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Input and Output in Judgment Aggregation

Input and Output in Judgment Aggregation. Gabriella Pigozzi Leon van der Torre Individual and Collective Reasoning University of Luxembourg. Claim. Working assumptions: judgment aggregation  preference aggregation judgment aggregation  probabilistic reasoning Claim:.

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Input and Output in Judgment Aggregation

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  1. Input and Output inJudgment Aggregation Gabriella Pigozzi Leon van der Torre Individual and Collective Reasoning University of Luxembourg

  2. Claim • Working assumptions: judgment aggregation  preference aggregation judgment aggregation  probabilistic reasoning • Claim: Input and output must be distinguished in judgment aggregation. Pigozzi & van der Torre Input and Output in Judgment Aggregation

  3. Outline • Discursive dilemma • Judgment aggregation framework • Running example • Conclusion independence • Towards new operators • A side issue: voting on rules? • Conclusions Pigozzi & van der Torre Input and Output in Judgment Aggregation

  4. 1. Discursive Dilemma P = Valid contract; Q = Breach; R = Defendant liable • Paradox: inconsistent collective judgment • Discursive dilemma: premises versus conclusions [Kornhauser & Sager, 1986] Pigozzi & van der Torre Input and Output in Judgment Aggregation

  5. Discursive Dilemma P = Candidate is worthy of tenure on teaching Q = Candidate is worthy of tenure on research R = The candidate is worthy of tenure tout court [Bovens & Rabinowicz, 2006] Pigozzi & van der Torre Input and Output in Judgment Aggregation

  6. Two Levels of Input/Output in JA 1. Input and output as premises and conclusion (PQ, R): if input PQ, then output R Pigozzi & van der Torre Input and Output in Judgment Aggregation

  7. Two Levels of Input/Output in JA 2. Input and output as individual and collective Profile Collective judgment (profile, collective judgment) Pigozzi & van der Torre Input and Output in Judgment Aggregation

  8. 2. Judgment Aggregation List & Pettit 2002: There exists no aggregation procedure satisfying the following conditions: • Universal Domain (UD): admissible inputs are any logically possible profile of individual sets of judgments. • Anonymity: all individuals have equal weight. • Systematicity: the aggregation procedure treats all propositions in an evenhanded way. Inspired by social choice theory: independence conditions and impossibility results Pigozzi & van der Torre Input and Output in Judgment Aggregation

  9. Mongin’s Impossibility Theorem Mongin (2006): UD + IIPA + Unanimity  Dictator IIPA Pigozzi & van der Torre Input and Output in Judgment Aggregation

  10. 3. Running Example • 3 agents • Agenda contains: The literals: P, Q, R, P, Q, R The rule RPQ: PQR, PR, QR More constraints: PR, QR, PQR • 26 = 64 inputs, 22 outputs, 6 dilemmas • Dagstuhl winner: in case of no conflict between premise and conclusion based procedures, adopt the majority rule. Pigozzi & van der Torre Input and Output in Judgment Aggregation

  11. 4. Conclusion Independence • Likewise for premise independence CIIPA Pigozzi & van der Torre Input and Output in Judgment Aggregation

  12. 5. Premise-Based Procedure • The procedure: P, Q := majority; R := PQ. • No conclusion independence (nor dictator) • Premise independence (and anonymity) • (If S=PQR, then “dilemma of the Paretian Rational”) Pigozzi & van der Torre Input and Output in Judgment Aggregation

  13. Conclusion-Based Procedure Revised • The revised procedure: • P:= R or P1  P2  P3; Q, R := majority • No premise independence (nor dictator) • Conclusion independence (and anonymity) Pigozzi & van der Torre Input and Output in Judgment Aggregation

  14. Conclusion Dictator • Conclusion dictator procedure: P:= R1 or P1  P2  P3; Q := Q1, R := R1 • No premise independence (nor dictator/anonymity) • Conclusion independence Pigozzi & van der Torre Input and Output in Judgment Aggregation

  15. 6. Voting on Rules • Doctrinal paradox no violations, in JA possible • Advantages analogous to “logic by translation” • What does it mean to vote for or against a rule? • ab: "If carbon dioxide emissions are above threshold x, then there will be global warming” [Dietrich and List, 2005] • False ab: "carbon dioxide emissions are above threshold x, and there will be no global warming" Pigozzi & van der Torre Input and Output in Judgment Aggregation

  16. 7. Conclusions • Two levels of input/output reasoning in JA: • Relating premises and conclusion • Relating individual and collective judgments • Escape routes from impossibility results: • Weakened notions of independence • Mixed premise and conclusion based operators • Not found in preference aggregation • (or in probabilistic reasoning) Pigozzi & van der Torre Input and Output in Judgment Aggregation

  17. Dilemma of the Paretian Rational P = Duty; Q = Negligence; R = Causation; S = Damages [Nehring, 2006] Pigozzi & van der Torre Input and Output in Judgment Aggregation

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