NOTE-263: The Possibility of Social Choice

Contribution

A retrospective lecture, not a research paper. Sen reframes the “constructive pessimism” that followed Arrow (1951) as a consequence of an artificially narrow informational basis — individual orderings only, no interpersonal comparisons — and argues that widening that basis both escapes the impossibility and makes welfare economics usable for inequality, poverty, famine and gender deprivation. It is the clearest place where Sen himself places the capability approach inside social choice theory: as one candidate content for the interpersonal comparisons that social choice needs.

Key insight

Impossibility results are statements about what information a procedure is allowed to use. Arrow’s axioms jointly confine social choice to voting-type rules that ignore the nature of the states and everyone’s relative position (fn. 16: “neutrality” is “a somewhat flattering name for what is after all only an informational restriction”). Admit comparisons of individual advantage — even partial, even ordinal — and constructive rules exist. Then the question moves from “is social choice possible?” to “comparison of what?”, and mental-state utility is a poor answer because desires adapt to deprivation.

Assumptions

Premises and authorities, since this is a lecture:

• Arrow’s framework as Sen states it informally (p. 183): Pareto, nondictatorship, independence (of irrelevant alternatives), and unrestricted domain, which he glosses as also requiring the social preference to be a complete, fully transitive ordering. Structural assumptions (fn. 7): at least two individuals (finitely many) and at least three social states. He refers to Arrow 1963 for the exact statements and to Sen 1995a for “a very short — and elementary — proof” (fn. 7).
• Social welfare functionals with invariance conditions as the formal device for encoding what interpersonal comparisons are admitted (p. 188, citing Sen 1970a, 1977c).
• Robbins (1938) as the source of the positivist rejection of interpersonal comparisons (“Every mind is inscrutable to every other mind…”, p. 182); Davidson (1986) as the authority that understanding other minds already involves comparison (p. 191).
• Every formal result in the lecture is cited to earlier work; none is proved here.

Key results

What the lecture argues, by section (pages are the Nobel volume’s).

• §§I–III (pp. 179–184). Origins and “obituary notices”. Borda and Condorcet founded voting-based social choice; Condorcet’s cycle (p. 180). Benthamite welfare economics used utility sums, which are distribution-blind — a person with “a uniformly lower capability to generate enjoyment and utility out of income (say, because of a handicap)” gets a lower share (p. 182), the “Equality of What?” example restated. After Robbins, interpersonal comparisons were dropped, leaving only Pareto comparisons, and Arrow’s theorem then made the pessimism general. Baumol (1965): welfare economics resembled “obituary notices” (p. 181).
• §IV (p. 184). Formal and informal reasoning are complementary; Arrow’s theorem “can hardly be anticipated on the basis of common sense”, and the same holds for the result that an Arrow-type impossibility arises “even without any imposed demand of internal consistency of social choice” (Sen 1993a, Theorem 3, cited).
• §V (p. 185). Proximity of possibility and impossibility. Any full axiomatic characterisation of a single rule lies “just short of” an impossibility, so the existence of impossibilities says nothing by itself about fragility; what matters is “the reach and reasonableness of the axioms”. Sen calls the process “brinkmanship”.
• §VI (pp. 185–187). Majority rule. Necessary and sufficient conditions for consistent majority decisions exist (Sen & Pattanaik 1969, cited) but are demanding. Majority rule is “thoroughly inconsistent” for cake-division problems and can be univocal in, e.g., outrage at a government’s failure to prevent famine (fn. 12: no famine “in an independent and democratic country”).
• §VII (pp. 187–190). Informational broadening. Voting is unsuitable for welfare judgements for two reasons: non-voters’ interests would be ignored, and votes carry no interpersonal comparisons (p. 187). The results reported:
  • Interpersonal comparisons “of various types can be fully axiomatized and exactly incorporated” via invariance conditions on social welfare functionals (p. 188).
  • Partial comparability — neither full nor none — can be made mathematically exact, and often suffices for definite decisions (Nero’s gain from burning Rome versus everyone else’s loss, pp. 188–189).
  • “Admitting cardinality of utilities without interpersonal comparisons does not change Arrow’s impossibility theorem at all” (Theorem 8*2 in Sen 1970a, cited). “In contrast even ordinal interpersonal comparisons is adequate to break the exact impossibility” (p. 189).
  • Full cardinal comparability allows classical utilitarianism (Harsanyi 1955); “even weaker forms of comparability would still permit making consistent social welfare judgments, satisfying all of Arrow’s requirements, in addition to being sensitive to distributional concerns (even though the possible rules will be confined to a relatively small class)” (p. 189).
  • The same broadening underlies Sen’s measures of inequality, poverty, distribution-adjusted national income and environmental evaluation (p. 190).
• §VIII (pp. 190–194). Informational basis of interpersonal comparisons: “interpersonal comparison of what?” (p. 190).
  • Social welfare functionals are not specific to utility; the comparisons can be of “individual well-being or freedom or substantive opportunities” (p. 190).
  • Even mental-state comparisons are defensible (Davidson), but they are a poor basis because “utilities may sometimes be very malleable in response to persistent deprivation”: the “hopeless destitute”, the “downtrodden laborer”, the “subjugated housewife”, the “tyrannized citizen” may “adjust her desires to take note of feasibility” (p. 191).
  • Rawls’s primary goods improve on this but miss “interpersonal differences in converting them into the capability to live well” (p. 192).
  • Where capabilities enter: “judging individual advantage in terms of the respective capabilities, which the person has, to live the way he or she has reason to value”. The approach “focuses on the substantive freedoms that people have, rather than only on the particular outcomes with which they end up”, which for responsible adults “has some merit” (p. 192). Comparisons “may only be partial — often based on the intersection of different points of view” (p. 192).
  • Pluralism: expenditure-based comparisons, questionnaires on relative well-being, Scandinavian living-conditions studies, basic-needs work, and the UNDP Human Development Reports are all forms of “informational broadening” with their own merits (pp. 192–193).
• §IX (pp. 194–197). Poverty and famine.
  • Poverty is better seen as “capability deprivation” than as low income. Four sources of variation in the conversion of income into “the capability to live a minimally acceptable life” (pp. 194–195): (1) personal heterogeneities (e.g. proneness to illness); (2) environmental diversities (storm- or flood-prone areas); (3) variations in social climate (crime, epidemiological vectors); (4) differences in relative deprivation, following Adam Smith — being relatively poor in a rich society can mean absolute deprivation in the capability to take part in the life of the community (fn. 35).
  • Pragmatic limit: income poverty “can[not] be dispensed with” in empirical work (p. 195). Famines are best explained by collapses in entitlements (incomes, prices), not food supply (Bengal 1943, Ethiopia 1973, Bangladesh 1974, fn. 38). In famine analysis income deprivation has “more immediacy and ready usability than the more subtle — and ultimately more informed — distinctions based on capability comparisons” (p. 196).
  • Aggregate poverty is a social-choice problem; distribution-sensitive measures (the “Sen index”, which he says is improved by the Sen–Shorrocks variant, fn. 40) are an “embarrassment of riches” rather than an impasse (pp. 196–197).
• §X (pp. 197–198). Comparative deprivation and gender. Adaptation hides deprivation, especially of women. Post-famine Bengal 1944: widows almost never reported “indifferent health”, while widowers “complained massively” (p. 197). Indian states with the worst health care and education report the lowest perceived morbidity, and Kerala the highest (p. 198). “Mental reactions … can be a very defective basis for the analysis of deprivation” (p. 198). Observed undernutrition, morbidity, illiteracy and “missing women” can be used instead.
• §XI (pp. 198–200). The liberal paradox. Restates the 1970 result (minimal liberty + Pareto + unrestricted domain are inconsistent). Liberty has an opportunity aspect and a process aspect (p. 199); the 1970 formulation concerned the opportunity aspect; an exclusive process focus (Sugden, Gaertner et al. 1992) is right that opportunity is not sufficient, but does not by itself resolve the paradox (fn. 46), and ignoring opportunity is the “opposite narrowness”. Unlike Arrow’s result, the paradox is not resolved by interpersonal comparisons, because neither liberty claims nor Pareto depend on the intensities of preferences (pp. 199–200). Resolution requires “an evaluative view of the acceptable priorities between personal liberty and overall desire fulfillment”, sensitive to the trade-offs “the persons may themselves endorse” — “an informational enrichment (taking note of people’s political values as well as individual desires)” of a different kind (p. 200); formally perhaps a multistage social choice exercise (fn. 49).
• §XII (pp. 200–202). Conclusion. The pessimism was misleading for two reasons: an informational base too narrow (overconcentration on mental states) and a demand for too much precision in comparisons (fn. 50: partial comparability can yield an optimum, or at least narrow the maximal set).

Claims

id	claim	strength	support
C1	Arrow’s axioms jointly restrict social choice to voting-type rules; this is derived, not assumed	strong by citation	fn. 16; Sen 1977c, 1979b cited; not proved here
C2	Cardinal, non-comparable utilities leave Arrow’s impossibility intact	strong by citation	Theorem 8*2 of Sen 1970a, cited, p. 189
C3	Even ordinal interpersonal comparability breaks the exact impossibility; weaker-than-full comparability permits consistent, Arrow-satisfying, distribution-sensitive rules	strong by citation	p. 189, fn. 21 (Sen 1970a, 1977c; Hammond 1976; d’Aspremont & Gevers 1977; Roberts 1980; etc.)
C4	Partial comparability can be made exact and is often sufficient for decisions	strong by citation	pp. 188–189, fns. 18–19 (Sen 1970a,c; Blackorby 1975)
C5	Any full axiomatic characterisation of one rule lies next to an impossibility, so impossibility does not imply fragility	informal argument	§V, p. 185
C6	Mental-state utility is a defective basis for interpersonal comparison because desires adapt to deprivation	moderate	Informal argument plus anecdotal evidence (Bengal 1944 widows/widowers; Kerala morbidity), pp. 191, 197–198, citing Sen 1985a App. B
C7	Advantage can be judged by capabilities “to live the way he or she has reason to value”, with partial comparability from intersecting views	assertion (in this text)	p. 192, citing Sen 1980, 1985a,b, 1992a and others; argued elsewhere
C8	Conversion of income into capability varies with four sources (personal, environmental, social-climate, relational)	informal argument	pp. 194–195, fn. 35; examples, no data
C9	Famines can occur without a decline in food supply; entitlement analysis explains them better	strong by citation	p. 195, fn. 38 (Sen 1981 on Bengal 1943, Ethiopia 1973, Bangladesh 1974)
C10	The liberal paradox cannot be resolved by interpersonal comparisons; it needs information on people’s priorities between liberty and desire-fulfilment	informal argument	pp. 199–200; formal version gestured at (multistage choice, fn. 49)
C11	Impossibility pessimism in welfare economics was misleading	informal argument	§XII, drawing on C2–C4

Concepts

• Social choice theory — the discipline “relating social judgments and group decisions to the views and interests of the different individuals” (p. 178).
• Constructive pessimism — the post-Arrow sense that systematic social choice is doomed (§II).
• Informational broadening — enlarging what a social choice procedure may use, above all interpersonal comparisons (§VII).
• Social welfare functional with invariance conditions — a map from profiles of individual welfare functions to social orderings, with conditions stating which transformations of welfare information leave the result unchanged; the device that encodes kinds of comparability (p. 188).
• Partial comparability — interpersonal comparisons possible for some but not all pairs, and not with full exactness (pp. 188–189).
• Neutrality (in Arrow’s derived features) — taking no note of the nature of the states, only votes for and against; “only an informational restriction” (fn. 16).
• Capabilities — “the capability to live the way he or she has reason to value”; “substantive freedoms” (p. 192).
• Capability deprivation — Sen’s account of poverty (p. 195).
• Entitlements — command over food through income, production and prices (pp. 195–196).
• Positional objectivity — what is objectively observable from a given position but may not hold in interpositional comparison (fn. 43).
• Opportunity aspect / process aspect of liberty (p. 199).

Connections

• Within this batch. “Equality of What?” (1979) is the origin of §VIII’s argument: the handicap example (p. 182), primary goods and conversion (p. 192) and adaptation (p. 191) are all there, though in 1979 the framing was needs, whereas here it is freedom: “substantive freedoms”, “reason to value”. “The Impossibility of a Paretian Liberal” (1970) is the result restated in §XI. What the lecture adds is Sen’s own later view that the 1970 formulation captured only the opportunity aspect of liberty, and that the conflict is not dissolved by the game-form or process reformulations. The secondary accounts in the batch cover what the lecture only asserts. These are the SEP entry by Robeyns & Byskov, Wells’s IEP entry and Robeyns 2017, which cover capabilities as freedom, the well-being/agency split and the no-list position. The lecture cites Nussbaum 1988 and Nussbaum & Sen 1993 but does not engage her list.
• Adaptive preferences (LIT-202). Sen’s “subjugated housewife” who adjusts desires to feasibility (p. 191) is a canonical source for the adaptive-preferences literature that Pettigrew’s “Consent and the Formation of Preferences” works in. Per NOTE-144, Pettigrew cites Khader, Elster and Superson rather than Sen, so the link is thematic, not a citation.
• Ontic structural realism and economics (LIT-218). Ross’s paper (per NOTE-189) contrasts its “Debreuvian” conception of economics with a “nostalgic” people-centred one attributed to Sen, and answers Sen 1977 on “rational fools”. The lecture is an example of that people-centred conception applied to welfare economics. LIT-067 (Debreu 1952) is the record’s only general-equilibrium neighbour and is not social choice.
• Anthology of the SOTA. No ANTH document mentions Sen or social choice.

Bearing on the record

• No THEORY bears on it. If the record files a THEORY on the informational basis of social evaluation, this lecture is the natural secondary source. The primary sources would be Sen 1970a and 1977c, which are not held. It should not be cited as a proof of C2–C4.
• No ML-practice content. Social choice with interpersonal comparisons has a distant analogue in aggregating human preferences for model alignment, but the lecture says nothing about it, and nothing here should be carried to the Anthology.
• For filing. society-and-governance first (social choice, democracy, famine, poverty policy), then social-science (welfare economics, poverty measurement) and ethics (interpersonal comparison, liberty). mathematics is not proposed, because the lecture contains no formal statement or proof.

Note of 2026-10-16: THEORY-025 and THEORY-027 now cite LIT-282 as a source.

Limitations

• Nothing is proved. Every formal result is cited, and several of the key ones are to Sen’s own Collective Choice and Social Welfare (1970a) and “On Weights and Measures” (1977c).
• The capability claim is only placed, not argued. Sen places capability-based comparison without arguing it (C7), and he flags that others “may well take a different view” (p. 193).
• The evidence on adaptation is anecdotal: one post-famine survey and cross-state self-reports.
• The liberal-paradox resolution is programmatic. It says what kind of information is needed, not a rule.
• Version. I cannot say whether the AER text differs from the lecture. The scan’s reference list is truncated.

Open questions

• Which comparability is enough? Which partial comparability structures, on which capability spaces, suffice for definite rankings in real poverty or inequality comparisons? The lecture asserts that limited comparability often suffices (p. 189) but gives no capability-specific case.
• Does resolving the liberal paradox need a formal model? Can the “priorities between personal liberty and overall desire fulfillment” that people “may themselves endorse” be formalised without collapsing into another impossibility? Fn. 49’s multistage exercise is only named.
• Is the AER text the same? Does the AER version (June 1999) differ from the Nobel volume text? Settling this needs the AER PDF.

Corrections to the seeded skim

• none (there was no seed or dossier)
• The scoping report says the lecture shows “how richer information (including functionings and capabilities) escapes impossibility”. The lecture’s escape from Arrow is interpersonal comparability, of whatever kind (§VII). Capabilities enter one step later, in §VIII, as an answer to “interpersonal comparison of what?” — and Sen explicitly declines to make them the only answer: “it would be overambitious to be severely exclusive in sticking only to one informational approach” (p. 192), and he puts the case for capability-based partial comparability “on which others may well take a different view” (p. 193). The word “functionings” does not occur in the lecture text; it appears only in cited titles (Balestrino 1994, 1996; Crocker 1992).
• The scoping report lists the liberal paradox among the things informational broadening handles. The lecture says the opposite for the kind of broadening it uses against Arrow: “unlike Arrow’s impossibility result, the liberal paradox cannot be satisfactorily resolved through the use of interpersonal comparisons” (p. 199). Its resolution needs information of “a rather different kind” (p. 200).
• Publication date: the lecture’s footnote gives the AER as “89 (July 1999)”; Crossref gives the issue as 89(3), 1 June 1999.
• The scan’s reference list is truncated at p. 215 (see read:); the scoping report describes p. 215 as “references Steiner–Ward” without noting that it breaks off mid-entry.