Abstract
This chapter contains the basic social choice of theoretic concepts, definitions and propositions that will be needed in the rest of the text. These include, among others, notion of a binary relation, important properties of binary relations, notions of social decision rule and social welfare function, important conditions on social decision rules, Arrow and Gibbard theorems and the notions of weak Latin Square and Latin Square.
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Notes
- 1.
- 2.
Gibbard (1969).
- 3.
Sen (1970).
- 4.
Gibbard (1969).
- 5.
Let A be a nonempty set. \((A_{1}, A_{2}, \ldots ,A_{m})\) is a partition of A iff \((\forall i,j \in \{1,2, \ldots ,m\}) [(A_{i} \ne \emptyset ) \wedge (i \ne j \rightarrow A_{i} \cap A_{j} = \emptyset )] \wedge \cup ^{m} _{i=1} A_{i} = A\).
- 6.
Throughout this text n() and N() will denote the number of individuals having the preferences specified in the parentheses.
References
Arrow, Kenneth J. 1951. Social choice and individual values, 2nd ed., 1963. New York: Wiley.
Gibbard, Allan. 1969. Social choice and the Arrow conditions. Discussion Paper: Department of Philosophy, University of Michigan.
Jain, Satish K. 1985. A direct proof of Inada-Sen-Pattanaik theorem on majority rule. The Economic Studies Quarterly 36: 209–215.
Sen, Amartya K. 1970. Collective choice and social welfare. San Francisco: Holden-Day.
Suppes, Patrick. 1957. Introduction to logic. New York: Van Nostrand.
Tarski, Alfred. 1941. Introduction to logic and to the methodology of deductive sciences. New York: Oxford University Press.
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Jain, S.K. (2019). The Preliminaries. In: Domain Conditions and Social Rationality. Springer, Singapore. https://doi.org/10.1007/978-981-13-9672-4_2
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DOI: https://doi.org/10.1007/978-981-13-9672-4_2
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