Summary
The text explores community standards as interval judgments aggregated by endpoint rules, emphasizing strategyproofness and single-peaked preferences. It characterizes aggregation rules that maintain fairness, responsiveness, and neutrality, and highlights the role of median and maximal rules in collective decision-making.
Highlights
- Community standards are modeled as intervals reflecting decency, fairness, or reasonableness.
- Endpoint rules aggregate judgments by independently combining interval endpoints.
- Strategyproofness requires preferences to be single-peaked or generalized single-peaked.
- Aggregation rules obey axioms: responsiveness, anonymity, continuity, neutrality, and translation equivariance.
- The median rule is well-defined even without a median judgment and is strategyproof under certain preferences.
- Maximal rule permits actions deemed reasonable by any individual, representing maximal liberalism.
- Strategyproof endpoint rules exclude averaging methods to prevent manipulation of community standards.
Key Insights
- Community Standards as Intervals: Modeling standards as intervals captures evolving and context-dependent societal expectations, allowing flexible aggregation of diverse judgments.
- Endpoint Rules and Independent Aggregation: By aggregating lower and upper bounds separately, endpoint rules avoid complexities of pointwise aggregation and maintain clear interpretability.
- Strategyproofness and Single-Peaked Preferences: Restricting preferences to (generalized) single-peaked forms ensures no incentive for agents to misrepresent views, preserving truthful collective outcomes.
- Axiomatic Characterization: Responsiveness, anonymity, continuity, neutrality, and translation equivariance axioms define a robust framework restricting aggregation rules to those preserving fairness and consistency.
- Median and Maximal Rules as Extremes: The median rule balances group opinion centrally, while the maximal rule embodies liberalism by accepting any reasoned action, illustrating a spectrum of democratic values.
- Exclusion of Averaging Rules: Averaging endpoints can invite strategic manipulation, so endpoint rules avoid this by focusing on order-based aggregation, reinforcing robustness against gaming.
- Implications for Policy and Social Choice: The framework informs legal and political contexts where community standards shift, ensuring decisions reflect collective fairness without dictatorial influence or vulnerability to strategic abuse.
Mindmap
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Citation
Miller, A. D. (2025). The limits of tolerance (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2501.00578