Abstract
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.
Highlights
Pivotal-voter models were pioneered by the seminal contribution of Palfrey and Rosenthal (1983)—PR
PR provide a partial characterization of these equilibria, some conjectures, and the analysis of two special cases
We focus on the pm solving (11) for pn ∈ (0, 1) and on the pn solving (12) for pm ∈ (0, 1). The intersections between those two sets in the space ∈ (0, 1)2 are the “Totally Mixed” equilibrium pairs (p∗m, p∗n), which are what we study
Summary
Pivotal-voter models were pioneered by the seminal contribution of Palfrey and Rosenthal (1983)—PR. In the remainder of the paper we analyze the more interesting case of a lower cost of voting ( c < 1∕2 ), so that individuals may vote with positive probability. The Proposition establishes the existence of a unique “Partially Mixed” equilibrium at which the members of the minority (i.e., the n-individuals) vote with certainty.
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