NOTE-258: Equality of What?

Contribution

The lecture asks which space equality should be sought in, and answers negatively first: three candidate metrics — equality of marginal utility (what utilitarianism delivers), equality of total utility (completed as leximin), and Rawls’s equality of primary social goods — each fail, “in rather different and contrasting ways”, and “an adequate theory cannot be constructed even on the combined grounds of the three” (p. 197). It then introduces, in about two pages, “basic capability equality”: judging advantage by what people are able to do rather than by goods held or by mental reactions. This is the first statement of what became the capability approach.

Key insight

Advantage is a relation between persons and goods, and people differ in how they convert goods into doings. Utility tracks the relation but through “mental reaction”, which a contented or resigned person can have in abundance while badly deprived; primary goods ignore the relation and treat goods “as the embodiment of advantage” — Sen’s “fetishism” charge (p. 216). If people were alike, both metrics would do tolerably; because they are not, both are “partially blind” (p. 216), and the missing information is what a person can actually do.

Assumptions

• Two ways to criticise a moral principle (pp. 197–198): a case-implication critique (derive stark implications in particular cases and test them against intuition) and a prior-principle critique (test consistency with a more fundamental principle, e.g. Rawls’s original position or Hare’s universalizability, “giving equal weights to the equal interests of the occupants of all the roles”). Both are used throughout; the decisive argument for capabilities is a case-implication one (p. 217).
• Utilities have descriptive content. Sen sets aside the route by which utilities are scaled so that equal marginal utility just means equal social importance: it “is non-controversial mainly because it says so little” (p. 200). The critique of utilitarianism assumes traditional, descriptively comparable utilities (pp. 200–201, 204).
• Human diversity is deep and pervasive: needs vary “with health, longevity, climatic conditions, location, work conditions, temperament, and even body size” (pp. 215–216). Every argument turns on this.
• Scope restricted to needs. For the capability argument Sen deliberately does not invoke non-well-being claims (non-exploitation, non-discrimination, desert, entitlements), though he says they would make the case easier (p. 217).
• The pure distribution problem (dividing a homogeneous cake; each person’s utility increasing at a diminishing rate in own share only) is the stylised setting for §§1–2 (p. 198).

Key results

What the lecture argues, section by section (page numbers are the Tanner pagination printed in the copy).

• §1 Utilitarian equality (pp. 198–205).
  • Sum-maximisation requires equal marginal utilities, which Hare and Harsanyi present as equal treatment of interests (pp. 198–199).
  • With identical utility functions, equal marginal utility coincides with equal total utility — “egalitarianism by serendipity: just the accidental result of the marginal tail wagging the total dog” (p. 202). With diversity (“John may be easy to please, but Jeremy not”) the two come apart, and if equality of total utilities has any value, “the utilitarian conception of equality — marginal as it is — must stand condemned” (p. 202).
  • Cripple vs. pleasure-wizard (pp. 203–204): if A, disabled, gets half the utility B does from any income level, utilitarianism gives B more income, so A is “doubly worse off”. Sen states what he is not claiming: (i) not that lower total utility implies lower marginal utility everywhere — only that nothing guarantees otherwise; (ii) the example relies on descriptive utility; (iii) it does not assume the disadvantage claim must dominate the marginal-utility claim — any system giving both some weight already departs from utilitarianism (his own earlier Weak Equity Axiom is “unnecessarily demanding”, fn. 16).
• §2 Total utility equality (pp. 205–213).
  • Defines welfarism: “the goodness of a state of affairs can be judged entirely by the goodness of the utilities in that state” (p. 205). Utilitarianism and utility-maximin are special cases.
  • Marginal utility is counterfactual; total utility (taken as observed) is not (pp. 205–206).
  • Total-utility equality only picks out perfect equality; it is completed to a full ordering by leximin, which (citing Hammond, Strasnick, d’Aspremont–Gevers, etc.) follows from “utility equality preference” (the extreme pair (a,d) no better than the intermediate (b,c)), the Suppes grading principle, unrestricted domain and independence (pp. 206–208). This derivation is cited, not proved here.
  • Critique: leximin ignores “how much” — it ranks (3,2) above both (10,1) and (4,1) without distinguishing them (p. 208) — and “how many”: the worst-off position wins against one person or a billion (p. 209). The weakening leximin-2 does not help: under unrestricted domain and independence it entails full leximin (Theorem 8 of Sen 1977, cited). “One innumeracy begets another” (p. 210).
  • Any mixture of utilitarianism and leximin stays inside welfarism (p. 210). Against welfarism: Rawls’s point about pleasures taken in others’ deprivation (quoted, pp. 210–211) is an argument against the adequacy of utility information as such, and a weaker premise suffices — such pleasures need only be disregarded, or weighted less; the issue is Mill’s lack of “parity” between sources of utility (p. 211). Scanlon’s “urgency” and objective well-being are endorsed with a correction: “Scanlon’s categories are too pure” — objective factors (hungry, cold, oppressed) can count alongside tastes and the result is still non-welfarist (p. 212). Urgency can also come from outside well-being entirely (non-exploitation; “equal pay for equal work”, p. 213).
• §3 Rawlsian equality (pp. 213–216).
  • Primary goods (“rights, liberties and opportunities, income and wealth, and the social bases of self-respect”) handle several welfarist defects: objective criteria, Mill’s non-parity, and expensive tastes (“deluged in champagne and buried in caviar”, p. 214).
  • But the Difference Principle gives the disabled person “neither more nor less on grounds of his being a cripple” (p. 215). Rawls’s reply that hard cases “distract our moral perception” is met with: leaving them out “may guarantee that the opposite mistake will be made” (p. 215).
  • The wider point is diversity: an index of primary goods would be a good measure only if people were similar; they are not, so it “leads to a partially blind morality” (p. 216).
  • Fetishism: “Rawls takes primary goods as the embodiment of advantage, rather than taking advantage to be a relationship between persons and goods.” Welfarism lacks this fetishism, since utilities reflect one such relation (p. 216).
  • Rawls also makes utility irrelevant to urgency, a stronger claim than that it is inadequate; “That a person’s interest should have nothing directly to do with his happiness or desire-fulfilment seems difficult to justify” (p. 216).
• §4 Basic capability equality (pp. 217–219).
  • The combined case: a disabled person with a marginal-utility disadvantage who, because of “a jolly disposition”, “a low aspiration level”, or religious consolation, has no total-utility deprivation. Utilitarianism gives him less; the Difference Principle ignores his disability; now leximin does nothing either. If he still has claims as a disabled person, the basis is none of marginal utility, total utility or primary goods (pp. 217–218).
  • Definition: “basic capabilities”: “a person being able to do certain basic things”. Examples: the ability to move about; to meet nutritional requirements; “the wherewithal to be clothed and sheltered”; “the power to participate in the social life of the community” (p. 218).
  • Primary goods are “concerned with good things rather than with what these good things do to human beings”; utility is concerned with what they do “but uses a metric that focusses not on the person’s capabilities but on his mental reaction” (p. 218).
  • Basic capability equality is “a natural extension of Rawls’s concern with primary goods, shifting attention from goods to what goods do to human beings”; Rawls “himself motivates judging advantage in terms of primary goods by referring to capabilities” (asserted, no citation) (pp. 218–219). “The conversion of goods to capabilities varies from person to person substantially” (p. 219) — asserted as supported by “evidence”, none cited.
  • Admitted difficulty: indexing capability bundles, “comparable with the indexing of primary good bundles”; a partial ordering from “broad uniformity of personal preferences must be supplemented by certain established conventions of relative importance” (p. 219). Weights are culture-dependent: “basic capability equality avoids fetishism, but remains culture-dependent” (p. 219).
• §5 What Sen does not claim (pp. 219–220).
  • Not “the sole guide to the moral good”: morality is not only about equality, and the other types of equality are not “morally irrelevant”. It is “a partial guide to the part of moral goodness that is associated with the idea of equality”.
  • The capability index can be used in several ways (leximin of basic capabilities; utilitarian-style incremental weighting); equality is only one use.
  • The main thesis is negative (none of the three, nor any combination, suffices even for the needs-part of equality); the constructive claim narrows the gap, and “the validity of the main thesis is not conditional on the acceptance of this constructive claim” (p. 220).

Claims

id	claim	strength	support
C1	Utilitarianism can give less income to a person who is worse off in both total and marginal utility (the “cripple” vs. “pleasure-wizard”)	strong (as a logical implication)	Direct consequence of sum-maximisation under the stated utility assumptions, pp. 203–204; Sen states the conditions under which it holds
C2	Utilitarian equality coincides with total-utility equality only when utility functions are identical (“egalitarianism by serendipity”)	strong	Elementary argument, p. 202 (fn. 13 notes extra assumptions when the cake is not fixed)
C3	Leximin follows from utility equality preference + Suppes principle + unrestricted domain + independence	strong by citation	Not proved here; cited to Hammond 1976, Strasnick 1976, d’Aspremont–Gevers 1977, Sen 1977 and others (fn. 18), pp. 207–208
C4	Under unrestricted domain and independence, leximin-2 entails leximin	strong by citation	Theorem 8 of Sen 1977 (fn. 21), p. 209; not proved here
C5	Welfarism (any rule using only utility information) is inadequate; a far weaker premise than Rawls’s suffices to reject it	moderate	Informal argument from Rawls’s discrimination example and Mill’s non-parity, pp. 210–213
C6	The primary-goods index ignores interpersonal variation in needs and so is “partially blind”; it is “fetishist”	moderate	Informal argument from diversity (health, climate, body size…), pp. 215–216; the empirical premise that variation is large is asserted, not documented
C7	No combination of utility and primary-goods information captures the claim of a contented disabled person	moderate	One case-implication argument, pp. 217–218; persuasive only if the reader shares the intuition that the claim persists
C8	Basic capabilities (“being able to do certain basic things”) supply the missing information	weak–moderate	Proposed, pp. 218–219; no list, no index, no weighting beyond “established conventions”; indexing problem acknowledged
C9	Rawls himself motivates primary goods by reference to capabilities	assertion	p. 219; no citation to Rawls given
C10	The negative thesis stands even if basic capability equality is rejected	strong (as a statement of logical structure)	p. 220; the negative arguments in §§1–3 do not use the capability notion

Concepts

• Case-implication critique / prior-principle critique — the two methods of testing a moral principle (pp. 197–198).
• Utilitarian equality — the equality of marginal utilities implied by maximising the utility sum (pp. 198–199).
• Total utility equality — equality of persons’ utility levels; completed to leximin (§2).
• Welfarism — “the goodness of a state of affairs can be judged entirely by the goodness of the utilities in that state” (p. 205).
• Leximin / leximin-2 — lexicographic maximin on utilities; leximin-2 applies it only when all but two persons are indifferent (p. 209).
• Utility equality preference — the ordinal axiom that an intermediate pair (b,c) is at least as good as an extreme pair (a,d) (p. 207).
• Urgency — Scanlon’s notion of the strength of a claim, dissociated from utility (pp. 212–213).
• Fetishism — taking goods “as the embodiment of advantage, rather than taking advantage to be a relationship between persons and goods” (p. 216).
• Basic capabilities — “a person being able to do certain basic things” (p. 218).
• Basic capability equality — equality in basic capabilities, as an interpretation of “needs and interests … often implicit in the demand for equality” (p. 218).

Connections

• Within this batch. The Nobel lecture (“The Possibility of Social Choice”, 1998) restates the same informational point in social-choice terms: the question “interpersonal comparison of what?”, the adaptation of desires to deprivation, and the conversion-variation argument now split into four named sources (personal, environmental, social-climate, relational). “The Impossibility of a Paretian Liberal” (1970) is cited here (fn. 24, as Sen 1970, ch. 6) for the claim that libertarian non-utility information may require rejecting the Pareto principle (p. 212). The later secondary accounts in the batch (the SEP entry by Robeyns & Byskov, Wells’s IEP entry, Robeyns 2017) formalise what is only sketched here (functionings, capability sets, well-being vs. agency); Nussbaum’s “Capabilities as Fundamental Entitlements” (2003) presses exactly the gap this lecture leaves — no list of which capabilities are basic.
• Adaptive preferences (LIT-202). Pettigrew’s “Consent and the Formation of Preferences” works on the same phenomenon Sen’s contented disabled person illustrates (low aspiration, religious resignation keeping utility high despite deprivation, p. 217), though for consent rather than for distributive metrics. Per NOTE-144 Pettigrew draws on Khader, Elster and Superson, not on Sen; the link is thematic, not a citation.
• Consequentialism (LIT-198). Hooker’s SEP survey of rule consequentialism surveys the consequentialist family, including utilitarianism, theories of welfare and non-welfare goods. Sen’s welfarism critique divides exactly that axis: it is an argument against welfarist theories of the good, not against consequentialism as such, which can take non-utility information.
• Anthology of the SOTA. No ANTH document mentions Sen, capabilities or social choice.

Bearing on the record

• No THEORY in the record bears on this. The record’s theories are on representation learning and contextuality. If the record acquires a THEORY about the informational basis of well-being comparisons (“utility and resource metrics each omit conversion variation”), this lecture is its primary source for the negative claim, with the capability proposal as a weaker, separate claim — Sen himself separates them (p. 220).
• No ML-practice content. The one distant bearing is on fairness metrics (“equality of what” is often cited in ML fairness writing), but the lecture itself says nothing about measurement practice beyond the indexing problem.
• For filing. ethics first (a theory of distributive equality), then society-and-governance (Rawls, justice, social policy) and social-science (welfare economics). agency is not justified: agency does not appear in this text.

Note of 2026-10-16: THEORY-025 now cites LIT-289 as a source.

Limitations

• The positive proposal is a sketch: no list of basic capabilities beyond four examples, no method for indexing or weighting beyond “established conventions of relative importance”, and no treatment of how capabilities (abilities) are to be observed.
• The central argument (C7) rests on a single case and on the intuition that the contented disabled person still has a claim. A welfarist can bite the bullet; the lecture does not engage that response.
• The empirical premise — that conversion of goods into capabilities “varies from person to person substantially” — is asserted with “there is evidence” and no source (p. 219).
• The formal results used against leximin (C3, C4) are cited, not proved.
• The lecture says nothing about freedom, choice or agency; later accounts that present “Equality of What?” as introducing capability as freedom read later Sen back into it.
• Period vocabulary (“cripple”) is used throughout.

Open questions

• Which capabilities are “basic”, and who decides? Sen’s answer here — culture-dependent conventions — is the opening for the list debate (Nussbaum 2003) and for Sen’s later appeal to public reasoning.
• How is a capability bundle indexed, and does the indexing problem in the end reintroduce either utility (via preferences over bundles) or a fixed list (via conventions)?
• Is “basic capability equality” an extension of Rawls, as Sen says (p. 219), or a rival to it? Pogge’s later resourcist reply (known here only through the scoping report) says the latter.

Corrections to the seeded skim

• none (there was no seed or dossier)
• The scoping report’s description (“Rejects utilitarian equality, total-utility equality and Rawlsian primary goods, and introduces ‘basic capability equality’ and the conversion-variation argument”) is accurate. Two things a reader might assume from later secondary accounts are not in this text: (a) the vocabulary of functionings, capability set, agency, well-being freedom — none of these words occurs; the only positive notion is “basic capabilities”, glossed as “a person being able to do certain basic things” (p. 218); (b) any argument that freedom or opportunity (rather than achievement) is the right focus. The lecture’s case for capabilities is entirely about needs and interpersonal variation in converting goods, not about freedom.
• Sen does not reject utility or primary goods as irrelevant. He says the others are not “morally irrelevant” (p. 220), that a rejection of welfarism “need not take us to the point in which utility is given no role whatsoever” (p. 216), and that the basic-capability index can be used in utilitarian-like or leximin-like ways (p. 220). Secondary shorthand that has Sen “replacing” utility and resources with capabilities overstates this text.
• The lecture sets aside Rawls’s priority of liberty (Hart’s critique noted, “with that question I shall not be concerned”, p. 214) and sets aside non-well-being claims (exploitation, discrimination, desert) when making the capability argument (p. 217). The capability case is made for the needs-part of equality only.