Social welfare function

A rule that assigns a social ranking or value to outcomes by combining information about individuals’ well-being. Its form determines how inequality, efficiency, and competing interests affect collective judgments.

Utility: A representation of how desirable an outcome is to an individual or decision-maker. Social welfare functions combine individual utilities or other measures of well-being.
Utilitarianism: The ethical view that actions or institutions should maximize the sum of individual utilities. It corresponds to maximizing an additive social welfare function.
Arrow's impossibility theorem: A theorem showing that no rank-order voting rule satisfies several plausible conditions for all preference profiles. It limits preference-based social rankings, while a welfare function may use richer information than ordinal rankings.
Optimal taxation: The study of tax systems that balance revenue needs against incentives and distributional goals. A social welfare function makes the distributional weights in tax design explicit.
Interpersonal utility comparison: The comparison of well-being levels or gains across different people. Many aggregation rules require judgments about whose utility level or gain is larger.
Rawlsian social welfare function: A rule that evaluates a society by the utility of its least advantaged member. It gives absolute priority to improving the position of the worst off.
Condorcet paradox: A cycle of majority preferences in which each of three alternatives defeats another. It shows why majority comparisons need not produce the coherent ranking a welfare function supplies.
Social welfare weights: The marginal social value assigned to an additional unit of income or well-being for a person or group. These weights translate the chosen welfare criterion into policy evaluations.
Pareto efficiency: A state is Pareto efficient when no feasible change can improve someone’s welfare without worsening another’s. A widely used condition requires social rankings to respect unanimous welfare improvements.
Atkinson index: A measure of income inequality derived from welfare comparisons and a parameter for inequality aversion. Its inequality-aversion parameter expresses how strongly welfare evaluation favors redistribution.

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