On 9/29/2011 11:06 AM, Toby Pereira wrote:
> Richard Fobes <[email protected]> wrote:
> > Some people have questioned why it is worth doing Condorcet-Kemeny
> > calculations when there are faster Condorcet methods. The answer is
> > that Condorcet-Kemeny results offer lots of advantages, including
> > one named advantage that is currently underappreciated and a
> > significant advantage that has not yet been named or widely
> > recognized.
> This is very cryptic. What is this named advantage and why haven't
> > you named it here? Is the unnamed advantage also indescribable?
The named criteria is "reinforcement". It requires that if all the
ballots are divided into separate races and the overall ranking for the
separate races are the same, then the same ranking occurs when all the
ballots are combined.
As far as I know, the Condorcet-Kemeny method is the only voting method
that meets this criteria.
Markus Schulze claims that this criteria is not important, yet recently
he removed from the discussion page of "his" Wikipedia "Schulze Method"
article the fact that "his" Condorcet-Schulze method does not meet the
reinforcement criteria:
http://en.wikipedia.org/w/index.php?title=Talk%3ASchulze_method&action=historysubmit&diff=454246530&oldid=439262253
One of the reasons I regard the reinforcement criteria as
underappreciated is that, unlike the other voting-method "fairness"
criteria, there is no Wikipedia article describing the reinforcement
criteria.
Of course many (most?) single-winner voting methods do not produce a
full ranking (or are not designed to do so), and only identify a single
winner, so it can be claimed that the reinforcement criteria is not
relevant to single-winner methods. In contrast, my claim is that one of
the strengths of the Condorcet-Kemeny method is that it not only
"correctly" (see below) identifies the most popular candidate/choice,
but it also "correctly" identifies the second-most popular
candidate/choice, and so on down to the least-popular candidate/choice.
Note that correctly identifying the _least_-popular choice is very
relevant in TV's American Idol contest because each week the "least
popular" singer is eliminated. To educate people that the contestant
with the fewest plurality ("first-choice") votes is not necessarily the
least popular, I conduct an unofficial weekly VoteFair American Idol
poll, which attracts about one thousand (unique) voters each week.
As a reminder, here are the voting criteria that the Condorcet-Kemeny
method meet:
* Condorcet criterion
* Majority criterion
* Non-imposition
* Non-dictatorship
* Unrestricted domain
* Pareto efficiency
* Monotonicity
* Smith criterion
* Independence of Smith-dominated alternatives
* Reinforcement
* Reversal symmetry
The other item, the "unnamed" criteria, relates to the simplicity of the
Condorcet-Kemeny method. Of course Approval voting and Range voting are
much simpler, yet Majority Judgment and the Condorcet-Schulze method are
more complex, and I am working on a way to quantify this "simplicity"
dimension, but I have not yet fully developed this idea.
The reason I didn't explain these points in the earlier message is that,
as you can see, they require lots of explanation, which would have
distracted from the main topic of that message, which was calculation time.
> > The only valid disadvantage is that in very rare cases it fails the
> >"independence of clones" criteria, yet this perceived disadvantage
> > does not yield unfair results if all aspects of VoteFair Ranking
> > are used.
> I'm not sure how rare it would be myself (an exact clone isn't
> required for a non-cloneproof method to have problems).
Keep in mind that the Condorcet-Kemeny method can only fail the
independence of clones criteria when there is circular ambiguity (i.e.
no Condorcet winner). In such cases I contend that it is debatable as
to who the winner really should be.
To clarify this point, imagine a group of people around a large table
being asked to elect a president. Imagine that in response to being
asked "who is your first choice?" each person points to the person on
the right. Then imagine that in response to being asked "who is your
second choice?" each person points to the person on the left. Finally
imagine that in response to being asked "who is your third choice?" each
person points to the person at the head of the table. In this situation
IRV advocates would claim that the person at the head of the table does
not deserve to win because he or she was the first choice of only one
voter. This kind of circular ambiguity, which is easily handled by the
Condorcet-Kemeny method, may involve electing the "wrong" candidate
according to the independence of clones criteria, but in such cases does
the "correct" clone deserve to win? This is debatable.
My point is that the conditions under which the Condorcet-Kemeny method
fails the independence of clones criteria involve circular ambiguity,
which in turn can involve lots of head scratching about who really
deserves to win.
> So VoteFair doesn't use the Kemeny method then?
VoteFair popularity ranking is mathematically equivalent to the
Condorcet-Kemeny method. VoteFair popularity ranking, which I created
without knowing about the Condorcet-Kemeny method, calculates a sequence
score that is the sum of all the pairwise counts that _support_ that
sequence, and the sequence with the _highest_ score indicates the
overall ranking. The original method described by Kemeny calculates a
sequence score that is the sum of all the pairwise counts that _oppose_
that sequence, and the sequence with the _lowest_ score indicates the
overall ranking.
I apologize for the long delay in replying to this message. Jameson
Quinn and I have been attempting to refine a couple of controversial
sentences in the Declaration of Election-Method Reform Advocates (which
I think we are close to achieving, and that edit will be posted here)
and, as I've said before, I don't earn income from anything related to
election-method reform.
Richard Fobes
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