A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Clemens ThielenStephan Westphal 3rd International Workshop on Computational.

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Presentation transcript:

A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Clemens ThielenStephan Westphal 3rd International Workshop on Computational Social Choice 15 September 2010

Problem Definition Social choice setting with private information: A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

Problem Definition (2) We saw (previous talk): A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

Our Results A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

System of Inequalities Implementation of a social choice function : A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Weak Implementation Strong Implementation

Node Potential Interpretation System can be interpreted as finding a node potential: A Combinatorial Algorithm for Strong Implementation of Social Choice Functions constant

Characterization (Weak Implementation) Characterization (Weak Implementation) A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Theorem:[Gui et al. 2005]

Characterization (Strong Implementation) Characterization (Strong Implementation) A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Theorem:[this paper]

The Algorithm The Algorithm A Combinatorial Algorithm for Strong Implementation of Social Choice Functions For weak implementation : For strong implementation : Strict inequalities in the system must be fullfilled.

Perturbation of Node Potentials Perturbation of Node Potentials A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

Perturbation in Graph G i Perturbation in Graph G i A Combinatorial Algorithm for Strong Implementation of Social Choice Functions Slack of arc ( x, x ´) Slack of incoming arcs becomes positive

Finding the Node x A Combinatorial Algorithm for Strong Implementation of Social Choice Functions You shrink it!

Summary of Results A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

Thank you! A Combinatorial Algorithm for Strong Implementation of Social Choice Functions

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