— Ch. 1 · Origins And Definitions —
Social welfare function.
~5 min read · Ch. 1 of 6
In February 1938, Abram Bergson published an article in the Quarterly Journal of Economics titled A Reformulation of Certain Aspects of Welfare Economics. This paper introduced the term social welfare function to state precise value judgments required for deriving conditions of maximum economic welfare. The function was real-valued and differentiable, designed to describe society as a whole rather than any single individual. Arguments within the function included quantities of commodities produced and consumed alongside resources used in production, including labor supplied by workers. Bergson argued that traditional welfare economics described standards of efficiency while dispensing with interpersonally comparable cardinal utility. He believed such comparisons might merely conceal subjective value judgments hidden behind mathematical formalism. Earlier neoclassical theories often treated diminishing marginal utility as implying measurable interpersonal utility differences. Lionel Robbins had rejected this view in 1935, arguing mental events could not be measured empirically or falsified through testing. Bergson's approach allowed economists to derive Pareto optimality conditions as necessary but insufficient criteria for defining interpersonal equity. Paul Samuelson later clarified how production and consumption efficiency remained distinct from ethical values embedded in the function itself.
Ordinal Versus Cardinal Approaches
Economists distinguish between ordinal functions using ranked voting data and cardinal functions utilizing numeric representations of utility levels. Ordinal methods determine whether one choice is better than another without measuring intensity of preference. Cardinal approaches assume individuals utilities can be placed on a common scale and compared numerically. Examples include life expectancy metrics or per capita income figures serving as measurable proxies for well-being. Kenneth Arrow demonstrated in his 1963 book Social Choice and Individual Values that dropping real-valued requirements made rational social behavior impossible. His impossibility theorem showed no ordinal social welfare function could satisfy independence of irrelevant alternatives alongside other standard axioms. This axiom requires changing one outcome's value should never affect choices unrelated to that specific outcome. A customer buying apples because they prefer them over blueberries would not suddenly choose blueberries if cherries went on sale. Arrow found such coherence unattainable at the societal level when relying solely on ordinal preferences. John Harsanyi later strengthened this result by showing societies making decisions under uncertainty must adopt utilitarian rules for coherent outcomes. The distinction remains critical for understanding why some economic models prioritize ranking while others require precise numerical comparisons.