When evaluating well-being distributions in an anonymous (and replication invariant) manner, one faces a dilemma between (i) assigning dictatorship to a single worst-off person, thus succumbing to a tyranny of non-aggregation and (ii) assigning dictatorship to (unboundedly) many better-off persons, thus succumbing to a tyranny of aggregation. We show how this corresponds to a population-ethical dilemma in the variable population setting between, on the one hand, a reversed repugnant conclusion (preferring a very small population with high well-being) and, on the other hand, a repugnant conclusion (preferring a sufficiently large population with lives barely worth living to a population with good lives) or very sadistic conclusion (not preferring a large population with lives worth living to a population with terrible lives). The dilemma can be resolved by relaxing replication invariance and thus allowing that evaluation in the fixed population setting might change with population size even though the relative distributions of well-being remain unchanged. Rank-dependent criteria are evaluation criteria that resolve this dilemma but fails replication invariance. We provide conditions under which rank-dependent criteria are the only way out of the dilemma. Furthermore, we discuss the following consequence of relaxing replication invariance: It becomes essential to take into account the existence and well-being of non-affected people when evaluating population policies with limited scope.
Authors
Related Organizations
- Bibliographic Reference
- Geir Asheim, Stéphane Zuber. Rank-discounting as a resolution to a dilemma in population ethics. G Arrhenius; K Bykvist; T Campbell; E Finneron-Burns. Oxford Handbook of Population Ethics, Oxford University Press, pp.86-C4.P172, 2022, 9780190907686. ⟨10.1093/oxfordhb/9780190907686.013.15⟩. ⟨halshs-03760526⟩
- DOI
- https://doi.org/10.1093/oxfordhb/9780190907686.013.15
- HAL Collection
- ["Sciences de l'Homme et de la Société", 'Université Panthéon-Sorbonne - Paris I', 'Ecole Normale Supérieure de Paris', 'Ecole des Ponts ParisTech', 'ParisTech', 'Paris School of Economics', 'CNRS - Centre national de la recherche scientifique', 'Ecole des Hautes Etudes en Sciences Sociales', "Centre d'Economie de la Sorbonne", "Archives ouvertes de l'Economie", 'Université Paris sciences et lettres', 'Institut National de Recherche en Agriculture, Alimentation et Environnement', 'PSE Post-Print', 'École normale supérieure - PSL', 'ANR']
- HAL Identifier
- 3760526
- Institution
- ['University of Oslo', 'Université Paris 1 Panthéon-Sorbonne', 'École normale supérieure - Paris', 'École des hautes études en sciences sociales', 'École des Ponts ParisTech', 'Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement']
- Laboratory
- Centre d'économie de la Sorbonne
- Published in
- Oxford
Table of Contents
- 1 Introduction 3
- 2 Framework and basic properties 5
- X x 5
- X x y X x y x y 6
- W W 6
- Anonymity X x x y 6
- Extended Continuity X 7
- Restricted Dominance 7
- Monotonicity X x 7
- Restricted Dominance X 7
- Pigou-Dalton 7
- Pigou-Dalton X x y 7
- Repli- 8
- ℓ ℓ ℓ 8
- ℓ k 8
- Replication Invariance X 8
- Trade-Off Consistency for Ordered Vectors X 9
- 3 Basic representation results 9
- Proposition 1 X 9
- W V n e 10
- V k e k φ e φ c 10
- V k e φ e e 11
- V k e φ e e x 11
- W φ x . 11
- W x 11
- Proposition 2 X 11
- Definition 1 X 12
- G φ 12
- V k z kz k e 12
- Definition 2 X 12
- Proposition 3 X 13
- F F 13
- F ρ ρ ρ 13
- F F F ρ ρ 13
- 4 Tyranny of aggregation tyranny of non-aggregation and 13
- Minimal Aggregation 14
- Minimal Aggregation 14
- I i . . . n x x 14
- I i . . . n x x 14
- Minimal Non-Aggregation 14
- Minimal Non-Aggregation 14
- Minimal Non-Aggregation Min- 15
- Minimal Aggregation Minimal Non-Aggregation 15
- Replication Invariance 15
- Proposition 4 X 15
- F ρ 15
- F ρ 15
- F ρ 15
- Minimal Aggregation 15
- 5 Escaping tyrannies through absolute rank-dependence 16
- Definition 3 X 16
- Same population independence of the existence of the best-off 16
- Definition 4 X 16
- Definition 5 X 17
- Proposition 5 X 17
- 6 Simple rank-dependence and population ethics 18
- Definition 6 X 18
- V k e 18
- Pigou-Dalton 19
- Pigou-Dalton 19
- Pigou-Dalton 19
- Independence of the Well-being of the Worst-off 19
- Avoidance of the Repugnant Conclusion X 20
- Avoidance of the Very Sadistic Conclusion X 20
- Avoidance of the Reversed Repugnant Conclusion X 21
- Proposition 6 X 21
- Mere Addition Principle X 22
- 7 Additional population ethics results 22
- Avoidance of the Very Sadistic Conclusion 22
- Weak Non-Sadism Condition X 22
- Proposition 7 X 22
- Negative Mere Addition Principle X 23
- Proposition 8 X 23
- Proposition 9 X 23
- Avoidance of the Repug- 23
- 8 Concluding remarks 23
- Appendix Proofs 25
- Proof of Proposition 1. X Montonicity Restricted 25
- Dominance 25
- Proof of Proposition 2. 25
- Pigou-Dalton 25
- Proof of Proposition 3. Replication Invariance 25
- Proof of Proposition 4. 26
- F ρ 26
- F F F ρ ρ 26
- F ρ 26
- ℓ ℓ 26
- ℓ F 26
- ℓ ℓ ℓ 26
- ℓ φ z δ φ z φ z φ z ε . 26
- Proof of Proposition 5. X 26
- Minimal 27
- Non-Aggregation x y 27
- Minimal Non-Aggregation 27
- Pigou-Dalton 27
- Minimal 27
- Aggregation Minimal Non-Aggregation 27
- R ℓ . . . k x x 28
- Proof of Proposition 6. X 28
- Avoidance of the Repugnant Conclusion 29
- Very Sadistic Conclusion 29
- Avoidance of 30
- ℓ y a a φ c φ y 30
- ℓ y z k z 30
- Avoidance of the Very Sadistic Conclusion 30
- Avoidance of the 30
- Repugnant Conclusion 30
- Avoidance of the Repugnant Conclusion 30
- Proof of Proposition 7. 30
- Weak Non-Sadism Condi- 30
- ℓ θ φ y φ θ 31
- Weak Non- 31
- Sadism Condition 31
- ℓφ ζ mφ w ℓ m φ z 31
- Avoidance of the Repugnant Conclusion 31
- Proof of Proposition 8. Weak Non-Sadism Condition 31
- Negative Mere Addition Principle 31
- Proof of Proposition 9. 31
- ℓ y y 33
- References 34
