[EM] VoteFair representation ranking recommended for Czech Green Party

[Richard Fobes]

Kristofer Munsterhjelm wrote:
> If Schulze and Kemeny produces the same result so often,
why not just
> switch to Schulze and gain clone independence and
polynomial runtime?
> Independence of clones seems more important than Kemeny's
unique
> Reinforcement criterion anyway.

The Condorcet-Kemeny method has significant advantages over
the Condorcet-Schulze method, but some of those advantages
have not yet been recognized.

Some of the advantages involve not-yet named criteria.  For
example, reversal symmetry just requires that the winner not
be the winner if all the ballot preferences are reversed,
and both Condorcet-Kemeny and Condorcet-Schulze meet that
criteria.  A not-yet named criteria beyond that, which I
would call "full reversal symmetry," would require a
complete symmetrical reversal of popularity ranking if all
the ballot preferences are symmetrically reversed, and
Condorcet-Kemeny meets that criteria, but Condorcet-Schulze
does not.  (I'm not saying this new criteria is significant,
I'm just pointing out that unnamed criteria do exist, and
this is an example.)

As long as we just focus on which criteria are met, and
which are failed (by each method), we are only skimming the
surface.  A deeper way to quantify fairness criteria would
be to count the percentage of (all possible) cases in which
a criteria is met.  (Subtracting that percentage from 100%
gives the failure rate.)  That will yield more meaningful
measurements of fairness criteria, far beyond the current
yes/no, meet/fail checklists.

At that point some overlooked advantages of the
Condorcet-Kemeny method will emerge.

(I point out in my reply to Markus Schulze why the
calculation runtime is not an issue.)

> If the answer is, as you hint later, that Kemeny somehow
produces better
> outcomes than Schulze in the cases they do differ, how
would you
> quantify better? ...

See above.

> ... Perhaps there's a better method still than Kemeny, say
> a method that is at least as good on average and satisfies
clone
> independence (or perhaps IPDA, etc).

Further improvements are certainly possible.

I've created an algorithm at NegotiationTool.com that
handles situations that go beyond the kind of voting
discussed here.  For example, it can handle the election of
Cabinet ministers, which involves far more complexity than
even proportional election methods.  One of those
complexities is that an MP (member of parliament) can be
nominated for multiple cabinet positions, yet can fill only
one (typically chosen as the most-favored position).  It
also ensures proportional representation throughout the
cabinet, taking into account that the Prime Minister is part
of the cabinet.  For that matter, the selection of Prime
Minister is part of the results.  (Of course the process is
interactive, just as for current deliberations.)  And the
algorithm handles rules about party-based quotas.  All of
those complexities go far beyond what we are talking about
here.

> On 5/4/2010 9:01 PM, Richard Fobes wrote:
>> The Condorcet-Schulze method and the Condorcet-Tideman
method use a
>> similar elimination approach, where one looks for the
biggest pairwise
>> numbers and the other looks for the biggest margins of
victory.
>
(Kristofer Munsterhjelm wrote:)
> Not necessarily. The beatpath approach (count number of
stronger
> beatpaths between all pairs of candidates - the winner is
the one with
> no stronger beatpath to him than away from him) doesn't
involve 
> elimination.

I used the word elimination in a different sense than
eliminating candidates.  My intent was to convey the idea
that the Condorcet-Schulze method looks at pairwise counts
to identify which paths to eliminate (because those paths
are weaker), whereas the Condorcet-Kemeny method looks at
Kemeny scores for (non-representative) sequences to
eliminate.

Richard Fobes