Equilibrium Analysis of Simple Majority Voting under Network Externalities

In practice, voting often involves participation costs, and voters’ decisions are determined not only by their private interests but also by others’ values within their social networks. This paper investigates the equilibrium characteristics of simple majority voting in a general model featuring costly voting and interdependent values. First, this paper proves the existence of voting equilibria and characterizes the two-threshold strategy structure adopted by voters in any equilibrium. Second, under the assumptions of linear network externalities and symmetric expected payoffs, this paper examines how network structure affects voting equilibria. The theoretical analysis reveals that if the social network is an irregular graph, only asymmetric equilibria exist. In contrast, symmetric equilibria always exist in regular graphs and are unique when network externalities are relatively weak. Numerical simulations further show that voters’ participation rates (i.e., the probabilities of voting rather than abstaining) decrease with increasing strength of network externalities or greater network connectivity.

• network externalities
• simple majority voting
• voting cost
• two-threshold strategy
• symmetric equilibrium

• Haoyang Ye — School of Computer Science, Peking University
• Jingyang Huang — School of Mathematical Sciences, Peking University
• Fanqi Shi — School of Economics, Peking University

• National Natural Science Foundation of China, Young Scientists Fund, grant 72303011
• Seed Fund of the School of Economics, Peking University

Ye, H., Huang, J., & Shi, F. (2025). Equilibrium Analysis of Simple Majority Voting under Network Externalities. Economic Science, 47(05), 119–137. https://doi.org/10.12088/PKU.jjkx.2025.05.06