Juho wrote:
On May 7, 2010, at 7:11 PM, Kristofer Munsterhjelm wrote:
Schulze's primary argument is that the use of paths let one make a
method that is very close to Minmax, yet is cloneproof and elects from
Smith. Thus, if one thinks the Minmax yardstick is a good one, yet
that Minmax's clone susceptibility means one has to diverge from it in
certain cases, Schulze is a good method.
Yes, Schulze has some such properties. If both criteria are considered
important, then one should just estimate which method is closer to
ideal. Minmax may ignore clones that have strong losses to each others
(it puts more weight on the distance to being a Condorcet winner). Path
based methods may defend "clones" also when there are no clones (and a
candidate that meets neither criterion might win).
Schulze also satisfies some "internal non-contradiction" criteria that I
like, such as reversal symmetry. It seems reasonable that a method
should handle "likes" and "hates" equally but opposite. However, it
would also be reasonable, at first observation, that a voter can never
be worse off by showing up, but that (Participation) is very strict and
almost no methods pass it.
Perhaps there is an element of aesthetics to those criteria
(monotonicity, reversal symmetry, and also monotonicity). This would
fall within the legitimacy meta-criterion, I think; voters would suspect
something fishy is going on if raising a candidate makes him lose, if
polling for "who do you dislike" doesn't return the loser of "who do you
like", etc.
As for your second part, there is naturally a tradeoff between strong
paths and short paths. Schulze considers paths equally no matter their
length, but the question is sensible. Methods that focus on short
paths are more like Copeland (which focuses on "paths" of a single
step), and methods that elect from the uncovered set would have short
paths from the winners to the candidates not in the uncovered set.
I see the "one step philosophy" as answering to question "if we would
elect x, would the society be happy with x or would it be interested in
changing candidate x to someone else" (not on questions on if the
society would be interested in multiple sequential changes). The
philosophy of Copeland's method would make sense in principle. I guess
the minmax philosophy can be said to focus only on the strength of the
losses and not on the number of them because of the clone related
problems that Copeland has. The number of losses also has no meaning if
the intention is to check how close each candidate is to being a
Condorcet winner.
I can see three philosophies/approaches, and associated simple methods
(neither cloneproof):
- The minmax approach: What matters is the worst outcome. Minmax is its
simple method. Schulze fits here because of the strength of a beatpath
being equal to the weakest link.
- The Copeland approach: What matters is the number of short paths.
Second-order Copeland goes here as well.
- The least reversal approach: What matters is the sum of victories or
defeats. Condorcet least-reversal fits here, as does the "attacker's
version" where the candidate with the greatest victory sum wins. These
methods seem to get low Bayesian Regret.
Ranked Pairs, I'm not sure. Its idea is more complex, perhaps embodied
by the immunity against majority complaints criterion, which goes like:
If voters that support Y (and Y beats the winner X) complain that Y
should have won, not X, then those who support X can point out that X
beats Y at least as strongly through an indirect path, no matter who Y is.
It's possible to get Ranked Pairs closer to the Copeland approach, as by
Short Ranked Pairs
(http://www.mail-archive.com/[email protected]/msg04266.html).
I have no idea where River fits into this - or Kemeny, for that matter.
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