Dissertation

Essays in Political Economy

Seoul National University, Department of Economics, 2025. 

Abstract:
This dissertation explores key issues in political economy through three essays that address distinct but interrelated topics in social welfare functions, electoral system design and public good provision. 

The first essay introduces and axiomatizes the Dual Nash social welfare function, a new approach to aggregating individual well-being into a social welfare measure. Unlike traditional utility-based frameworks, the Dual Nash function incorporates a probabilistic perspective, enabling a more robust analysis of interdependencies among agents' well-being indices. By leveraging copula and co-copula functions, this essay extends classical Nash criteria, elucidating the dualities in aggregation mechanisms and providing a probabilistic foundation for social welfare analysis in social choice theory. 

The second essay examines manipulability and proportional representation (PR) efficiency in mixed electoral systems, with a focus on vote splitting strategies involving allies or satellite parties. By comparing standard and new PR rules, this essay reveals inherent trade-offs between non-manipulability and PR efficiency. It shows that achieving PR efficiency often necessitates sacrificing non-manipulability, particularly in semi-mixed-member proportional (semi-MMP) systems such as mixed-member majority rule (MMM) and mixed-member proportional rule (MMP). The constrained equal losses rule and constrained equal gains rule are shown to uniquely address disproportionality and vote splitting gains, respectively. However, to achieve PR efficiency, measures preventing vote splitting strategies must be implemented.

The third essay focuses on public choice problem with mechanism design. It explores the design of strategy-proof mechanisms in the context of public good provision and extends the analysis to probabilistic settings. Traditional deterministic mechanisms make binary yes/no decisions regarding the provision of public goods. In contrast, probabilistic mechanisms assign probabilities to the provision of the public good, offering a more flexible framework for decision-making. Building on prior research that characterized necessary and sufficient conditions for undominatedness in deterministic mechanisms, this study extends the results for probabilistic mechanisms. 

Together, these essays contribute to the broader understanding of mechanism design in political economy, offering theoretical frameworks and practical solutions for improving fairness, efficiency, and stability in public decision-making and electoral systems.