A Voting Power Measure for Liquid Democracy with Multiple Delegation

We generalize the classical model of liquid democracy by proposing a voting power measure that allows each agent to split and delegate their vote to multiple agents. We prove that this measure is well defined and inherits the most important properties of the classical model. Among these properties we prove the so-called delegation property, which guarantees us that delegating power to an agent is equivalent to copying her delegation profile. Secondly we study the existence of equilibrium states in a delegation game using the proposed measure, for which we prove the existence of pure strategy Nash equilibria.