Complete information pivotal-voter model with asymmetric group size

We study the equilibria of the standard pivotal-voter participation game between two groups of voters of asymmetric sizes (majority and minority), as originally proposed by Palfrey and Rosenthal (Public Choice 41(1):7-53, 1983). We find a unique equilibrium wherein the minority votes with certainty and the majority votes with probability in (0, 1); we prove that this is the only equilibrium in which voters of only one group play a pure strategy, and we provide sufficient conditions for its existence. Equilibria where voters of both groups vote with probability in (0, 1) are analyzed numerically.