Bound-State Beta Decay of $\mathbf{\mathrm{^{205}{Tl}^{81+}}}$ Ions and the LOREX Project

Bound-State Beta Decay of $\mathbf{\mathrm{^{205}{Tl}^{81+}}}$ Ions and the LOREX Project

Summary

Community standards of decency, fairness, and reasonableness guide judgments in ambiguous contexts, modeled as intervals aggregated by endpoint rules. These rules are strategyproof under generalized single-peaked preferences, ensuring fair, independent aggregation of judgments.

Highlights

  • Community standards influence judgments by evolving norms of decency and fairness.
  • Obscene speech may be criminalized based on contemporary community standards in the US.
  • Standards modeled as intervals, aggregated via p,q-th endpoint rules.
  • Endpoint rules aggregate independently by lower and upper endpoints, not pointwise.
  • Strategyproofness requires single-peaked preferences and independent endpoint aggregation.
  • Median and maximal rules represent spectrum ends between liberalism and democracy.
  • Responsiveness, anonymity, continuity, and neutrality axioms characterize endpoint rules.

Key Insights

  • Community standards adapt over time, reflecting diversity and fluid social norms, which necessitates flexible aggregation methods rather than fixed absolutes.
  • Modeling standards as intervals enables formal aggregation of individual judgments, capturing variability in perceptions of decency and reasonableness.
  • Endpoint rules aggregate judgments by independently combining lower and upper bounds, addressing challenges where median judgments may not exist.
  • Strategyproof aggregation mandates restrictions on preference structures, specifically generalized single-peakedness, preventing manipulative reporting of intervals.
  • The median rule is strategyproof within this framework, ensuring collective judgments reflect a stable consensus despite individual preference variation.
  • Responsiveness and neutrality axioms enforce fairness and consistency, such that aggregate judgments appropriately adjust to shifts in individual standards.
  • The framework bridges liberal and democratic values by situating endpoint and consent rules along a spectrum, balancing inclusiveness with reasoned consensus.

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

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