The Strong Consistency of Neutral and Monotonic Binary Social Decision Rules

Jain, Satish (2020): The Strong Consistency of Neutral and Monotonic Binary Social Decision Rules.

Abstract

The purpose of this paper is to investigate the strong consistency of neutral and monotonic binary social decision rules. Individuals are assumed to satisfy von Neumann-Morgenstern axioms of individual rationality. The main result of the paper shows that there does not exist any neutral and monotonic non-null non-dictatorial binary social decision rule which is strongly consistent. The relationship between restricted preferences and the existence of strong equilibria is also investigated. It is shown that for every non-dictatorial social decision function satisfying the conditions of independence of irrelevant alternatives, neutrality, monotonicity and weak Pareto-criterion there exists a profile of individual orderings satisfying value-restriction corresponding to which there is no strong equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: Binary Social Decision Rules, Strong Consistency, Neutrality, Monotonicity, Value-Restricted Preferences
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

Arrow, K.J. (1963), Social Choice and Individual Values, second edition, Wiley, New York.

Danilov, V.I. and Sotskov, A.I. (1993), `On strongly consistent social choice functions', Journal of Mathematical Economics, 22, 327-346.

Dutta, B. (1980), `On the possibility of consistent voting procedures', Review of Economic Studies, 47, 603-16.

Farquharson, R. (1969), Theory of Voting, Basil Blackwell, Oxford.

Gibbard, A. (1969), `Intransitive social indifference and the Arrow dilemma', unpublished manuscript.

Gibbard, A. (1973), `Manipulation of voting schemes: A general result', Econometrica 41, 587-601.

Jain, S.K. (1987), `Maximal conditions for transitivity and monotonic binary social decision rules', The Economic Studies Quarterly, 38, 124-30.

Luce, R.D. and Raiffa, H. (1957), Games and Decisions, Wiley, New York.

Oren, I. (1981), `The structure of exactly strongly consistent social choice functions', Journal of Mathematical Economics, 8, 207-20.

Moulin, H. (1983), The Strategy of Social Choice, North-Holland, Amsterdam.

Peleg, B. (1978), `Consistent voting systems', Econometrica, 46, 153-61.

Peleg, B. (1984), Game-Theoretic Analysis of Voting in Committees, Cambridge University Press, Cambridge.

Satterthwaite, M.A. (1975), `Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions', Journal of Economic Theory, 10, 187-217.

Sen, A.K. (1970), Collective Choice and Social Welfare, Holden-Day, San Francisco.