Utilitarian or Quantile-Welfare Evaluation of Social Welfare? With Application to Health Cost-Effectiveness Analysis

Charles F. Manski; John Mullahy

arxiv: 2509.05529 · v3 · submitted 2025-09-05 · 💰 econ.EM

Utilitarian or Quantile-Welfare Evaluation of Social Welfare? With Application to Health Cost-Effectiveness Analysis

Charles F. Manski , John Mullahy This is my paper

Pith reviewed 2026-05-18 18:01 UTC · model grok-4.3

classification 💰 econ.EM

keywords quantile welfaresocial welfare evaluationtime-tradeoff experimentsnonparametric boundshealth cost-effectivenessordinal utilitybinary choice datautilitarian evaluation

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The pith

Quantile welfare of health states can be nonparametrically bounded from binary time-tradeoff responses without cardinal utility scales.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper transfers the quantile utility model from individual decision making to social welfare evaluation. It argues that maximizing quantile welfare requires only ordinal information and provides an alternative to expected-utility maximization. In the setting of health cost-effectiveness analysis, the authors develop a procedure that uses binary responses from standard time-tradeoff experiments to place nonparametric bounds on the quantile welfare of different health states. The approach avoids any need for cardinal utility measurement or parametric assumptions about preference distributions. A sympathetic reader would see this as a way to perform welfare comparisons with the limited data that health economists already collect.

Core claim

Quantile welfare is the welfare level such that a given fraction of the population experiences at least that level. The paper shows that binary choice data from time-tradeoff experiments identify sets of possible quantile welfare values for health states. These bounds are obtained directly from the observed response frequencies without recovering a full utility function or assuming a distribution over preferences.

What carries the argument

The nonparametric bounding procedure applied to binary time-tradeoff responses, which produces interval estimates for the quantile welfare of each health state.

If this is right

Health cost-effectiveness rankings can rely on ordinal preference data alone rather than full cardinal utility measures.
The method delivers interval rather than point estimates, making explicit the uncertainty that remains after observing binary responses.
Social planners gain a way to compare interventions that does not depend on choosing a specific utility scale or error distribution.
The same bounding logic extends in principle to other binary-choice settings where only rank-order welfare information is available.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applying the bounds to large existing TTO datasets could show how often the intervals remain informative for policy decisions.
The approach might be combined with other limited-information methods in welfare economics that also avoid cardinal assumptions.
One could examine whether quantile-welfare bounds produce different recommended rankings than traditional QALY calculations on the same data.
Extensions to multi-period or multi-attribute health states would test how the bounding procedure scales with richer choice environments.

Load-bearing premise

Binary responses from standard time-tradeoff experiments contain enough information to nonparametrically bound quantile welfare without requiring cardinal utility scales or parametric assumptions on preference distributions.

What would settle it

If the bounding procedure applied to existing time-tradeoff datasets yields bounds too wide to separate any commonly studied health states, the claim that the data suffice for useful quantile-welfare evaluation would be contradicted.

read the original abstract

This paper considers quantile-welfare evaluation of social welfare as an alternative to utilitarian evaluation. Manski (1988) originally proposed and studied maximization of quantile utility as a model of individual decision making under uncertainty, juxtaposing it with maximization of expected utility. That paper's primary motivation was to exploit the fact that maximization of quantile utility requires only an ordinal formalization of utility, not a cardinal one. This paper transfers these ideas from analysis of individual decision making to analysis of social planning. We begin by summarizing basic theoretical properties of quantile welfare in general terms. We then turn attention to health cost-effectiveness analysis and consider measurement and econometric issues arising in that context. We propose a procedure to nonparametrically bound the quantile welfare of health states using data from binary-choice time-tradeoff (TTO) experiments of the type regularly performed by health economists.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Manski and Mullahy adapt quantile utility maximization to social welfare evaluation and propose a nonparametric bounding procedure for health states from binary TTO data.

read the letter

Manski and Mullahy take the quantile welfare concept from Manski's 1988 work on individual decisions and apply it to social planning, particularly in health cost-effectiveness analysis. They propose a nonparametric procedure to bound the quantile welfare of health states using binary-choice time-tradeoff data. This is the main thing to know: the paper shifts the ordinal-only logic to a social setting and tailors a bounding method to data that health economists already collect routinely. The combination looks new relative to the cited prior work. The paper does well by first laying out basic theoretical properties of quantile welfare and then turning to the practical measurement problems in health applications. It keeps the approach nonparametric and avoids cardinal utility scales or parametric restrictions on preferences, which directly addresses a frequent complaint in that literature. The argument stays internally consistent, with the bounds derived from the ordinal information in binary responses and no obvious hidden assumptions that would undermine the nonparametric claim. Soft spots are modest. The bounds may turn out wide in typical samples, which could limit how much they guide actual decisions, and the paper could usefully add more on how the results compare to standard utilitarian calculations in the same data. These are checkable details rather than core problems. This work is for health economists who handle cost-effectiveness studies and for social choice researchers who want welfare criteria that stay close to observable ordinal data. A reader interested in robust methods for applied welfare analysis would find it relevant. It shows clear thinking by connecting the individual model to the social case without overclaiming. I would bring it to a reading group to walk through the bounding steps. It deserves peer review so experts can examine the derivation and test the bounds on real TTO data.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes quantile-welfare evaluation as an alternative to utilitarian (expected-utility) evaluation of social welfare. Drawing on Manski (1988), it first summarizes theoretical properties of quantile welfare and then develops a nonparametric bounding procedure for the quantile welfare of health states that uses only the ordinal information contained in binary responses from standard time-tradeoff (TTO) experiments routinely conducted by health economists.

Significance. If the proposed bounds are correctly derived and identified, the paper supplies a practical, assumption-light method for health cost-effectiveness analysis that avoids both cardinal utility scales and parametric restrictions on preference distributions. This could improve robustness of welfare rankings in a field where TTO data are already collected at scale and where cardinal assumptions have long been debated.

major comments (2)

[§3] §3 (proposed bounding procedure): the manuscript states that binary TTO responses suffice to nonparametrically bound quantile welfare without cardinal scales or parametric assumptions on preferences, but the explicit identification argument and the construction of the bounds (including any trimming or inversion steps) are only sketched; a fully worked derivation with the precise mapping from observed choice probabilities to the quantile-welfare bounds is required to confirm the nonparametric character.
[§4] §4 (health CEA application): the central claim that the procedure can be applied directly to existing TTO datasets rests on the maintained assumption that the binary responses are generated by the same ordinal preference relation that defines quantile welfare; the paper should state the precise maintained assumptions on the data-generating process and discuss whether any auxiliary conditions (e.g., monotonicity of health states) are needed for the bounds to be informative.

minor comments (2)

[Abstract and §1] The abstract and introduction could more explicitly contrast the new bounding procedure with existing parametric or cardinal approaches in the health-economics literature to clarify the incremental contribution.
[§2 and §3] Notation for the quantile-welfare functional and for the TTO choice probabilities should be introduced once and used consistently across the theoretical and empirical sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below and will revise the manuscript to provide greater detail on the identification argument and maintained assumptions.

read point-by-point responses

Referee: [§3] §3 (proposed bounding procedure): the manuscript states that binary TTO responses suffice to nonparametrically bound quantile welfare without cardinal scales or parametric assumptions on preferences, but the explicit identification argument and the construction of the bounds (including any trimming or inversion steps) are only sketched; a fully worked derivation with the precise mapping from observed choice probabilities to the quantile-welfare bounds is required to confirm the nonparametric character.

Authors: We agree that the current presentation sketches the bounding procedure and would benefit from a fully explicit derivation. In the revised manuscript we will expand Section 3 to include a complete identification argument that maps the observed binary TTO choice probabilities directly to the nonparametric quantile-welfare bounds, detailing the trimming and inversion steps while preserving the ordinal and assumption-light character of the approach. revision: yes
Referee: [§4] §4 (health CEA application): the central claim that the procedure can be applied directly to existing TTO datasets rests on the maintained assumption that the binary responses are generated by the same ordinal preference relation that defines quantile welfare; the paper should state the precise maintained assumptions on the data-generating process and discuss whether any auxiliary conditions (e.g., monotonicity of health states) are needed for the bounds to be informative.

Authors: We will add an explicit statement of the maintained assumptions in the revised Section 4, including that binary TTO responses are generated by the ordinal preference relation that underlies quantile welfare. We will also discuss auxiliary conditions such as monotonicity across health states and their role in ensuring the resulting bounds are informative. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new bounding procedure is distinct from cited prior result

full rationale

The paper cites Manski (1988) to motivate transferring the quantile-utility concept from individual decision making to social planning, but the load-bearing contribution is the distinct nonparametric bounding procedure that uses only ordinal binary TTO responses to bound quantile welfare of health states. No equations or claims reduce the proposed bounds by construction to fitted parameters, self-definitions, or a self-citation chain; the procedure is presented as relying solely on the ordinal information in the data without cardinal scales or parametric restrictions. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on transferring the quantile-welfare concept from individual to social settings and on the claim that binary TTO responses suffice for nonparametric bounds; no free parameters or new invented entities are introduced in the abstract.

axioms (1)

domain assumption Quantile welfare is a meaningful and applicable criterion for social planning when only ordinal individual preferences are available.
Abstract states that the approach transfers ideas from individual decision making (Manski 1988) to social planning without additional justification for the transfer.

pith-pipeline@v0.9.0 · 5678 in / 1373 out tokens · 66736 ms · 2026-05-18T18:01:19.457600+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We propose a procedure to nonparametrically bound the quantile welfare of health states using data from binary-choice time-tradeoff (TTO) experiments
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

maximization of quantile utility requires only an ordinal formalization of utility, not a cardinal one

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

Regression Analysis When the Dependent Variable i s Truncated Normal ,

Amemiya, T. (1973), “Regression Analysis When the Dependent Variable i s Truncated Normal ,” Econometrica, 41, 997-1016. Arabmazur, A. and P. Schmidt (1983), “An Investigation of the Robustness of the Tobit Estimator to Non- Normality,” Econometrica, 50, 1055-1063. Austin, P. (2002), “A Comparison of Methods for Analyzing Health- Related Quality-of-Life M...

work page doi:10.1007/s10198-013-0503-2 1973
[2]

Econometric Methods for Fractional Response with an Application to 401(K )Plan Participation Rates,

https://www.nice.org.uk/process/pmg36 Papke, L and J. Wooldridge (1996), “Econometric Methods for Fractional Response with an Application to 401(K )Plan Participation Rates,” Journal of Applied Econometrics, 11, 619-632. Powell, J. (1986), “Censored Regression Quantiles,” Journal of Econometrics, 32, 143-155. Rawls, J. (1971), A Theory of Justice, Cambrid...

work page 1996
[3]

UK Valuation of EQ- 5D-5L, a Generic Measure of Health -Related Quality of Life: A Study Protocol,

Rowen, D., C. Mukuria, N. Bray, J. Carlton, S. Cooper, L. Longworth, D. Meads, C. O’Neill, and Y. Yang (2023), “UK Valuation of EQ- 5D-5L, a Generic Measure of Health -Related Quality of Life: A Study Protocol,” Value in Health, 26, 1625-1635. Samuelson, P. (1947), Foundations of Economic Analysis, Cambridge, MA: Harvard University Press. Sen, A. (1977), ...

work page 2023

[1] [1]

Regression Analysis When the Dependent Variable i s Truncated Normal ,

Amemiya, T. (1973), “Regression Analysis When the Dependent Variable i s Truncated Normal ,” Econometrica, 41, 997-1016. Arabmazur, A. and P. Schmidt (1983), “An Investigation of the Robustness of the Tobit Estimator to Non- Normality,” Econometrica, 50, 1055-1063. Austin, P. (2002), “A Comparison of Methods for Analyzing Health- Related Quality-of-Life M...

work page doi:10.1007/s10198-013-0503-2 1973

[2] [2]

Econometric Methods for Fractional Response with an Application to 401(K )Plan Participation Rates,

https://www.nice.org.uk/process/pmg36 Papke, L and J. Wooldridge (1996), “Econometric Methods for Fractional Response with an Application to 401(K )Plan Participation Rates,” Journal of Applied Econometrics, 11, 619-632. Powell, J. (1986), “Censored Regression Quantiles,” Journal of Econometrics, 32, 143-155. Rawls, J. (1971), A Theory of Justice, Cambrid...

work page 1996

[3] [3]

UK Valuation of EQ- 5D-5L, a Generic Measure of Health -Related Quality of Life: A Study Protocol,

Rowen, D., C. Mukuria, N. Bray, J. Carlton, S. Cooper, L. Longworth, D. Meads, C. O’Neill, and Y. Yang (2023), “UK Valuation of EQ- 5D-5L, a Generic Measure of Health -Related Quality of Life: A Study Protocol,” Value in Health, 26, 1625-1635. Samuelson, P. (1947), Foundations of Economic Analysis, Cambridge, MA: Harvard University Press. Sen, A. (1977), ...

work page 2023