Social Choice

Semester and Year Offered: 3rd Semester, 2nd year

Course Coordinator and Team: Taposik Banerjee

Email of course coordinator: taposik[at]aud[dot]ac[dot]in

Pre-requisites: Mathematics at 10+2 level and must possess good analytical skill.

Aim: The course- “Social Choice” has been designed to introduce students with the idea of social decision making process. This course analyzes this decision making process by delineating a structure that assimilates the preferences of individuals to reach at social decision. Analyzing social decision process is important primarily because such process has significant bearing on the wellbeing and equality of a society. If it is acceded that any decision process of the society must respect a set of values like egalitarianism, non-dictatorship etc, then it seems indispensible to any societal rule to incorporate those values. This course therefore is important not only in terms giving an overview of different rules those are used to reach at social decision but also in terms of exploring what set of values those rules represent.

While doing this course students will go through rigorous application of their analytical skill that on one hand would help grasp the content of the course as discussed above and enable them to draw logical inferences which would be useful for their further study.

Course Outcomes:

On successful completion of this course students will be able to:

1. Develop and sustain an argument using the concepts that are commonly used by economists.
2. Demonstrate how individual choices in a society can be aggregated and translated into a collective choice.
3. Analyse implications of and contradictions between different democratic values in the process of aggregating individual preferences into social/collective preference.
4. Construct collective choice rules that respect certain values that individuals in a society consider important.
5. Examine how collective decision making processes influence the well-being of society.
6. Use mathematics in formalising and analysing an economic problem.
7. Discuss the limitations of and critically evaluate collective decision making processes.

Brief description of modules/ Main modules:

The course introduces students to a class of theories that deals with collective decision making process. These theories try to address the question of how a society may aggregate individual preferences in order to take a collective choice decision. The course will highlight some fundamental conflicts between different apparently benign normative criteria and indicate the limitations of a collective decision making process. The following would be the broad outline of the course.

Module 1: Individual Preference, best and maximal elements, existence of best elements, preference to choice, differences between individual and collective choices.

Module 2: Binary relations, properties of binary relations: reflexivity, transitivity, acyclicity, quasitransitivity, rationality conditions, some fundamentals of logic: using connectives, quantifiers, logics of deduction: direct methods, proof by contradictions. Logical relationship among different properties of binary relations.

Module 3: Introduction to binary decision rules, construction of binary rule, component and properties of binary rule. Different choice rule: collective choice rule, collective decision rule, social welfare functions, social choice functions.

Module 4: Some seminal results: Arrow’s impossibility result, manipulability of collective choice rule: the Gibbard and Satterthwaite result. Some popular voting rules: majority decision, median voter rule, 2\3 majority decision, dictatorial rule. Interesting properties of voting rule: anonymity, monotonicity, neutrality, May’s Theorem.

Module 5: Weighted voting rules, voting power, misreporting true preference: some example, mechanism designing to prevent manipulation conflict between Efficiency and Individual Rights.

Assessment Details with weights:

Three class tests with following weights: Test 1 (25%), Test 2 (35%) and Test 3 (40%).

Test 1 will be a class test based on material covered during first half of the semester.

Test 2 will be a class test based on material covered during second half of the semester.

Test 3 will be an end of semester class test based on all material covered in the course.

Reading List:

• Arrow, K.J. (1963), Social Choice and Individual Values, second edition, Wiley, New York.
• Gaertner, W. (2009) A Primer in Social Choice Theory, Oxford University Press, New York.
• Sen, A. K. (1970), The Impossibility of a Paretian Liberal, The Journal of Political Economy, 78, 152-157.
• Sen, A. K. (1970), Collective Choice and Social Welfare, Holden-Day, San Francisco, republished 1979 by North-Holland, Amsterdam .
• Suzumura, K. (1983), Rational Choice, Collective Decisions, and Social welfare. CUP.

ADDITIONAL REFERENCE:

1. Arrow, K. J. (1973), Some Ordinalist-Utilitarian Notes on Rawls's Theory of Justice, Journal of Philosophy, 70, 254-263.
2. Black, D. (1948), On the Rationale of Group Decision Making, The Journal of Political Economy, 56, 23-34.
3. Black, D. (1958), The Theory of Committees and Elections, Cambridge University Press, Cambridge.
4. Fishburn, P.C. (1970), Conditions for Simple Majority Decision Functions with Intransitive Individual Indifference, Journal of Economic Theory, 2, 354-367.
5. Gaertner, W. (2001), Domain Conditions in Social Choice Theory, Cambridge University Press, Cambridge.
6. Harsanyi, J. C. (1953), Cardinal Utility in Welfare Economics and in the Theory of Risk Taking, Journal of Political Economy, 61, 434-435.
7. Harsanyi, J. C. (1955), Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility, Journal of Political Economy, 63, 309-321.
8. Harsanyi, J. C. (1975), Can the Maximin Principle Serve as a Basis of Morality?, American Political Science Review, 69, 594-606.
9. Inada, K.-I. (1964), A Note on the simple majority decision rule, Econometrica, 32, 525-531.
10. Inada, K.-I. (1969), The simple majority decision rule, Econometrica, 37, 490-506.
11. Inada, K.-I. (1970), Majority rule and rationality, Journal of Economic Theory, 2, 27-40.
12. Jain, S.K. (1986), Special majority rules: A necessary and sufficient condition for quasitransitivity with quasi-transitive individual preferences, Social Choice and Welfare, 3, 99-106.
13. Kalai, E. (1977), Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons, Econometrica, 45, 1623-1630.
14. Kalai, E. and M. Smorodinsky (1975), Other Solutions to Nash’s Bargaining Problem, Econometrica, 43, 513-518.
15. Kelly, J.S. (1974), Necessity conditions in voting theory, Journal of Economic Theory, 8, 149-160.
16. Leininger, W. (1993), The Fatal Vote: Berlin versus Bonn, Finanzarchiv, 50, 1-20.
17. Nash, J. (1950), The Bargaining Problem, Econometrica, 18, 155-162
18. Pattanaik, P.K. (1970), On social choice with quasitransitive individual preferences,
19. Journal of Economic Theory, 2, 267-275.
20. Pattanaik, P.K. (1971), Voting and Collective Choice, Cambridge University Press, Cambridge.
21. Rawls, J. (1971), A Theory of Justice, Harvard University Press.
22. Rawls, J. (1974), Some Reasons for the Maximin Criterion, American Economic Review (Papers and Proceedings), 64, 141-146
23. Reny, Ph. J. (2001), Arrow’s Theorem and the Gibbard - Satterthwaite Theorem: A Unified Approach, Economics Letters, 70, 99-105
24. Roemer, J. (1986), TheMismarriage of Bargaining Theory and Distributive Justice, Ethics, 97, 88-110.
25. Sen, A.K. (1966), A possibility Theorem on Majority Decisions, Econometrica, 34, 491-499.
26. Sen, A.K. and Pattanaik, P.K. (1969), Necessary and Sufficient Conditions for Rational Choice Under Majority Decision, Journal of Economic Theory, 1, 178-202.