The computational complexity of choice sets

Social choice rules are often evaluated and compared by inquiring whether they fulfill certain desirable criteria such as the Condorcet criterion, which states that an alternative should always be chosen when more than half of the voters prefer it over any other alternative. Many of these criteria can be formulated in terms of choice sets that single out reasonable alternatives based on the preferences of the voters. In this paper, we consider choice sets whose definition merely relies on the pairwise majority relation. These sets include the Copeland set, the Smith set, the Schwartz set, and von Neumann-Morgenstern stable sets (a concept originally introduced in the context of cooperative game theory). We investigate the relationships between these sets and completely characterize their computational complexity. This allows us to obtain hardness results for entire classes of social choice functions.

• Type: Conference
• Year: 2007
• Where: TARK
• Authors: Felix Brandt, Felix A. Fischer, Paul Harrenstein
• Keywords: Choice Sets, Social Choice, Social Choice Rules, TARK 2007