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Consider a social welfare function (SWF) defined as \(SWF = f(U_{1}, U_{2}, \ldots, U_{m})\), where \(U_{i}\) is the utility function of the \(i^{th}\) person, given that there are \(m\) people in the society. Identify which one of the following statements is CORRECT.

  • A.Jeremy Bentham and John Stuart Mill proposed \(SWF = \sum_{i=1}^{m} w_{i}U_{i}\), where \(w_{i}\) is the weight assigned to individual \(i\) for their unique characteristics and \(w_{1} \neq w_{2} \neq \cdots \neq w_{m}\).
  • B.Since SWF reflects value judgements, interpersonal comparisons can be made on scientific grounds.
  • C.John Rawls proposed \(SWF = maximum\{U_{1}, U_{2}, \ldots, U_{m}\}\).
  • D.If \(SWF = \sum_{i=1}^{m} U_{i}\), it is referred as the utilitarian function.

Answer: D

The correct statement is If \(SWF = \sum_{i=1}^{m} U_{i}\), it is referred as the utilitarian function.

Adding up individual utilities with equal weight is the classical utilitarian (Benthamite) social welfare function: society's welfare is the total of everyone's utility.

The other statements are wrong. Bentham and Mill gave every person's utility the same weight, so a function with weights that differ by individual characteristics is not their proposal. Because a social welfare function embodies value judgements, interpersonal comparisons of utility cannot be made on scientific grounds; that is the point the statement reverses. Rawls proposed the maximin rule, \(SWF = \min\{U_{1}, U_{2}, \ldots, U_{m}\}\), judging society by its worst-off member, not by the maximum utility.

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