COST Action IC1205 on Computational Social Choice: STSM Report

During my STSM to LAMSADE at Universite Paris – Dauphine, I worked together with my host Jerome Lang on problems regarding Approval Voting elections. During the last months before my visit, we have been collaborating on these topics with my host (and together with our phd students). Partly, the purpose of this visit was to finalize a joint paper of ours, which will appear in AAMAS 2015. In particular, we have been studying a family of voting rules, the Ordered Weighted Averaging Operators for Approval Voting. This is a family that generalizes the minisum and the minimax solution. Each voting rule in the family is determined by a vector of weights w = (w_1,...,w_n), where w_i is the weight assigned to the i-th highest Hamming distance between the voters and an election outcome. The outcome of such a rule is then a committee that minimizes the weighted sum of the Hamming distances of the voters (after ordering them from largest to smallest). The questions of interest here are i) to determine which vectors can be implemented in polynomial time. E.g., we know that for w = (1,0,0,...,0) (i.e., the minimax solution), the problem is NP-hard, ii) to design efficient approximation algorithms in the cases where we have NP-hardness results, iii) to identify which rules from this family are manipulable. For example, we know that the minisum solution, i.e., w = (1/n,,1/n,...,1/n) is nonmanipulable, whereas the minimax solution is manipulable.