5) Work out the new Vote Fair winner (S).  This candidate is the 2nd
place for this round.

6) All ballots that rank W over S are considered to support W.

7) The weight for every ballot which supports W is multiplied by a
value (k).  k is selected so that the total weight drops by half.

8) If there are more seats to fill goto 3)


Note on 7):

- If 70% of the voters prefer W to S, then each of them would be deweighted by

(70-50)/70 = 2/7

- This would mean that their total weight would be reduced from 70% to 20%.
- The other 30% would be from voters who prefer S to W.
- This means that in each round, the total weighting of the ballot is
reduced by 50%.

It seems like a faction with >1/3 of the voters could guarantee to get
a seat in a 2 seat election.  They would just need to place their
candidate first choice.  If the lose the first round, their ballots
won't be deweighted (as their candidate is ranked first), so they will
take the 2nd seat.  This is Droop proportional for 2 seats at least.

I think this method might be proportional even when electing more than
2 candidates.  Does it meet Droop proportionality?

Also, is it guaranteed that the number from 6) is always more than 50%
of the remaining ballot weight?  If not, then k could be negative :).
In most cases, it would be OK, since W must be a condorcet winner.
However, if there is a condorcet tie, then S might be one of the
candidates which defeats W pairwise.