Measuring a Priori Voting Power - Taking Delegations Seriously

In this paper, we introduce new power indices to measure the criticality of voters involved in different elections where delegations play a key role, namely, two variants of the proxy voting setting and a liquid democracy setting. We argue that our power indices are natural extensions of the Penrose-Banzhaf index in classic simple voting games; we show that recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time; and we provide numerical results to illustrate how introducing delegation options modifies the voting power of voters.