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Social Choice and Individual Values
Kenneth Arrow's monograph Social Choice and Individual Values (1951; revised in 1963 and 2012) and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how social values from the set of individual orderings would be implemented under the constitution. Less formally, each social choice corresponds to the feasible set of laws passed by a "vote" (the set of orderings) under the constitution even if not every individual voted in favor of all the laws.
The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requirements. The result generalizes the voting paradox, which shows that majority voting may fail to yield a stable outcome.
The Introduction contrasts voting and markets with dictatorship and social convention (such as those in a religious code). Both exemplify social decisions. Voting and markets facilitate social choice in a sense, whereas dictatorship and convention limit it. The former amalgamate possibly differing tastes to make a social choice. The concern is with formal aspects of generalizing such choices. In this respect it is comparable to analysis of the voting paradox from use of majority rule as a value.
Arrow asks whether other methods of taste aggregation (whether by voting or markets), using other values, remedy the problem or are satisfactory in other ways. Here logical consistency is one check on acceptability of all the values. To answer the questions, Arrow proposes removing the distinction between voting and markets in favor of a more general category of collective social choice.
The analysis uses ordinal rankings of individual choice to represent behavioral patterns. Cardinal measures of individual utility and, a fortiori, interpersonal comparisons of utility are avoided on grounds that such measures are unnecessary to represent behavior and depend on mutually incompatible value judgments (p. 9).
Following Abram Bergson, whose formulation of a social welfare function launched ordinalist welfare economics, Arrow avoids locating a social good as independent of individual values. Rather, social values inhere in actions from social-decision rules (hypostatized as constitutional conditions) using individual values as input. Then 'social values' means "nothing more than social choices" (p. 106).
Topics implicated along the way include game theory, the compensation principle in welfare economics, extended sympathy, Leibniz's principle of the identity of indiscernibles, logrolling, and similarity of social judgments through single-peaked preferences, Kant's categorical imperative, or the decision process.
The book defines a few terms and logical symbols used thereafter and their applied empirical interpretation (pp. 11–19, 23). Key among these is the "vote" ('set of orderings') of the society (more generally "collectivity") composed of individuals ("voters" here) in the following form:
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Social Choice and Individual Values
Kenneth Arrow's monograph Social Choice and Individual Values (1951; revised in 1963 and 2012) and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how social values from the set of individual orderings would be implemented under the constitution. Less formally, each social choice corresponds to the feasible set of laws passed by a "vote" (the set of orderings) under the constitution even if not every individual voted in favor of all the laws.
The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requirements. The result generalizes the voting paradox, which shows that majority voting may fail to yield a stable outcome.
The Introduction contrasts voting and markets with dictatorship and social convention (such as those in a religious code). Both exemplify social decisions. Voting and markets facilitate social choice in a sense, whereas dictatorship and convention limit it. The former amalgamate possibly differing tastes to make a social choice. The concern is with formal aspects of generalizing such choices. In this respect it is comparable to analysis of the voting paradox from use of majority rule as a value.
Arrow asks whether other methods of taste aggregation (whether by voting or markets), using other values, remedy the problem or are satisfactory in other ways. Here logical consistency is one check on acceptability of all the values. To answer the questions, Arrow proposes removing the distinction between voting and markets in favor of a more general category of collective social choice.
The analysis uses ordinal rankings of individual choice to represent behavioral patterns. Cardinal measures of individual utility and, a fortiori, interpersonal comparisons of utility are avoided on grounds that such measures are unnecessary to represent behavior and depend on mutually incompatible value judgments (p. 9).
Following Abram Bergson, whose formulation of a social welfare function launched ordinalist welfare economics, Arrow avoids locating a social good as independent of individual values. Rather, social values inhere in actions from social-decision rules (hypostatized as constitutional conditions) using individual values as input. Then 'social values' means "nothing more than social choices" (p. 106).
Topics implicated along the way include game theory, the compensation principle in welfare economics, extended sympathy, Leibniz's principle of the identity of indiscernibles, logrolling, and similarity of social judgments through single-peaked preferences, Kant's categorical imperative, or the decision process.
The book defines a few terms and logical symbols used thereafter and their applied empirical interpretation (pp. 11–19, 23). Key among these is the "vote" ('set of orderings') of the society (more generally "collectivity") composed of individuals ("voters" here) in the following form: