Social Welfare Aggregation

Social Welfare Functions

A social welfare function aggregates individual utilities into a single measure of social good. Different welfare functions embody different ethical principles about how to balance efficiency (total welfare) against equality (distribution of welfare).

Key Welfare Functions

• Utilitarian (Bentham): W = Σu_i. Maximize total utility regardless of distribution. Justifies sacrificing some for greater total good.
• Prioritarian: W = Σu_i^1-ε. Gives extra weight to worse-off individuals. Parameter ε controls priority strength (ε=0 is utilitarian, higher ε is more egalitarian).
• Egalitarian/Rawlsian (Maximin): W = min(u_i). Maximize welfare of worst-off person. From Rawls's "difference principle" - inequalities justified only if they benefit the least advantaged.
• Nash Product: W = Πu_i. Geometric mean of utilities. Used in Nash bargaining solution. Balances efficiency with some concern for equality.

Efficiency vs Equality Tradeoff

Different welfare functions make different tradeoffs between total welfare (efficiency) and equal distribution:

• Utilitarian: Purely efficiency-focused. Would give all resources to whoever benefits most.
• Prioritarian: Balances efficiency and equality. Willing to sacrifice some total welfare for better distribution.
• Egalitarian: Equality-focused. Ignores gains to better-off individuals entirely.
• Nash: Moderate balance. Zero utility for anyone means zero social welfare (veto power).

Philosophical Issues

• Interpersonal comparisons: Can we meaningfully compare utilities across people? Is one person's happiness commensurable with another's?
• Leveling down: Egalitarian functions can rank equally-poor outcomes above unequal but better outcomes (problematic for some).
• Separability: Should adding happy people always increase welfare? Population ethics creates puzzles (repugnant conclusion).
• Diminishing marginal utility: An extra dollar matters more to poor than rich. Prioritarian functions capture this.
• Rights and constraints: Welfare maximizing might violate individual rights. Deontological constraints may override welfare.

Applications

Social welfare functions inform policy decisions in taxation, healthcare allocation, climate change mitigation, and development economics. The choice of welfare function encodes ethical judgments about fairness and efficiency.