Normative Foundations and Mathematical Modelling of Egalitarian and Utilitarian Welfare.

MSc Logic – Project January 2011 (link)


Many classical models of distributive justice rely on utilitarian foundations: the welfare of an individual is the sum of his pleasures and pains and the welfare of a society can be discussed by aggregating individual levels of welfare. This view assumes that it is meaningful to measure and to compare the welfare of individuals, and this assumption is reflected in the mathematical models by the possibility of defining utility functions for each individual and to talk about the overall utility of a society. John Rawls’ justice as fairness approach constituted the strongest response to the utilitarian view, stressing in particular that individual conceptions of good are not commensurable. Rawls’ celebrated book “A Theory of Justice” (1971) changed the agenda of the debate on normative foundations of theories of welfare, stressing questions such as: is it possible to measure individual welfare? is it just? can we compare different individual conceptions of good? what does it mean for institutions to be just? Different answers to these questions entail huge differences in the way in which a model of a well-ordered society is conceived and of course different views of what constitutes a formal theory of a fair distribution of resources. In this project we are going to discuss a selection of classical works related to the reactions after Rawls by scholars from the economic tradition: Arrow’s review of Rawls, Harsanyi’s critique of the Rawlsian distribution principle, Sen’s notion of capability, Roemer’s discussion of primary goods. Two complementary aspects will be covered: the normative assumption justifying the axiomatizations at issue and the mathematical modelling of those assumptions. The aim of this project is to provide a grasp of the tension between (at least) two paradigms of normativity in modelling theories of welfare and to show how different normative intuitions are strictly connected with different mathematical frameworks.


The project is particularly suitable for those who have already taken a relevant course, such as Computational Social Choice or Cooperative Games, Political Philosophy, but open to all interested students.


Each student will present one of the selected topic, read the essential refernce, look for other relevant references. Then write a short essay at the end of the course (on the same topic or on another). Participation in the discussions will form part of the assessment.


  • R. Arneson, 1990, Primary Goods Reconsidered, Nous, 24, 429-454
  • Kenneth J. Arrow, Social Choice and Individual Values. 2nd edition. Cowles Foundation, Yale University Press, 1963.
  • K. Arrow, 1973, Some Ordinalist-Utilitarian Notes on Rawls’ Theory of Justice, Journal of Philosophy, 70, 9, 245-63.
  • Kenneth J. Arrow, 1977, Extended Sympathy and the Possibility of Social Choices, American Economic Review. Supplementary issue of the proceedings, 219-225.
  • K. Binmore, 2008, Naturalizing Harsany and Rawls, in Fleubaey et al., 2008, pp. 303-334.
  • M. Fleurbaey, Théories économiques de la justice, Economica, Economie et statistiques avancées, Paris, 1996 .
  • M. Fleurbaey, M. Salles, J. A. Weymark, Justice, Political Liberalism and Utilitarianism. Themes form Harsany and Rawls, Cambridge, 2008.
  • A. Gibbard, 1974, A Pareto Consistent Liberal Claim, Journal of Economic Theory, 7, 399-410.
  • J. Harsany, 1953, Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking, Journal of Political Economy, 61, 434-435
  • J. Harsany, 1955, Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility, Journal of Political Economy, 63, 309-321.
  • J. Harsany, 1975, Review: Can The Maximin Principle Serve as a Basis for Morality? A Critique of John Rawls Theory, American Political Science Review, 69 (2), 594-606
  • J. Harsany, 1982, Morality and the theory of rational behaviour, in Sen and Williams, 1982.
  • H. J. Moulin, Fair Division and Collective Welfare, MIT Press, 2003
  • J. Rawls, A Theory of Justice, 1971, Second Edition, Cambidge Mass., Harvard University Press, 1999.
  • J. Rawls, 1974, Reply to Alexander and Musgrave, The Quarterly Journal of Economics, 88 (4), 633-55.
  • J. Rawls, 1982, Social Unity and Primary Goods, in Sen and Williams, 1982.
  • J. Rawls, 2001, Justice as Fairness: A Restatement, Cambridge Mass., Harvard University Press.
  • J. E. Roemer, Theories of Distributive Justice, Harvard University Press, 1996.
  • J. E. Roemer, 2008, Harsany Impartial Observer is Not a Utilitarian, in Fleubaey et al, 2008.
  • A. Sen, 1982, Equality of What?, in Choice, Welfare and Measurement, Harvard University Press, 365-366.
  • A. Sen, 1992, Inequality Reexamined, Harvard University Press.
  • A. Sen and B. Williams (eds), Utilitarianism and Beyond, Cambridge, 1982.
  • B. Skyrms, 2008, The Social Contract Naturalized, in Fleubaey et al., 2008, pp. 334-351.

Important dates

  • 11 January: Overview of the literature. Introduction to some aspects of justice as fairness.
  • 17 January: Choose the topic.
  • 27 January: 14.00-17.00. Presentation
  • 1 February: 14.00-17.00. Two presentations.
  • 3 February: 11.00-14.00. Presentation. Final discussion.
  • 20 February: Deadline for submitting the papers.