The straight forward question which criteria are important and which
not is a bit confusing to me since I tend to think that in many cases
there is no such absolute order of importance. We know that election
methods typically need to make some compromises between different
criteria since all criteria can not be met. It depends quite often on
personal preferences or the environment for which the method is
planned for. Different environments ay lead to different preference
order. There can thus be valid reasons for sometimes respecting some
criterion ore than another and sometimes the other way around.
Juho Laatu
On Sep 22, 2007, at 23:16 , John Wong wrote:
That sorta answers my question about Landau, but what about the
Schwartz criterion? Is it important?
Date: Sat, 22 Sep 2007 21:50:16 +0930
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: [Election-Methods] How important is the Schwartz
criterion? Also, what is the Landau set, and how is different from the
John Wong wrote:
...what is the Landau set, and how is differentfrom the Smith and
the Schwartz set?
http://lists.electorama.com/mmsearch.cgi/election-methods-
electorama.com
http://lists.electorama.com/htdig.cgi/election-methods-
electorama.com/2000-April/003908.html
[EM] Landau Winners/Fishburn Set
Norman Petry [EMAIL PROTECTED]
Sun, 9 Apr 2000 09:58:20 -0600
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Here is another message from Markus answering some of my questions
about'Landau Winners'. This issue arose because Markus included
the algorithmfor Landau along with his Schwartz algorithm, and I
had some questions aboutit. Again, I thought it might be something
of interest to EM generally, so I amforwarding it to the list for
further discussion.N.**********Dear Norman,you wrote (8 Apr 2000):>
You mentioned the Landau set in your message, but I do not recall
that> Landau has ever been discussed on the EM list. Does it have
any merits or> uses we should consider? I did a quick search on
the Internet, but turned> up nothing useful, so if you have any
references to Landau I would> appreciate it.I should have said that
the set of Landau winners is called 'uncovered set'or 'Fishburn
set.' If you search for these words, then you will find
somereferences.******A Landau winner is a candidate, who defeats
every other candidate with apath of length 1 or 2.Candidate A is a
Landau winner iff for every other candidate B at least oneof the
following two statements is correct:(1) A >= B.(2) There is a
candidate C such that A >= C >= B.******There must always be at
least one Landau winner.******Miller demonstrated that if (1) the
electorate is 2-dimensional, (2) thevoters are sophisticated and
(3) the used election method meets themajority criterion, then the
winner must always be a Landau winner.Therefore, many scholars
consider the Landau winners to be the naturalgeneralization of the
Condorcet winner.[a] Nicholas R. Miller, 'Graph-Theoretical
Approaches to the Theory ofVoting,' American Journal of Political
Science, vol. 21, p. 769-803, 1977,[b] Nicholas R. Miller, 'A New
Solution Set for Tournaments and MajorityVoting: Further Graph-
Theoretic Approaches to Majority Voting,' AmericanJournal of
Political Science, vol. 24, page 68-96, 1980,[c] Norman J.
Schofield, 'Social Choice and Democracy,' Berlin,Springer-Verlag,
1985,[d] Philip D. Straffin, 'Spatial Models of Power and Voting
Outcomes,'Applications of Combinatorics and Graph Theory to the
Biological and SocialSciences, edited by Fred S. Roberts, New York-
Berlin, Springer, 1989,page 315-335.******I mentioned the Fishburn
set only because the calculation of the Fishburnset is almost
identical to the calculation of the Smith set and becausesomebody
might ask in the future how to calculate the Fishburn set.******You
wrote (8 Apr 2000):> Also, I think your message would be a valuable
contribution to the EM list> archives, for anyone trying to
implement Smith, Schwartz, etc. May I have> your permission to
forward the message to the list?Of course, you may.Markus Schulze
Gear up for Halo® 3 and get a $25 Best Buy gift card. It’s our way
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