  We introduce new power indices to measure the a priori voting power of voters
in liquid democracy elections where an underlying network restricts
delegations. We argue that our power indices are natural extensions of the
standard Penrose-Banzhaf index in simple voting games. We show that computing
the criticality of a voter is #P-hard even when voting weights are
polynomially-bounded in the size of the instance. However, for specific
settings, such as when the underlying network is a bipartite or complete graph,
recursive formulas can compute these indices for weighted voting games in
pseudo-polynomial time. We highlight their theoretical properties and provide
numerical results to illustrate how restricting the possible delegations can
alter voters' voting power.
