Voting systems that combine approval and preference

Abstract Information on the rankings and information on the approval of candidates in an election, though related, are fundamentally different-one cannot be derived from the other. Both kinds of information are important in the determination of social choices. We propose a way of combining them in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that satisfy several desirable properties, including monotonicity. Both systems may give different winners from standard ranking and nonranking voting systems. PAV, especially, encourages candidates to take coherent majoritarian positions, but it is more information-demanding than FV. PAV and FV are manipulable through voters' contracting or expanding their approval sets, but a 3-candidate dynamic poll model suggests that Condorcet winners, and candidates ranked first or second by the most voters if there is no Condorcet winner, will be favored, though not necessarily in equilibrium

Solving Hard Control Problems in Voting Systems via Integer Programming

Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control problems. Our ILP formulations are flexible in the sense that they can work with an arbitrary number of candidates and voters. Using the off-the-shelf solver Cplex, we show that our approaches can manipulate elections with a large number of voters and candidates efficiently

Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting

A central theme in computational social choice is to study the extent to which voting systems computationally resist manipulative attacks seeking to influence the outcome of elections, such as manipulation (i.e., strategic voting), control, and bribery. Bucklin and fallback voting are among the voting systems with the broadest resistance (i.e., NP-hardness) to control attacks. However, only little is known about their behavior regarding manipulation and bribery attacks. We comprehensively investigate the computational resistance of Bucklin and fallback voting for many of the common manipulation and bribery scenarios; we also complement our discussion by considering several campaign management problems for Bucklin and fallback.Comment: 28 page

Voces Populi and the Art of Listening

The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favorite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing this strategy. Theorems 2, 3, and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others "conditional IRV" gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard-Satterthwaite type, describing 3 specific strategies that cannot all be avoided in meaningful anonymous and neutral elections.Preferential Election methods; Plurality Election methods