The Complexity of Probabilistic Lobbying

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.