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The Limits of Tolerance

Alan D. Miller

Abstract

I propose a model of aggregation of intervals relevant to the study of legal standards of tolerance. Seven axioms: responsiveness, anonymity, continuity, strategyproofness, and three variants of neutrality are then used to prove several important results about a new class of aggregation methods called endpoint rules. The class of endpoint rules includes extreme tolerance (allowing anything permitted by anyone) and a form of majoritarianism (the median rule).

The Limits of Tolerance

Abstract

I propose a model of aggregation of intervals relevant to the study of legal standards of tolerance. Seven axioms: responsiveness, anonymity, continuity, strategyproofness, and three variants of neutrality are then used to prove several important results about a new class of aggregation methods called endpoint rules. The class of endpoint rules includes extreme tolerance (allowing anything permitted by anyone) and a form of majoritarianism (the median rule).
Paper Structure (14 sections, 7 theorems, 4 equations, 1 figure)

This paper contains 14 sections, 7 theorems, 4 equations, 1 figure.

Key Result

Theorem 1

An aggregation rule $f$ satisfies responsiveness, anonymity, continuity, and weak neutrality if and only if it is an endpoint rule.

Figures (1)

  • Figure 1: Endpoint Rules

Theorems & Definitions (16)

  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Proposition 1
  • Claim 1
  • Theorem 3
  • Lemma 2
  • proof : Proof of Lemma \ref{['piphi']}
  • proof : Proof of Theorem \ref{['mainthm']}
  • proof : Proof of Theorem \ref{['thm2']}
  • ...and 6 more