The Complexity of Probabilistic Lobbying

Authors:
Gábor Erdélyi;Henning Fernau;Judy Goldsmith;Nicholas Mattei;Daniel Raible;Jörg Rothe
Affiliations:
Institut für Informatik, Universität Düsseldorf, Düsseldorf, Germany 40225;FB 4--Abteilung Informatik, Universität Trier, Trier, Germany 54286;Department of Computer Science, University of Kentucky, Lexington, USA 40506;Department of Computer Science, University of Kentucky, Lexington, USA 40506;FB 4--Abteilung Informatik, Universität Trier, Trier, Germany 54286;Institut für Informatik, Universität Düsseldorf, Düsseldorf, Germany 40225
Venue:
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Year:
2009

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Abstract

We propose various models for lobbying in a probabilistic environment, in which an actor (called "The Lobby") seeks to influence the voters' preferences of voting for or against multiple issues when the voters' preferences are represented in terms of probabilities. In particular, we provide two evaluation criteria and three bribery methods to formally describe these models, and we consider the resulting forms of lobbying with and without issue weighting. We provide a formal analysis for these problems of lobbying in a stochastic environment, and determine their classical and parameterized complexity depending on the given bribery/evaluation criteria. Specifically, we show that some of these problems can be solved in polynomial time, some are NP-complete but fixed-parameter tractable, and some are W[2]-complete. Finally, we provide (in)approximability results.