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Anyone but him: The complexity of precluding an alternative
How Hard Is Bribery in Elections?
This work obtains both polynomial-time bribery algorithms and proofs of the intractability of bribery, and results show that the complexity of bribery is extremely sensitive to the setting.
Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates
For voters who follow the most central political-science model of electorates — single-peaked preferences — those protections vanish, and it is shown that NP-hard bribery problems — including those for Kemeny and Llull elections- — fall to polynomial time.
Threshold Computation and Cryptographic Security
Simon proved that for unbounded-error polynomial-time machines these two notions yield the same class, PP, and this result seemed to collapse the threshold and probabilistic modes of computation.
The shield that never was: societies with single-peaked preferences are more open to manipulation and control
It is argued that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place and it is shown that for electorates having single-peaked preferences, many existing NP-hardness results on manipulation and control evaporate.
The Boolean Hierarchy I: Structural Properties
The complexity of sets formed by boolean operations (union, intersection, and complement) on NP sets are studied, showing that in some relativized worlds the boolean hierarchy is infinite, and that for every k there is a relativization world in which the Boolean hierarchy extends exactly k levels.
Multimode Control Attacks on Elections
This paper model and study the case in which the attacker launches a multipronged (i.e., multimode) attack, and proves that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time.
The complexity of manipulative attacks in nearly single-peaked electorates
This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates, for various notions of nearness and various election systems.
Llull and Copeland Voting Computationally Resist Bribery and Constructive Control
- P. Faliszewski, E. Hemaspaandra, L. A. Hemaspaandra, J. Rothe
- MathematicsJ. Artif. Intell. Res.
- 1 May 2009
Among systems with a polynomial-time winner problem, Copeland voting is the first natural election system proven to have full resistance to constructive control and vulnerability results for microbribery are proven via a novel technique involving min-cost network flow.
Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP
It follows that determining the winner in Carroll's elections is not NP-complete unless the polynomial hierarchy collapses, and the stronger lower bound and upper bound are provided that matches the lower bound.