Complete Information Pivotal-Voter Model with Asymmetric Group Size

Abstract

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Complete information pivotal-voter model with asymmetric group size and asymmetric benefits

“…And, naturally, if B is very high (i.e., greater than 1), the cost of voting is much greater than the benefit, thus no-one votes. 13 Cost-continuity. Beginning from a high B we will have to be on the "Pure" equilibrium in the bottom panel of the Figure . As B decreases and gets lower than 1, a unique equilibrium exists which is the "Partially Mixed" equilibrium which is drawn in the same panel.…”

“…We can use a voting station analogy to explain the reasoning of the above. If the voting 13 The probability of being pivotal is at most 1, and thus the voting condition ( 4) is never satisfied.…”

“…We are left to analyze the "Partially Mixed" equilibria in which players of one group are voting with certainty and the others are playing a mixed strategy. There cannot be an equilibrium in which the majority group votes with certainty and the minority group plays a mixed strategy (see Mavridis and Serena (2018) for a proof). Therefore the equilibria left to analyze are of the type p * n = 1 and p * m ∈ (0, 1).…”

“…First, Nöldeke and Peña (2016) focus on the two groups having symmetric number of members and symmetric benefit from the favored alternative winning the election. Second, Mavridis and Serena (2018) focus on the two groups having asymmetric number of members and symmetric benefit from the favored alternative winning the election.…”

“…We consider only benefits that accrue from changing the policy to the voters' preferred outcome, despite a number of other benefits playing an important role in real-life; for instance, Wiese and Jong-A-Pin (2017) empirically examine the benefits arising from "expressive" motives of voting. In our model, we follow the main strand of the literature on complete-information pivotal-voter model with costly voting, started by Palfrey and Rosenthal (1983), and further developed by Nöldeke and Peña (2016) and Mavridis and Serena (2018). And as we generalize this strand of the literature to the asymmetric-asymmetric setup described above, we abstract away from other interesting forces that typically play an important role in real life voting.…”