Tournament Solutions and Majority VotingSpringer Berlin Heidelberg, 1997. júl. 17. - 256 oldal This book is a survey on the problem of choosing from a tournament. It brings together under a unified and self-contained presentation results and concepts from Graph Theory, Choice Theory, Decision Science and Social Choice which were discovered in the last ten years. Classical scoring and ranking methods are introduced, including the Slater orderings, as well as new statistical methods for describing a tournament, graph-theoretical methods based on the covering relation and game-theoretical methods. As an illustration, results are applied to the classical problem of Majority Voting: How to deal with the Condorcet Paradox. |
Részletek a könyvből
253. oldal
... Axioms of Cooperative Decision Making , Cambridge University Press , Cambridge . Muller , V. , J. Nesetril and J. Pelant ( 1975 ) " Either tournaments or algebras ? " Discrete Mathematics 11 : 37-66 . Myerson , R. ( 1991 ) Game Theory ...
... Axioms of Cooperative Decision Making , Cambridge University Press , Cambridge . Muller , V. , J. Nesetril and J. Pelant ( 1975 ) " Either tournaments or algebras ? " Discrete Mathematics 11 : 37-66 . Myerson , R. ( 1991 ) Game Theory ...
Tartalomjegyzék
Introduction | 1 |
Definitions and Notations | 9 |
4 | 23 |
Copyright | |
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Aïzerman property alternatives associated beats binary relation binary tree Bipartisan set BP(T component composition-consistent Condorcet winner Copeland score Copeland Value Copeland winner decomposition deduced defined Definition denote eigenvalue eigenvector exists finite Game Theory hence idempotent implies induction integer labelled binary tree Laffond Laslier lemma Let Te T(X losers Markov scores matrix maximal elements MC(T Minimal Covering set mixed strategies monotonous Nash equilibrium node players Proof proposition prove regular tournament result sequence simple agenda SL(T Slater order social choice Social Choice Theory solution concept sophisticated agenda subset Supp(p Suppose symmetric symmetric game T+(x T+(y TC(T TEQ(T TeT(X theorem Theory Top-Cycle Tournament Equilibrium set tournament game tournament of order tournament solution transitive chain two-player UC(T Uncovered set unique vector voting weak covering relation Weak Saddle Y₁ yes yes yes