Video recordings of lectures

• Week 1

• Week 2

• Week 3

• Week 4

• Week 5

• Week 6 (unfortunately, the last 25 minutes of recording are lost due to technical errors caused by interruptions)

• Week 7

• Week 8

• Week 9

Lecture notes (very messy)

• Week 1

• Week 2

• Week 3 

• Week 4  

• Week 5  

• Week 6  

• Week 7  

• Week 8 

• Week 9

Key literature for for each week

• Week 1

• Week 2

• Week 3  (Social welfare functions; invariance and other axioms)

  • • Jacob M. Nebel (2021), Utils and Shmutils,  Ethics 131, pp. 571–599 (A commentary on Adler's book, and on "invariance" properties in SWOs more broadly. Nebel's conclusion: the SWO framework makes sense if (and only if) we specify the units in which individual well-being is measured.) 

• Week 4 (Harsanyi's social aggregation theorem and Bayesian social aggregation)

  • • Philippe Mongin (1995), Consistent Bayesian aggregation, Journal of Economic Theory 66, pp.  313–351.

    • Philippe Mongin (2016), Spurious Unanimity and the Pareto Principle, Economics and Philosophy, 32, pp. 511–532

    • Philippe Mongin and M. Pivato (2015), Ranking multidimensional alternatives and uncertain prospects. Journal of Economic Theory 157, pp.146–171 

• Week 5 (Bayesian Social Aggregation and Spurious Unanimity)

  • • Itzhak Gilboa, Dov Samet, and David Schmeidler (2004), Utilitarian aggregation of beliefs and tastes. Journal of Political Economy 112, pp. 932–938. 

    • Philippe Mongin and Marcus Pivato (2020), Social preference under twofold uncertainty.  Economic Theory 70(#3), pp. 633–663 (see section 6).

• Week 6 (Difference orders, their utility representations in linearly ordered abelian groups, and utilitarianism)

  • • Charles M. Harvey, (1999). Aggregation of individuals‘ preference intensities into social preference intensity. Social Choice and Welfare, 16(#1), pp. 65–79.

    • Veronika Köbberling (2006). Strength of preference and cardinal utility. Economic Theory 27(#2), pp. 375–391.

    • Robert Raschka (2025),  A Single Relation Theory of Welfarist Social Evaluation. Journal of Mathematical Economics 121, 103168

    • Jacob M. Nebel (2023), Ethics without numbers. Philosophy and Phenomenological Research 108, pp. 289–319. (Appendix B  contains another characterization of utilitarianism using difference orders.)

    • Two papers on difference (pre)orders and their (multi)utility representations:

      • • M. Pivato (2015), Social choice with approximate interpersonal comparison of welfare gains, Theory and Decision 79, pp. 181–216

        • M. Pivato (2013), Multiutility representations for incomplete difference preorders. Mathematical Social Sciences 66(#3), 196–220

    • Two other papers on utility representations using linearly ordered abelian groups:

      • • M. Pivato (2014), Additive representation of separable preferences over infinite products. Theory and Decision 77(#1), pp. 31–83 

        • M. Pivato and Élise Flore Tchouante (2024), Bayesian social aggregation with non-Archimedean utilities and probabilities.  Economic Theory 77, pp. 561–595

• Week 7 (Abstract Welfarism)

  • • Jacob M. Nebel (2023), Ethics without numbers. (op. cit.)  (Section 2 and Appendix A contain the abstract Welfarism Theorem)

    • John A. Weymark (2016) “Social welfare functions”,  pp.126-159 of  The Oxford Handbook of Well-Being and Public Policy. (Section 5.10  contains another good discussion of the (classical)  Welfarism Theorem). (Here is a much smaller PDF file but with poor typesetting.)

• Week 8 (Population ethics)

  • • Charles Blackorby, Walter Bossert, and David Donaldson (2009), Population Ethics, Chapter 20 (pp.483-500) of The Handbook of Rational and Social Choice

    • Hilary Greaves (2017)  “Population axiology.” Philosophy Compass 12, no. 11 e12442.

• Week 9 (Intergenerational justice)

  • • Han Bleichrodt, Kirsten IM Rohde, and Peter P. Wakker (2008) Koopmans’ constant discounting for intertemporal choice: A simplification and a generalization. Journal of Mathematical Psychology 52(#6), pp.341-347.

    • Charles Harvey (1986) Value functions for infinite-period planning. Management Science 32(#9), pp.1123-1139.

    • Charles Harvey (1995) Proportional discounting of future costs and benefits. Mathematics of Operations Research 20(#2), pp.381-399.

    • Martin Weitzman (2009) On modeling and interpreting the economics of catastrophic climate change. The Review of Economics and Statistics 91(#1), 1-19.

    • Marc Fleurbaey and Philippe Michel (2003) Intertemporal equity and the extension of the Ramsey criterion. Journal of Mathematical Economics 39(#7), pp.777-802.

    • M. Pivato and Marc Fleurbaey (2024) Intergenerational equity and infinite-population ethics: A survey. Journal of Mathematical Economics 113, p.103021.

Further Literature 

On social welfare

• Section 4 of Marc Fleurbaey, “Normative Economics and Economic Justice”, in The Stanford Encyclopedia of Philosophy. 

• Section 4 of Christian List, “Social Choice Theory”, in The Stanford Encyclopedia of Philosophy. 

On population ethics

• Charles Blackorby, Walter Bossert, and David Donaldson, Population Issues in Social Choice Theory, Welfare Economics, and Ethics, Cambridge University Press, 2005.

• Walter Bossert, “Anonymous welfarism, critical-level principles, and the repugnant and sadistic conclusions”, pp.63-85 of The Oxford Handbook of Population Ethics 

• Gustaf Arrhenius, Jesper Ryberg, and Torbjörn Tännsjö, “The Repugnant Conclusion”, in The Stanford Encyclopedia of Philosophy .

• John Broome, "The well-being of future generations",  pp.901-928 of The Oxford Handbook of Well-Being and Public Policy.

Further literature 

• Richard Chappell, Darius Meissner and William MacAskill (2024), An Introduction to Utilitarianism: From Theory to Practice, Hackett Publishing. [FREE ONLINE]

• Kohei Kamaga (2020). Social Welfare Evaluation and Intergenerational Equity, Springer: Singapore. [FREE ONLINE]

• Claude d'Aspremont and Louis Gevers. “Social welfare functionals and interpersonal comparability.”   Chapter 10 (pp. 459-541)  of Kenneth J. Arrow, Amartya Sen, and Kotaro Suzumura, eds. Handbook of Social Choice and Welfare. Volume 1. Elsevier, 2002.

• Charles Blackorby,  Walter Bossert, and David Donaldson. “Utilitarianism and the theory of justice.” Chapter 11 (pp. 543-596)  of Handbook of Social Choice and Welfare, Volume 1 (op. cit.) 

• John E. Roemer, Theories of distributive justice. Harvard University Press, 1996.

• Kenneth J. Arrow, Amartya Sen, and Kotaro Suzumura, eds. Handbook of Social Choice and Welfare. Volume 2. Elsevier, 2010.

• Salvador Barbera, Peter Hammond, and Christian Seidl, eds. Handbook of Utility Theory: Volume 1: Principles.  Springer, 1998.

• Salvador Barbera, Peter Hammond, and Christian Seidl, eds. Handbook of Utility Theory: Volume 2: Extensions. Springer, 2004.

• Other articles in The Oxford Handbook of Well-Being and Public Policy (op. cit.), The Oxford Handbook of Population Ethics (op. cit.), The Handbook of Rational and Social Choice (op. cit.), and the  Handbook of Social Choice and Welfare, Volume 1 (op. cit.)