  We propose models for lobbying in a probabilistic environment, in which an
actor (called "The Lobby") seeks to influence 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
two 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 and on various natural parameterizations.
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 approximability and inapproximability
results for these problems and several variants.
