Gallo, O. (2024). Anonymity and strategy-proofness on a domain of single-peaked and single-dipped preferences (No. 2410.03387). arXiv.
This paper aims to characterize strategy-proof and type-anonymous social choice rules for locating a public facility on a line when agents have either single-peaked or single-dipped preferences. The research seeks to identify rules that incentivize truthful preference revelation while ensuring equal decision-making power for all agents, regardless of their preference type.
The paper employs a theoretical and axiomatic approach. It builds on existing literature on strategy-proofness in single-peaked and single-dipped domains, particularly the works of Moulin (1980, 1983) and Alcalde-Unzu et al. (2024). The authors introduce the concept of "type-anonymity" to address the mixed preference domain and analyze the constraints it imposes on strategy-proof rules.
The paper presents two characterizations of strategy-proof and type-anonymous rules:
The paper proves the equivalence of these two characterizations.
The research demonstrates that strategy-proof and type-anonymous rules in this mixed preference domain can be characterized by intuitive procedures that combine elements of median voter rules and quota majority methods. The findings contribute to the understanding of mechanism design in settings with heterogeneous preferences.
This research is significant for its contribution to social choice theory and mechanism design, particularly in the context of public facility location. The results have implications for designing fair and efficient decision-making mechanisms in situations where individuals may have conflicting preferences due to the nature of the public facility.
The paper focuses on a specific mixed preference domain with single-peaked and single-dipped preferences. Future research could explore the implications of relaxing these assumptions or considering other types of restricted preference domains. Additionally, investigating the computational complexity of implementing these rules and their robustness to strategic manipulation by coalitions could be valuable extensions of this work.
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