Skip to main content
Top
Published in: Social Choice and Welfare 4/2023

01-07-2023 | Original Paper

Cesàro average utilitarianism in relativistic spacetime

Author: Marcus Pivato

Published in: Social Choice and Welfare | Issue 4/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Widely accepted theories in modern cosmology say that spacetime is probably infinite. This raises the question how to define a social welfare order (SWO) for an infinite population of people dispersed throughout time and space. Any such SWO should be Lorentz invariant: it should yield the same value independent of the position and velocity of the social observer. I define and axiomatically characterize spatiotemporal Cesàro average utilitarian SWOs as a solution to this problem.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Footnotes
1
See also Tegmark (2004, §II), Ellis (2007, §2.6), Dorr and Arntzenius (2017, §6) and Askell (2018, §1.1) for brief overviews of this literature.
 
2
See Asheim (2010) and Askell (2018, §1.3\(-\)1.4) surveys of this literature.
 
3
See Section 3 of Pivato (2022) for more detailed summaries of the earlier papers in this list.
 
4
A Poisson point process is a random process that generates a random scatter of points in space. A good way to visualize it is as a scatter of raindrops falling on a pavement.
 
5
Completeness is not actually required; it just makes the theorem statement slightly shorter.
 
6
The elements of \({{\mathcal {N}}}\) are just abstract “labels”; they contain no information about personal identity. To the extent that personal identity is meaningful or ethically relevant, it is encoded in the elements of \({{\mathcal {X}}}\).
 
7
Indeed, this is true if \({{\mathcal {X}}}\) is any locally compact metric space –e.g. \({{\mathbb {R}}}^N\).
 
8
If \({{\mathcal {X}}}\) is locally compact, then \({{\mathfrak {B}}}({{\mathcal {X}}})=\{\)all locally compact subsets of \({{\mathcal {X}}}\}\). But we don’t use this fact.
 
9
u is a “universal utility function”, which evaluates the lifetime utility of every possible life outcome for every possible person. The well-known difficulties in defining such a function are compounded by the fact that future civilizations may contain artificially sentient machines, genetically engineered animals of near-human intelligence, and technologically enhanced “post-humans”, in addition to homo sapiens And the universe may also contain other intelligent species. But these issues are beyond the scope of this paper.
 
10
See d’Aspremont and Gevers (2002) for background.
 
11
Papers on infinite-population social welfare such as Lauwers (1998) call this a bounded permutation.
 
12
This is often called Monotonicity. The term loose Pareto is due to Lauwers and Vallentyne (2004).
 
13
Recall the density \(\delta ({{\mathcal {M}}})\) from formula (9). If \(\delta ({{\mathcal {M}}})\) exists, then \({\underline{\delta }}({{\mathcal {M}}})=\delta ({{\mathcal {M}}})\). But the liminf in formula (10) always exists, whereas the limit in formula (9) sometimes does not exist. Thus, \({\underline{\delta }}({{\mathcal {M}}})\) can be seen as a robust generalization of \(\delta ({{\mathcal {M}}})\).
 
14
Since our policy choices can only affect our future light cone, it might seem that we could just ignore everyone outside this light cone in our social welfare evaluations. But this assumes an infinite-population SWO for which the population inside any light cone is separable from the population outside of it (a form of separability distinct from Axiom  A3). And this SWO must still be both anonymous and Lorentz-invariant. Thus, this paper could be read with \({{\mathcal {O}}}\) interpreted as “the future light cone” rather than “the universe”.
 
15
Confusingly, Gale himself calls this relation overtaking, and reserves the term catching up for the slightly weaker condition that \(\liminf _{N{\rightarrow }{\infty }}\sum _{n=1}^N \Big ( u({{\widetilde{x}}}_n)-u({{\widetilde{y}}}_n)\Big )\geqslant 0\).
 
16
Dubey (2011) uses a similar condition to show the nonconstructability of SWOs satisfying Finite Anonymity and Weak Pareto, generalizing an earlier result of Zame (2007).
 
17
In the case \({{\mathcal {X}}}={{\mathbb {R}}}\), these are similar to what Khan and Stinchcombe (2023, §3.7) refer to as ergodic sequences.
 
18
This is the only place in this paper where the completeness of \(({{\mathcal {X}}},d)\) is used.
 
19
The italicised stipulation is important, even in Newtonian mechanics. The kinetic energy of a particle depends nonlinearly on the reference frame of the observer. Thus, the kinetic energy change needed to go from velocity \({{\textbf{v}}}\) to velocity \({{\textbf{w}}}\) also depends on the reference frame of the observer.
 
20
For instance, if \({{\mathcal {G}}}\) is a compact topological group, then it always has a right-invariant metric. In particular, if \({{\mathcal {G}}}\) is a compact Lie group, then it has a right-invariant Riemann metric.
 
21
This is true if \(\Phi\) is a homogeneous reference system induced by a Lie group acting differentiably on \({{\mathcal {S}}}={{\mathbb {R}}}^N\). In particular, it is true for the Galilean and Relativistic reference systems in Appendix  B.
 
Literature
go back to reference Arntzenius F (2014) Utilitarianism, decision theory and eternity. Philos Perspect 28:31–58CrossRef Arntzenius F (2014) Utilitarianism, decision theory and eternity. Philos Perspect 28:31–58CrossRef
go back to reference Asheim G, Tungodden B (2004) Resolving distributional conflicts between generations. Econ Theory 24(1):221–230CrossRef Asheim G, Tungodden B (2004) Resolving distributional conflicts between generations. Econ Theory 24(1):221–230CrossRef
go back to reference Asheim G, Zuber S (2013) A complete and strongly anonymous leximin relation on infinite streams. Soc Choice Welf 41(4):819–834CrossRef Asheim G, Zuber S (2013) A complete and strongly anonymous leximin relation on infinite streams. Soc Choice Welf 41(4):819–834CrossRef
go back to reference Asheim G, Zuber S (2016) Evaluating intergenerational risks. J Math Econ 65:104–117CrossRef Asheim G, Zuber S (2016) Evaluating intergenerational risks. J Math Econ 65:104–117CrossRef
go back to reference Asheim G, Bossert W, Sprumont Y, Suzumura K (2010) Infinite-horizon choice functions. Econ Theory 43(1):1–21CrossRef Asheim G, Bossert W, Sprumont Y, Suzumura K (2010) Infinite-horizon choice functions. Econ Theory 43(1):1–21CrossRef
go back to reference Asheim G, d’Aspremont C, Banerjee K (2010) Generalized time-invariant overtaking. J Math Econ 46(4):519–533CrossRef Asheim G, d’Aspremont C, Banerjee K (2010) Generalized time-invariant overtaking. J Math Econ 46(4):519–533CrossRef
go back to reference Asheim GB, Kamaga K, Zuber S (2022a) Infinite population utilitarian criteria, CESifo Working Paper No. 9576 Asheim GB, Kamaga K, Zuber S (2022a) Infinite population utilitarian criteria, CESifo Working Paper No. 9576
go back to reference Asheim GB, Kamaga K, Zuber S (2022) Maximal sensitivity under strong anonymity. J Math Econ 103:102768CrossRef Asheim GB, Kamaga K, Zuber S (2022) Maximal sensitivity under strong anonymity. J Math Econ 103:102768CrossRef
go back to reference Askell A (2018) Pareto principles in infinite ethics. Ph.D. thesis, New York University Askell A (2018) Pareto principles in infinite ethics. Ph.D. thesis, New York University
go back to reference Atsumi H (1965) Neoclassical growth and the efficient program of capital accumulation. Rev Econ Stud 32:127–136CrossRef Atsumi H (1965) Neoclassical growth and the efficient program of capital accumulation. Rev Econ Stud 32:127–136CrossRef
go back to reference Banerjee K (2006) On the extension of the utilitarian and Suppes-Sen social welfare relations to infinite utility streams. Soc Choice Welf 27(2):327–339CrossRef Banerjee K (2006) On the extension of the utilitarian and Suppes-Sen social welfare relations to infinite utility streams. Soc Choice Welf 27(2):327–339CrossRef
go back to reference Barrow JD, Davies P, Harper CL (eds) (2004) Science and ultimate reality: from quantum to cosmos. Cambridge University Press, Cambridge, UK Barrow JD, Davies P, Harper CL (eds) (2004) Science and ultimate reality: from quantum to cosmos. Cambridge University Press, Cambridge, UK
go back to reference Basu K, Mitra T (2003) Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 71(5):1557–1563CrossRef Basu K, Mitra T (2003) Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 71(5):1557–1563CrossRef
go back to reference Basu K, Mitra T (2007a) On the existence of Paretian social welfare relations for infinite utility streams with extended anonymity. In: Roemer and Suzumura (2007), pp. 85–100 Basu K, Mitra T (2007a) On the existence of Paretian social welfare relations for infinite utility streams with extended anonymity. In: Roemer and Suzumura (2007), pp. 85–100
go back to reference Basu K, Mitra T (2007b) Possibility theorems for aggregating infinite utility streams equitably. In: Roemer and Suzumura (2007), pp. 69–84 Basu K, Mitra T (2007b) Possibility theorems for aggregating infinite utility streams equitably. In: Roemer and Suzumura (2007), pp. 69–84
go back to reference Basu K, Mitra T (2007) Utilitarianism for infinite utility streams: a new welfare criterion and its axiomatic characterization. J Econ Theory 133(1):350–373CrossRef Basu K, Mitra T (2007) Utilitarianism for infinite utility streams: a new welfare criterion and its axiomatic characterization. J Econ Theory 133(1):350–373CrossRef
go back to reference Bostrom N (2011) Infinite ethics. Anal Metaphys 10:9–59 Bostrom N (2011) Infinite ethics. Anal Metaphys 10:9–59
go back to reference Brock WA (1970) An axiomatic basis for the Ramsey-Weizsäcker overtaking criterion. Econometrica 38(6):927–929CrossRef Brock WA (1970) An axiomatic basis for the Ramsey-Weizsäcker overtaking criterion. Econometrica 38(6):927–929CrossRef
go back to reference Chichilnisky G (1996) An axiomatic approach to sustainable development. Soc Choice Welf 13(2):231–257CrossRef Chichilnisky G (1996) An axiomatic approach to sustainable development. Soc Choice Welf 13(2):231–257CrossRef
go back to reference Chichilnisky G (1997) What is sustainable development? Land Econ 73(4):467–91CrossRef Chichilnisky G (1997) What is sustainable development? Land Econ 73(4):467–91CrossRef
go back to reference Chichilnisky G, Heal G (1997) Social choice with infinite populations: construction of a rule and impossibility results. Soc Choice Welf 14(2):303–318CrossRef Chichilnisky G, Heal G (1997) Social choice with infinite populations: construction of a rule and impossibility results. Soc Choice Welf 14(2):303–318CrossRef
go back to reference Cowen T (2007) Caring about the distant future: why it matters and what it means. Univ Chic Law Rev 74:5–40 Cowen T (2007) Caring about the distant future: why it matters and what it means. Univ Chic Law Rev 74:5–40
go back to reference d’Aspremont C, Gevers L (2002) Social welfare functionals and interpersonal comparability. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, pp 459–541CrossRef d’Aspremont C, Gevers L (2002) Social welfare functionals and interpersonal comparability. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, pp 459–541CrossRef
go back to reference Diamond PA (1965) The evaluation of infinite utility streams. Econometrica 33(2):170–177CrossRef Diamond PA (1965) The evaluation of infinite utility streams. Econometrica 33(2):170–177CrossRef
go back to reference Dorr C, Arntzenius F (2017) Self-locating priors and cosmological measures. In: Barrow JD, Silk J, Chamcham K, Saunders S (Eds) Philosophy of Cosmology. Cambridge University Press, Ch. 20, pp 396–428 Dorr C, Arntzenius F (2017) Self-locating priors and cosmological measures. In: Barrow JD, Silk J, Chamcham K, Saunders S (Eds) Philosophy of Cosmology. Cambridge University Press, Ch. 20, pp 396–428
go back to reference Dubey RS (2011) Fleurbaey-Michel conjecture on equitable weak Paretian social welfare order. J Math Econ 47(4–5):434–439CrossRef Dubey RS (2011) Fleurbaey-Michel conjecture on equitable weak Paretian social welfare order. J Math Econ 47(4–5):434–439CrossRef
go back to reference Dubey RS, Mitra T (2011) On equitable social welfare functions satisfying the weak Pareto axiom: a complete characterization. Int J Econ Theory 7(3):231–250CrossRef Dubey RS, Mitra T (2011) On equitable social welfare functions satisfying the weak Pareto axiom: a complete characterization. Int J Econ Theory 7(3):231–250CrossRef
go back to reference Dubey RS, Mitra T (2014) Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams. Soc Choice Welf 43(3):591–602CrossRef Dubey RS, Mitra T (2014) Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams. Soc Choice Welf 43(3):591–602CrossRef
go back to reference Ellis GFR (2007) Issues in the philosophy of cosmology. In: Butterfield J, Earman J (eds) Handbook of the Philosophy of Physics. Elsevier, pp 1183–1286CrossRef Ellis GFR (2007) Issues in the philosophy of cosmology. In: Butterfield J, Earman J (eds) Handbook of the Philosophy of Physics. Elsevier, pp 1183–1286CrossRef
go back to reference Ellis GFR, Brundrit GB (1979) Life in the infinite universe. Q J R Astron Soc 20:37–41 Ellis GFR, Brundrit GB (1979) Life in the infinite universe. Q J R Astron Soc 20:37–41
go back to reference Fleurbaey M, Michel P (2003) Intertemporal equity and the extension of the Ramsey criterion. J Math Econ 39(7):777–802CrossRef Fleurbaey M, Michel P (2003) Intertemporal equity and the extension of the Ramsey criterion. J Math Econ 39(7):777–802CrossRef
go back to reference Gale D (1967) On optimal development in a multi-sector economy. Rev Econ Stud 34(1):1–18CrossRef Gale D (1967) On optimal development in a multi-sector economy. Rev Econ Stud 34(1):1–18CrossRef
go back to reference Guth AH (2007) Eternal inflation and its implications. J Phys A Math Theor 40(25):6811CrossRef Guth AH (2007) Eternal inflation and its implications. J Phys A Math Theor 40(25):6811CrossRef
go back to reference Hamkins JD, Montero B (2000) Utilitarianism in infinite worlds. Utilitas 12(1):91–96CrossRef Hamkins JD, Montero B (2000) Utilitarianism in infinite worlds. Utilitas 12(1):91–96CrossRef
go back to reference Jonsson A (2020) Infinite utility: time, counterparts and ultimate locations, (preprint) Jonsson A (2020) Infinite utility: time, counterparts and ultimate locations, (preprint)
go back to reference Jonsson A, Peterson M (2020) Consequentialism in infinite worlds. Analysis 80(2):240–248CrossRef Jonsson A, Peterson M (2020) Consequentialism in infinite worlds. Analysis 80(2):240–248CrossRef
go back to reference Jonsson A, Voorneveld M (2015) Utilitarianism on infinite utility streams: Summable differences and finite averages. Econ Theory Bull 3(1):19–31CrossRef Jonsson A, Voorneveld M (2015) Utilitarianism on infinite utility streams: Summable differences and finite averages. Econ Theory Bull 3(1):19–31CrossRef
go back to reference Jonsson A, Voorneveld M (2018) The limit of discounted utilitarianism. Theor Econ 13(1):19–37CrossRef Jonsson A, Voorneveld M (2018) The limit of discounted utilitarianism. Theor Econ 13(1):19–37CrossRef
go back to reference Khan U, Stinchcombe MB (2018) Planning for the long run: programming with patient, Pareto responsive preferences. J Econ Theory 176:444–478CrossRef Khan U, Stinchcombe MB (2018) Planning for the long run: programming with patient, Pareto responsive preferences. J Econ Theory 176:444–478CrossRef
go back to reference Lauwers L (1997) Rawlsian equity and generalised utilitarianism with an infinite population. Econ Theory 9(1):143–150CrossRef Lauwers L (1997) Rawlsian equity and generalised utilitarianism with an infinite population. Econ Theory 9(1):143–150CrossRef
go back to reference Lauwers L (1997) Topological aggregation, the case of an infinite population. Soc Choice Welf 14(2):319–332CrossRef Lauwers L (1997) Topological aggregation, the case of an infinite population. Soc Choice Welf 14(2):319–332CrossRef
go back to reference Lauwers L (1998) Intertemporal objective functions: strong pareto versus anonymity. Math Soc Sci 35(1):37–55CrossRef Lauwers L (1998) Intertemporal objective functions: strong pareto versus anonymity. Math Soc Sci 35(1):37–55CrossRef
go back to reference Lauwers L (2010) Ordering infinite utility streams comes at the cost of a non-ramsey set. J Math Econ 46(1):32–37CrossRef Lauwers L (2010) Ordering infinite utility streams comes at the cost of a non-ramsey set. J Math Econ 46(1):32–37CrossRef
go back to reference Lauwers L (2012) Intergenerational equity, efficiency, and constructibility. Econ Theory 49(2):227–242CrossRef Lauwers L (2012) Intergenerational equity, efficiency, and constructibility. Econ Theory 49(2):227–242CrossRef
go back to reference Lauwers L, Vallentyne P (2004) Infinite utilitarianism: more is always better. Econ Philos 20(2):307–330CrossRef Lauwers L, Vallentyne P (2004) Infinite utilitarianism: more is always better. Econ Philos 20(2):307–330CrossRef
go back to reference Letavaj P, Mišík L, Sleziak M (2015) Extreme points of the set of density measures. J Math Anal Appl 423(2):1150–1165CrossRef Letavaj P, Mišík L, Sleziak M (2015) Extreme points of the set of density measures. J Math Anal Appl 423(2):1150–1165CrossRef
go back to reference Li C, Wakker P (2023) A simple and very general axiomatization of average utility maximization for infinite streams, (working paper) Li C, Wakker P (2023) A simple and very general axiomatization of average utility maximization for infinite streams, (working paper)
go back to reference Linde AD (1990) Particle physics and inflationary cosmology. Harwood AcademicCrossRef Linde AD (1990) Particle physics and inflationary cosmology. Harwood AcademicCrossRef
go back to reference Marinacci M (1998) An axiomatic approach to complete patience and time invariance. J Econ Theory 83(1):105–144CrossRef Marinacci M (1998) An axiomatic approach to complete patience and time invariance. J Econ Theory 83(1):105–144CrossRef
go back to reference Obata N (1988) A note on certain permutation groups in the infinite dimensional rotation group. Nagoya Math J 109:91–107CrossRef Obata N (1988) A note on certain permutation groups in the infinite dimensional rotation group. Nagoya Math J 109:91–107CrossRef
go back to reference Petri H (2019) Asymptotic properties of welfare relations. Econ Theory 67(4):853–874CrossRef Petri H (2019) Asymptotic properties of welfare relations. Econ Theory 67(4):853–874CrossRef
go back to reference Pivato M (2014) Additive representation of separable preferences over infinite products. Theory Decis 77(1):31–83CrossRef Pivato M (2014) Additive representation of separable preferences over infinite products. Theory Decis 77(1):31–83CrossRef
go back to reference Pivato M (2021) Intertemporal choice with continuity constraints. Math Oper Res 46(3):1203–1229CrossRef Pivato M (2021) Intertemporal choice with continuity constraints. Math Oper Res 46(3):1203–1229CrossRef
go back to reference Pivato M (2022) A characterization of Cesàro average utility. J Econ Theory 201:105440CrossRef Pivato M (2022) A characterization of Cesàro average utility. J Econ Theory 201:105440CrossRef
go back to reference Pivato M (2023) Population ethics in an infinite universe, (working paper) Pivato M (2023) Population ethics in an infinite universe, (working paper)
go back to reference Rébillé Y (2007) Patience in some non-additive models. J Math Econ 43(6):749–763CrossRef Rébillé Y (2007) Patience in some non-additive models. J Math Econ 43(6):749–763CrossRef
go back to reference Roemer J, Suzumura K (eds) (2007) Intergenerational equity and sustainability. Palgrave Macmillan, Basingstoke Roemer J, Suzumura K (eds) (2007) Intergenerational equity and sustainability. Palgrave Macmillan, Basingstoke
go back to reference Sakai T (2003) An axiomatic approach to intergenerational equity. Soc Choice Welf 20(1):167–176CrossRef Sakai T (2003) An axiomatic approach to intergenerational equity. Soc Choice Welf 20(1):167–176CrossRef
go back to reference Sakai T (2006) Equitable intergenerational preferences on restricted domains. Soc Choice Welf 27(1):41–54CrossRef Sakai T (2006) Equitable intergenerational preferences on restricted domains. Soc Choice Welf 27(1):41–54CrossRef
go back to reference Sakai T (2010) A characterization and an impossibility of finite length anonymity for infinite generations. J Math Econ 46(5):877–883CrossRef Sakai T (2010) A characterization and an impossibility of finite length anonymity for infinite generations. J Math Econ 46(5):877–883CrossRef
go back to reference Sakai T (2010) Intergenerational equity and an explicit construction of welfare criteria. Soc Choice Welf 35(3):393–414CrossRef Sakai T (2010) Intergenerational equity and an explicit construction of welfare criteria. Soc Choice Welf 35(3):393–414CrossRef
go back to reference Sakai T (2016) Limit representations of intergenerational equity. Soci Choice Welf 47(2):481–500CrossRef Sakai T (2016) Limit representations of intergenerational equity. Soci Choice Welf 47(2):481–500CrossRef
go back to reference Sleziak M, Ziman M (2008) Lévy group and density measures. J Number Theory 128(12):3005–3012CrossRef Sleziak M, Ziman M (2008) Lévy group and density measures. J Number Theory 128(12):3005–3012CrossRef
go back to reference Steinhardt PJ, Turok N (2002) A cyclic model of the universe. Science 296(5572):1436–1439CrossRef Steinhardt PJ, Turok N (2002) A cyclic model of the universe. Science 296(5572):1436–1439CrossRef
go back to reference Svensson L-G (1980) Equity among generations. Econometrica 48(5):1251–1256CrossRef Svensson L-G (1980) Equity among generations. Econometrica 48(5):1251–1256CrossRef
go back to reference Tegmark M (2004) Parallel universes. In: Barrow et al. (2004), Ch. 21, pp 459–491 Tegmark M (2004) Parallel universes. In: Barrow et al. (2004), Ch. 21, pp 459–491
go back to reference Vallentyne P, Kagan S (1997) Infinite value and finitely additive value theory. J Philos 94(1):5–26CrossRef Vallentyne P, Kagan S (1997) Infinite value and finitely additive value theory. J Philos 94(1):5–26CrossRef
go back to reference von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite time horizon. Rev Econ Stud 32:85–104CrossRef von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite time horizon. Rev Econ Stud 32:85–104CrossRef
go back to reference Wilkinson H (2021) Infinite aggregation: expanded addition. Philos Stud 178(6):1917–1949CrossRef Wilkinson H (2021) Infinite aggregation: expanded addition. Philos Stud 178(6):1917–1949CrossRef
go back to reference Wilkinson H (2023) Infinite aggregation and risk. Australas J Philos 101(2):340–359CrossRef Wilkinson H (2023) Infinite aggregation and risk. Australas J Philos 101(2):340–359CrossRef
go back to reference Wilkinson H (2023b) Chaos, add infinitum, (preprint) Wilkinson H (2023b) Chaos, add infinitum, (preprint)
go back to reference Zame WR (2007) Can intergenerational equity be operationalized? Theor Econ 2:187–202 Zame WR (2007) Can intergenerational equity be operationalized? Theor Econ 2:187–202
go back to reference Zuber S, Asheim GB (2012) Justifying social discounting: the rank-discounted utilitarian approach. J Econ Theory 147(4):1572–1601CrossRef Zuber S, Asheim GB (2012) Justifying social discounting: the rank-discounted utilitarian approach. J Econ Theory 147(4):1572–1601CrossRef
Metadata
Title
Cesàro average utilitarianism in relativistic spacetime
Author
Marcus Pivato
Publication date
01-07-2023
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 4/2023
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-023-01470-6

Other articles of this Issue 4/2023

Social Choice and Welfare 4/2023 Go to the issue

Premium Partner