Modeling optimal social choice: matrix‐vector representation of various solution concepts based on majority rule

Modeling optimal social choice: matrix‐vector representation of various solution concepts based on majority rule

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Article ID: iaor20134139
Volume: 56
Issue: 2
Start Page Number: 737
End Page Number: 756
Publication Date: Jun 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: Condorcet principle, social choice theory, tournament games
Abstract:

Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped set, classes of k‐stable alternatives and k‐stable sets. The main focus of the paper is to construct a unified matrix‐vector representation of a tournament solution in order to get a convenient algorithm for its calculation. New versions of some solutions are also proposed.

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