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  • 1
    Book
    Book
    Geometry of voting; 3 (1994)
    Berlin u.a. :Springer,
    Details
    Title: Geometry of voting; 3
    Author: Saari, Donald G.
    Publisher: Berlin u.a. :Springer,
    Year of publication: 1994
    Pages: 372 S.
    Series Statement: Studies in economic theory 3
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 2
    Electronic Resource
    Electronic Resource
    Mathematical structure of voting paradoxes (2000)
    Springer
    Economic theory 15 (2000), S. 55-102 
    Details
    ISSN: 1432-0479
    Keywords: Keywords and Phrases:Positional voting, Voting paradoxes, Social choice. ; JEL Classification Number:D71.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary. A theory is developed to explain all positional voting outcomes that can result from a single but arbitrarily chosen profile. This includes all outcomes, paradoxes, and disagreements among positional procedure outcomes as well as all discrepancies in rankings as candidates are dropped or added. The theory explains why each outcome occurs while identifying all illustrating profiles. It is shown how to use this approach to derive properties of methods based on pairwise and positional voting outcomes. Pairwise voting is addressed in the preceding companion paper [15]; the theory for positional methods is developed here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001990050002
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Mathematical structure of voting paradoxes (2000)
    Springer
    Economic theory 15 (2000), S. 1-53 
    Details
    ISSN: 1432-0479
    Keywords: Keywords and Phrases:Positional voting, Voting paradoxes, Social choice. ; JEL Classification Number:D71.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary. A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes pairwise voting where new results include explanations for all paradoxes, cycles, conflict between Borda and Condorcet rankings, differences among procedures using pairwise votes (such as the Borda Count, Kemeny's method, and the Arrow-Raynaud rule), and discrepancies among the societal rankings as candidates are dropped or added. Other new results include new relationships among the Borda and Condorcet “winners” and “losers.” The theory also shows how to construct all supporting profiles. The following companion paper does the same for positional methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001990050001
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The Copeland method I.: Relationships and the dictionary (1996)
    Springer
    Economic theory 8 (1996), S. 51-76 
    Details
    ISSN: 1432-0479
    Keywords: Key words Copeland method ; Borda count ; Dictionary ; Positional Voting ; Voting paradoxes.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary.  A central political and decision science issue is to understand how election outcomes can change with the choice of a procedure or the slate of candidates. These questions are answered for the important Copeland method (CM) where, with a geometric approach, we characterize all relationships among the rankings of positional voting methods and the CM. Then, we characterize all ways CM rankings can vary as candidates enter or leave the election. In this manner new CM strengths and flaws are detected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212012
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    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The generic existence of a core for q-rules (1997)
    Springer
    Economic theory 9 (1997), S. 219-260 
    Details
    ISSN: 1432-0479
    Keywords: JEL Classification Numbers: C7.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary.  A q-rule is where a winning coalition has q or more of the n voters. It is important to understand when, generically, core points exist; that is, when does the core exist in other than highly contrived settings? As known, the answer depends upon the dimension of issue space. McKelvey and Schofield found bounds on these dimensions, but Banks found a subtle, critical error in their proofs. The sharp dimensional values along with results about the structure of the core are derived here. It is interesting how these dimensional values correspond to the number of issues that are needed to lure previously supporting voters into a new coalition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213800
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    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    The generic existence of a core forq-rules (1997)
    Springer
    Economic theory 9 (1997), S. 219-260 
    Details
    ISSN: 1432-0479
    Keywords: C7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary Aq-rule is where winning coalition hasq or more of then voters. It is important to understand when, generically, core points exist; that is, when does the core exist in other than highly contrived settings? As known, the answer depends upon the dimension of issue space. McKelvey and Schofield found bounds on these dimensions, but Banks found a subtle, critical error in their proofs. The sharp dimensional values along with results about the structure of the core are derived here. It is interesting how these dimensional values correspond to the number of issues that are needed to lure previously supporting voters into a new coalition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213800
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    The likelihood of dubious election outcomes (1999)
    Springer
    Economic theory 13 (1999), S. 345-363 
    Details
    ISSN: 1432-0479
    Keywords: Keywords and Phrases: Voting ; Central limit theorem ; Paradoxes. ; JEL Classification Numbers: D71 ; D72.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary. A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the “correct” one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001990050258
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    The aggregated excess demand function and other aggregation procedures (1992)
    Springer
    Economic theory 2 (1992), S. 359-388 
    Details
    ISSN: 1432-0479
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn≧2 commodities to all of the 2 n −(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k≧2 candidates over a space of n≧2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 n −1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this “anything can happen” conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211422
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    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    The Copeland method (1996)
    Springer
    Economic theory 8 (1996), S. 51-76 
    Details
    ISSN: 1432-0479
    Keywords: Copeland method ; Borda count ; Dictionary ; Positional Voting ; Voting paradoxes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary A central political and decision science issue is to understand how election outcomes can change with the choice of a procedure or the slate of candidates. These questions are answered for the important Copeland method (CM) where, with a geometric approach, we characterize all relationships among the rankings of positional voting methods and the CM. Then, we characterize all ways CM rankings can vary as candidates enter or leave the election. In this manner new CM strengths and flaws are detected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212012
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Celestial mechanics Orbits of all sorts (1998)
    [s.l.] : Macmillan Magazines Ltd.
    Nature 395 (1998), S. 19-20 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Can we predict how three bodies, attracting each other by gravity, should move? Isaac Newton is said to have got a headache trying to solve the three-body problem — and in the form of the more general n-body problem, it has been giving mathematicians a headache ever since. Two centuries after ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/25607
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    Paper (German National Licenses)
    Fulltext
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