Hybrid Elections Broaden Complexity-Theoretic Resistance to Control

Authors


  • A preliminary version was presented at the COMSOC-06 workshop and a preliminary, seven-page version of this paper appeared in IJCAI-07 [2]. Supported in part by DFG grants RO-1202/{9-1, 9-3, 11-1, 12-1}, NSF grants CCR-0311021, CCF-0426761, and IIS-0713061, the Alexander von Humboldt Foundation's TransCoop program, the ESF's EUROCORES program LogICCC, and two Friedrich Wilhelm Bessel Research Awards. Work done in part while the first two authors were visiting Heinrich-Heine-Universität Düsseldorf and while the third author was visiting the University of Rochester.

Abstract

Electoral control refers to attempts by an election's organizer (“the chair”) to influence the outcome by adding/deleting/partitioning voters or candidates. The important paper of Bartholdi, Tovey, and Trick [1] that introduces (constructive) control proposes computational complexity as a means of resisting control attempts: Look for election systems where the chair's task in seeking control is itself computationally infeasible.

We introduce and study a method of combining two or more candidate-anonymous election schemes in such a way that the combined scheme possesses all the resistances to control (i.e., all the NP-hardnesses of control) possessed by any of its constituents: It combines their strengths. From this and new resistance constructions, we prove for the first time that there exists a neutral, anonymous election scheme (whose winner problem is computable in polynomial time) that is resistant to all twenty standard types of electoral control (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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