  We study the robustness of approval-based participatory budgeting (PB) rules
to random noise in the votes. Our contributions are twofold. First, we study
the computational complexity of the #Flip-Bribery problem, where given a PB
instance we ask for the number of ways in which we can flip a given number of
approvals in the votes, so that a specific project is selected. The idea is
that #Flip-Bribery captures the problem of computing the funding probabilities
of projects in case random noise is added. Unfortunately, the problem is
intractable even for the simplest PB rules. Second, we analyze the robustness
of several prominent PB rules (including the basic greedy rule and the Method
of Equal Shares) on real-life instances from Pabulib. Since #Flip-Bribery is
intractable, we resort to sampling to obtain our results. We quantify the
extent to which simple, greedy PB rules are more robust than proportional ones,
and we identify three types of (very) non-robust projects in real-life PB
instances.
