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
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To: [EMAIL PROTECTED]
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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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message: [EM] YES versus Head toHead Tiebreakers Messages sorted by: [
date ] [ thread ] [ subject ] [author ] 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
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