The lectures start out from Kenneth Arrow's famous Impossibility Theorem, discuss possibility results under restricted domains of preferences, consider the issue of manipulability or strategy-proofness, the exercise of individual rights in the framework of collective decisions, scoring functions and related schemes, Rawlsian and utilitarian justice, various bargaining solutions and finally consider empirical studies in relation to distributive justice.
1. Introduction and Arrow’s Impossibility Result from Different Angles: Arrow has a famous impossibility theorem which states that under certain plausible axioms there does not exist a so-called Social Welfare Function. We shall look into the details of his proof. (Arrow, K. J. 1963. Social choice and individual values. Chapter 3; Bergson, A. 1966. “A Reformulation of Certain Aspects of Welfare Economics”, in Essays in Normative Economics. Cambridge, MA: Harvard University Press; Sen, A. K. 1995. “Rationality and Social Choice”, American Economic Review 85:1–24.)
2. Domain Restrictions, Qualitative and Quantitative: We shall weaken Arrow’s “unrestricted domain condition” and shall examine some conditions which restrict the domain of individual preferences. (Gaertner, Wulf. 1979. “An Analysis and Comparison of Several Necessary and Sufficient Conditions for Transitivity Under the Majority Decision Rule”, in Aggregation and Revelation of Preferences, J. J. Laffont (ed.) Amsterdam: North Holland; Gaertner, Wulf. 2001. Domain Conditions in Social Choice Theory. Cambridge: Cambridge University Press; Maskin, E. 1995. “Majority Rule, Social Welfare Functions, and Game Forms”, in Choice, Welfare and Development, K. Basu, P. K. Pattanaik and K. Suzumura (eds.) Oxford: Oxford University Press; Sen, Amartya. 1966. “A Possibility Theorem on Majority Decision”, Econometrica 34:75–79; Sen, Amartya, and P. K. Pattanaik. 1969. “Necessary and Sufficient Conditions for Rational Choice under Majority Decision”, Journal of Economic Theory 1:178–202.)
3. Rights and Social Choice: This lecture will deal with the exercise of individual rights within the procedure of aggregating individual preferences. Sen has an impossibility result which says that the exercise of individual rights clashes with the Pareto principle. (Gaertner, W., P. K. Pattanaik, and K. Suzumura. 1992. “Individual Rights Revisited”. Economica 59:161–177; Gibbard, Allan. 1974. “A Pareto Consistent Libertarian Claim”. Journal of Economic Theory 7:388–410; Sen, Amartya. 1970. “The Impossibility of a Paretian Liberal”. Journal of Political Economy 78:152–157; Sen, Amartya. 1992. “Minimal Liberty”. Economica 59:139–159.)
4. Manipulability: Gibbard and Satterthwaite came up with another impossibility result which claims that within the Arrovian context it is in general to the advantage of an individual not to state his or her true or honest preferences. (Gibbard, Allan. 1973. “Manipulation of Voting Schemes: A General Result”. Econometrica 41 (4):587–601; Kelly, S. J. 1988. Social Choice Theory. Chapters 10 & 11; Moulin, H. 1980. “On Strategy-Proofness and Single-Peakedness”. Public Choice 35:437–455.)
5. Social Choice Rules: This lecture discusses various scoring functions and their properties. One of the best known scoring functions is the Borda count developed by de Borda in the 18th century. (Gärdenfors, P. 1973. “Positionalist Voting Functions”. Theory and Decision 4:1–24; Kelly, S. J. 1988. Social Choice Theory. Chapters 5 & 6; Sen, Amartya. 1977. “Social Choice Theory: A Re-examination”. Econometrica 45:53–89; Young, H. P. 1974. “An Axiomatisation of Borda's Rule”. Journal of Economic Theory 9:43–52.)
6. Rawlsian and Utilitarian Justice: We describe axiomatically and discuss both the Rawlsian maximin principle and the utilitarian rule of summation of individual utility values. Both mechanisms share some common properties but, of course, diverge on others. (Blackorby, C., D. Donaldson, and J. A. Weymark. 1984. “Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction”. International Economic Review 25:327–356; Gevers, L., and C. d'Aspremont. 1977. “Equity and informational basis of collective choice”. Review of Economic Studies 46:199–210; Hammond, P. J. 1976. “Equity, Arrow's Conditions, and Rawls' Difference Principle”. Econometrica 44:793–804; Harsanyi, J. C. 1978. “Bayesian Decision Theory and Utilitarian Ethics”. American Economic Review 68:223–228; Roemer, J. E. 1996. Theories of Distributive Justice. Cambridge, MA: Harvard University Press.)
7. Cooperative Bargaining: We discuss two of the best known bargaining procedures which use cardinal individual utilities but do not assume the possibility of interpersonal comparability of these utility values, namely the Nash bargaining solution and the Kalai-Smorodinsky solution. (Gaertner, W. 2009. A Primer in Social Choice Theory, rev. ed. Oxford: Oxford University Press; Kalai, E. and M. Smorodinsky. 1975. “Other Solutions to Nash’s Bargaining Problem”. Econometrica 43:513-518; Luce, R.D. and H. Raiffa. 1957. Games and Decisions. New York: John Wiley (chapter 6); Nash, J.F. 1950. “The Bargaining Problem”. Econometrica 18: 155-162.
In order to count as a four-hour course (with the corresponding credits), participants are required to give a short presentation in class, together with a short essay (6-8 pages) to be handed in after the presentation (ungraded). A list of possible topics will be provided at the beginning of the course. Own suggestions for presentation are more than welcome.
General readings: Arrow, K. J. 1963. Social choice and individual values, 2nd ed. New York: John Wiley.
Craven, J. 1992. Social Choice: A Framework for Collective Decisions and Individual Judgements, Cambridge: Cambridge University Press.
Gaertner, Wulf. 2009. A Primer in Social Choice Theory, rev. ed. Oxford: Oxford University Press.
Kelly, S. J. 1988. Social Choice Theory, Berlin, Heidelberg: Springer-Verlag.
Nurmi, H. 1999. Voting Paradoxes and How to Deal with Them. Springer-Verlag.
Sen, Amartya. 1987. “Social Choice”, in The New Palgrave, J. Eatwell, M. Milgate and P. Newmann (eds.) London: MacMillan.
Sen, Amartya K. 1984. Collective Choice and Social Welfare, Amsterdam; New York: North-Holland.
New expanded edition (with additional chapters) published as a paperback in 2017, Penguin Books.
Additional readings will be provided during the course.