[Election-Methods] How important is the Schwartz criterion? Also, what is the Landau set, and ho

[Juho Laatu]

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: chrisjbenham at optusnet.com.au
> To: johnwong00 at hotmail.com
> CC: election-methods at electorama.com
> 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 election-methods-list at eskimo.com
> Sun, 9 Apr 2000 09:58:20 -0600
> Previous message: [EM] New Smith,Schwartz Algorithms
> Next message: [EM] YES versus Head toHead Tiebreakers
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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
>
>
>
>
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