A utility reading for the history of welfare economics
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A utility reading
∗
for the history of welfare economics
Antoinette Baujard†
December 3, 2014
Abstract
Welfare economics has evolved during the twentieth century and
came, some say, to a fateful dead end, preventing any rigorous contri-
bution to policy recommendations. This trend is standardly explained
by the controversy over the possibility and the relevance of interper-
sonal comparisons of utility. This analysis does not provide any hope
to go beyond the bad news. Moreover, it fails to explain the possi-
bility of a new welfare economics without comparisons. Against the
interpersonal comparisons reading, I claim a reasonable assumption is
that under the discussion on comparisons, lies a fundamental evolution
in the properties of utility. This paper presents a historical overview
of the evolution of welfare economics through the XXth century, and
derives a challenging explanation, the “utility reading”. It shows the
evolution of welfare economics is related to the characteristics of util-
ity, notably its operational ability and its normative content. The
paper concludes that the revival of welfare economics needs a specific
notion of welfare, distinct from the utility concept used in microeco-
nomics.
Keywords: Welfare economics, history, utility, interpersonal compar-
isons of utility, cardinality, ordinality, welfare
∗
Though substantially different, a previous and extended version of this paper has been presented at the Summer
School in History of Economic Thought and Methodology organized by BETA, Strasbourg University and Charles Gide
Association in September 2003, and published as a Crem working paper in 2011 under the title: ‘Welfare economics is
dead. Long live welfare economics!”. A previous version has also been presented at the ESHET conference that was hel
in Lausanne in May 2014. I thank the participants for their constructive comments, especially R. Sturn. I remain fully
responsible for the views and mistakes remaining in the paper.
†
Université Jean Monnet, Université de Lyon. GATE L-SE (UMR 5824) Antoinette.Baujard@univ-st-etienne.fr
1Welfare economics is the economic study of the definition and the measure
of social welfare. Its assesses the consequences of individual actions and
public decisions on social states. It offers the theoretical framework used in
public economics to help collective decision making, to design public policies,
and to make social evaluations. The now old news of the death of welfare
economics implies some inability to make any policy recommendation.1 This
paper aims to provide an historical explanation of the reasons why welfare
economics has evolved towards an inability or difficulty to provide sound
prescriptions. This analysis may therefore contribute to imagine or settle
new ways to forgo this bad news.
An historical review describes an evolution of welfare economics through
successive steps, as well as its division in schools, and the clear cut partion-
ning between disciplines. According to a standard reading —I shall call it the
“comparisons reading”—, the evolution of welfare economics is explained by
changes in the status of the interpersonal comparisons of utility.2 Let us re-
call the definition of comparisons. In the case of intra-personal comparisons
of utility, individual utility is called cardinal if it helps to account for the
intensity of utilities. In such case, intrapersonal comparisons are meaningful:
for one individual, she can compare social states at different times or differ-
ent levels of utility. Conversely, it is ordinal if such intensity cannot be taken
into account. Utilities just conveys information on orderings of social states:
intrapersonal comparisons are meaningful to merely order social states. In-
terpersonal comparisons concern comparisons between different individuals.
If I say individual i derives a higher utility of her receiving good x than indi-
vidual j receiving the same good x, I make comparisons of i and j’s utilities
derived from x.Comparisons of the utilities of different individuals reveal nec-
1
J. R. Hicks (1939: 697)[27] notably wrote “Economic positivism might easily become
an excuse for the shirking of live issues, very conducive to the euthanasia of our science.”
Chipman and Moore (1978: 548)[11] added: “Judged in relation to its basic objective of
enabling economists to make welfare prescriptions without having to make value judgments
and, in particular, interpersonal comparisons of utility, the New Welfare Economics must
be considered a failure.” E. J. Mishan (1981)[36] considers welfare economics was stuck in
a dead-end. D. M. Hausman et M. S. MacPherson (1996: 96)[23] regretted that “Welfare
economics is in limbo.” Ph. Mongin (2002: 165)[37] at least provisionally, concluded:
“Welfare economics died, or rather disintegrated progressively.”
2
This debate is particularly illustrated by the exchanges between Robbins (1932, 1938)
[46, 47] and Harrod (1938)[21]. See also Hammond (1991)[20]. On the reading of the
evolution of welfare economics through the status of interpersonal comparisons of utility,
see among many others, Hicks (1975: 310)[28].
2essary to justify redistributive devices: “it is better to give x to individual i
than to j”. They are also necessary to assess public policies who impact dif-
ferently different individuals, i.e., in the general case: “even though policy x
reduces j’s utility, it sufficiently increases i’s utility to consider that x’s over-
all impact is positive for the society”. If no comparisons can be made, welfare
economics cannot formulate any policy recommendations of such kinds. As
we shall see in further details, the controversy on the status of interper-
sonal comparisons of utility is marked by a pendulum: from possibility to
impossibility, from impossible to possible comparisons. The first movement
(1890-1950) describes the transition from welfare economics of Marshall and
Pigou, whose recommendations are based on interpersonal comparisons, to
the new welfare economics, where they are mostly prohibited. Either be-
cause such comparisons are not meaningful, or because they are value-laden,
or both, they should be banished out of economic science, hence of welfare
economics in particular. The second movement (1950-nowadays) describe the
evolution from the arrovian impossibility theorem where they are banned, to
new theses where such interpersonal comparisons are deemed necessary to
address the specific issues of welfare economics, such as endorsing normative
collective views and a possibility for recommendations.
Now, this explanation can just hold if the possibility for collective nor-
mative judgments requires comparisons. A corollary is that, conversely, if no
comparisons are possible, no collective judgement could be made. Neverthe-
less, in the theory of fair allocation and equivalence approach, social welfare
functions in which interpersonal comparisons of utility are still forbidden may
exist. They can be used for evaluations, even considering distributive devices
or in the general case of tradeoffs of interests. These new results contradicts
seriously the reading of the evolution of welfare economics based exclusively
on the status of comparisons (Fleurbaey and Blanchet 2013: 138–141[17]).
Beyond this recent evidence of the failure of the comparisons reading, I claim
it does fully explain the evolution of the field since the very beginning. More-
over, it is unable to lift the difficulties lead with the death sentence.
I therefore suggest to scrutinize further the explanations of the driving
forces of the evolution of welfare economics, and conduct this study since the
first stages of welfare economics. Behind the status of comparisons indeed, it
is necessary to consider the framework constraints, and the properties of the
used tools, entailed by the different stages of welfare economists to under-
stand what fundamentally explains the successive judgments of comparisons.
3I do not contest the importance of comparisons in the evolution. Farther and
more importantly, my claim is that the analyses of the status of comparisons
cannot but be explained by the properties of utilities. This paper aims at
showing that the evolution of the concept of utility in economics through the
XXth century therefore appears to be the primary explanation to the histor-
ical evolution and the fate of welfare economics —I shall call this alternative
reading the “utility reading”.
The history of welfare economics is hardly known and studied. Most text-
books on history of economic thought do not even develop a chapter on wel-
fare economics (except maybe the still forthcoming Baujard 2010,2011,2012[5,
4, 6]). Even more, very few articles consider the history of welfare economics
as a whole. A notable and important exception is Mongin (2002[37]), which
addresses the issue of its evolution yet does not question the driving force of
such an evolution. A difficulty is indeed that welfare economics covers a wide
scope of sub-disciplines, including theoretical foundations of microeconomics,
public economics, cost-benefit analysis, social choice theory, theory of fair al-
location... There exist historical links between all these knowledges, moved
by common questions or solutions, whose divergences come from different
solutions to similar questions. But they are hardly commented anywhere as
a whole.
The thesis according to which the properties of utility is the most fun-
damental issue for welfare economics is present in the philosophical and the
formal analysis of Mongin and d’Aspremont (1998)[39]. The rejection of
the comparisons reading is explicit in Mongin and Fleurbaey (2005[18]) as
well as in Fleurbaey and Blanchet (2013[17]), but just concerns the last
stage of welfare economics. The utility reading is implicit in both Moscati’s
(2013a,b[40, 41]) articles. He defends the idea that behind the actual formal
definition of cardinal or ordinal utility, authors may have retained differ-
ent properties of utility, in particular for the sake of measurement. Yet he
does not tackle the specific normative context of welfare economics in which
comparisons are central. To my knowledge, no papers have ever made an
historical reconstruction of the evolution of welfare economics through the
utility reading, let alone have eventually concluded on the importance of the
interpretation and formal properties of utilities in this evolution.
The interest of this paper primarily lie in the defense of the “utility read-
ing” of the evolution of welfare economics which challenges the well estab-
4lished “comparisons reading”. A side product of this study is the provision of
a presentation of the history of welfare economics, while this unfortunately
appears to be a scarce resource. Another side product is to establish a link
between comparisons and properties of utility.
I first present the historical overview on the basis of which this analysis
shall be conducted, and I shall recall the status of comparisons at each stage
of welfare economics (section 1). After this, I will consider each period and
study what in the properties of utility, beyond comparisons, explain the
evolution. I shall not come back to the utilitarian heritage, and I shall
start the discussion with the old welfare economics. In the first described
period, section 2 describes which interpretation of utilities was assumed for
making comparisons. Section 3 describes what notion of utility entailed
their banishment, well explicated in the literature since the thirties. Section
4 discusses the relevance of Arrow’s result of the early fifties for studying
interpersonal comparisons of utility, and opposes a slightly but substantially
alternative explanation, in terms of richness of information on utility. Section
5 explains under which conditions on the properties of utility the impossibility
verdict can be overcome, should interpersonal comparisons be reintegrated
or not.
1 An historical overview of welfare economics
Although storyboards in successive periods are always somewhat artificial,
we can expect a better understanding of the studied dynamics to emerge
from it. Let us keep in mind that there should be no fetishism of the dates
and of the blocks of contributions here proposed: this presentation is only
instrumental. I provide a presentation of the historical evolution of welfare
economics and its different approaches. I distinguish four successive steps3 ,
the two last being the most important for our scrutiny:
[1790–1890] Since Bentham’s works on the principle of utility, the util-
itarian legacy shall weigh heavily on the future welfare economics. Social
welfare is assessed on the basis of individual utilities. The utility principle
3
For lack of space, I shall not recall extensively in this article the details of each of
these steps. The division in successive periods I here retain is presented through Mongin
(2002)[37], Baujard (2010,2011,2012)[5, 4, 6]. See also, yet only partial presentations,
Samuelson (1947)[50], Hicks (1975)[28], Cooter and Rappoport (1984)[?].
5says that an individual shall and should promote her utility. It also says that
the collective aim is to promote social welfare. This duality of the utility
principle, defined at the individual and the collective level, generates some
tensions. Although the issue of interpersonal comparisons of utilities is not
explicitly raised at the time, the problem of the sacrifice of some individuals’
utilities for others which is directly linked to it is already important. This
may explain the evolution within the family of the utilitarian philosophical
theories (Baujard 2013[?]). As it is not formally part of welfare economics, I
shall not develop this period further in this paper.
[1890–1940] “The old welfare economics”, which foundations are found in
A. Marshall (1890)[34], is well represented by A. C. Pigou (1920)[44]. This
work aims to study the conditions of well-being in terms of market Pareto
optimality. It is historically first applying the utilitarian project within the
economic framework although authors wanted to become more independent
of these philosophical traces. Interpersonal comparisons of utilities are well
accepted as far as distributive aspects are central in the project of the first
welfare economics.
[1940–1950] The “new welfare economics” emerged in the late thirties,
early fourties. It establishes a clear separation between the study of op-
timality conditions of social situations the study of the functioning of the
market. We can distinguish between two approaches which we choose to
label ”American” or ”Bristish” for the sake of clarity4 .
The British approach is well-represented by N. Kaldor (1939), J. Hicks
(1941) and T. Scitovsky (1941). They developed a new concept of Pareto im-
provements, the ‘Pareto efficiency criterion’, which considers the possibility
of hypothetical compensations among individuals, and then applies the test
of unanimity. Because the compensations are just hypothetical, their con-
sideration are supposed not to imply any actual interpersonal comparisons
of utility.
4
What goes well without saying, goes even better when you say it. Although we have
here labeled the schools by some of their representative countries—US, GB—, no fetishism
of the label should hold. Each of these school is before all international. For instance, the
”Critics of welfare economics” of the Englishman Ian Little could be considered as belong-
ing primarily to the the american Approach (Little 1950[33]). Conversely, many people in
the US and elsewhere shall ground their practice on the Kaldor-Hicks justification, notable
the hypothetical (or equivalent variations) among others, to justify cost-benefit analysis,
is well established in American agencies.
6The American approach, represented by A. Bergson (Burk 1938)[10], O.
Lange (1942)[32] and P. Samuelson (1947)[50], considers that normative judg-
ments are contained to a subset of acceptable value judgments. The Pareto
criterion is one of them. They shall try to conceive a framework based on
strictly ordinal utilities.
[1950–nowadays] K. Arrow (1951,1963)[1, 2] established the impossibility
of deriving a social utility function on the basis of individual preferences
without resorting to interpersonal comparisons, as he himself interpreted. A
clear separation between disciplines has resulted from this bad news.
The problem was to be able to say something about social welfare and
public decision. Arrow’s theorem was saying something that could be inter-
preted as an impossibility to build a social welfare function, as developed in
the American approach. The British approach therefore had a much greater
appeal. It could be considered as immune from the Arrow’s result and it ac-
tually allowed for public recommendations. Contemporary welfare economics
developed in the wake of what I have called ‘the British approach of welfare
economics’. It is well-represented by public agencies and most economic the-
orists in international, geographical or industrial economics in their welfare
analyses, Important names are for instance Tinbergen, Haberger or Marglin.
Welfare is there analyzed through surplus computations or cost-benefit anal-
ysis. Important researches have been conducted to be able to understand
the theoretical foundations of the welfare evaluations based on compensating
variation (or equivalent variations), as well as develop new tools to compute
shadow prices. Normative issues as such are excluded from the scope of these
analyses. They are left for an independent political treatment of distributive
issues. It can be shown that interpersonal comparisons are made, but at least
they are not made explicitly.
Besides, the French school of public economics focuses on theoretical re-
flection on the economic role and the decisions of the public sector (Kolm
(2010[31]) . New tools are designed to settle optimal pricing of public goods,
regulation, contribute to evaluate projects of public investments. Some “nor-
matively motivated agents having some power” are supposed to chose and
use economic tools to enhance social welfare through the choice of public poli-
cies. Some instances of such civil servants may be, after Jules Dupuit, Pierre
Massé, Marcel Boiteux, François Divisia, René Roy or Serge Kolm. There
the problem of interpersonal comparisons of utilities is hardly raised because
7there is no need to consider individual utilities as such. What is at stake is
the personal judgment of a benevolent and higher technically trained civil
servant on what is the public interest, as captured through the choice of a
social welfare function. Interpersonal comparisons are hence made, but they
are normatively defined and personally justified by the view of the public
decision maker.
On a totally different approach, a normative economics emerged again to
go beyond Arrow’s impossibility. Social choice theory constitutes consistent
answer to the arrovian challenge and try to go beyond an impossibility. They
eventually focus on a strict problem of aggregation, and has more or less
became a part of voting theories, often letting alone the actual welfare issues.
The theory of fair allocation was born in the 1970ies. The technics they used
were inspired by the arrovian framework but they deliberatly The question
of normative criteria is the central stake. There interpersonal comparisons
are perfectly identified, analyzed and justified when they exist.
2 The age of interpersonal comparisons of ob-
jective and normative utilities
In the old welfare economics, I denote two domains, surplus and Pigou-Dalton
transfers, which criticisms have led to the evolution of welfare economics. It
is common to summarize it by considering the implications of these criteria
on interpersonal comparisons of utility. I shall defend that the interpretation
of utilities is eventually at stake in both cases.
The need, the computation and the intellectual origin of comparisons of
utilities is well illustrated by the consumer’s surplus. The notion of surplus,
or rent – which goes back to the similar ‘total relative utility’ of J. Dupuit
(1844)[14] – became a standard tool in economics after A. Marshall (1890)[34]
to assess the intensity of the happiness of each individual. Dupuit needed
to answer this question to be able to assess whether it was worth spending
money on building new public infrastructures, e.g. concert hall, roads or
navigation channels. Marshall used the surplus notably to study the impact
of a modification of prices, for instance due to consumption taxes or subsidies,
on each individual’s utility, and from then on, on the society’s welfare. As
we all know, consumer’s surplus is the area between the demand curve, and
8the price line; the producer’s surplus is the area between the price line and
the supply curve. At the individual level, utility is objectified by a monetary
measure 5 . By summing the willingness to pay at different quantities, it
provides a metric of intensity of utilities, assesses cardinal individual utilities,
and implies intrapersonal comparisons. At the collective level, when used to
sum or weigh different individuals surpluses – as necessary to consider social
welfare –, it assumes the possibility of interpersonal comparisons.
Surplus computations are very much used in welfare economics – even
nowadays. If we accept that intrapersonal comparisons are meaningful, do
interpersonal comparisons make sense? First, assuming that the metric of
cardinal utility provided by surpluses is satisfying, whether we can use them
as such to compare different individual’s utility depends. It depends on the
heterogeneity of agents. They are homogeneous if each of their demand
curve looks the same, and their ability to produce utility from the commodi-
ties or the policy at stakes are similar. Unfortunately, people in a society
are not homogenous in this sense: it is difficult to consider producers and
consumers on the same ground, or that winners or losers of a policy belongs
to the same class of the society. Marshall is well aware of this restriction,
so that, when elaborating on surplus, he assumes that most of the situa-
tions studied by political economy affect in approximately equal proportions
the different classes of society, and consider the social utility, as the individ-
ual utility of an average man6 . This strong assumption allows to erase the
problem of heterogeneity of agents, and thus that of difficulties in justifying
interpersonal comparisons. Second, Walras raised an objection at Dupuit’s
‘relative utility’. Even though the analysis of the latter is different (due to
a different demand curve in both case: Dupuit plots it on a price-quantity
axis, while Marshall considers a quantity-price axis), the criticism holds for
both cases. Walras regrets that this construction is based on a confusion
between the utility function and the demand function, whose interpretation,
and properties may be different. He could have thought of the differences be-
tween interpreting a choice and a necessary positive utility, but focuses on a
5
“ The excess of the price which he would be willing to pay rather than go without
the thing, over that which he actually does pay, is the economic measure of this surplus
satisfaction. It may be called consumer’s surplus.” It should be noted that this is a quote
of the 9th edition. In the original text of 1890, Marshall speaks not of ‘consumer surplus’
but the‘rent consumer ’. (Marshall 1890: 124[34])
6
For a detailed presentation of the ‘average man’ or ‘normal’ and considerations on the
“median man”, see Martinoia (1999: 322 ff.) [35].
9strict internal criticism, proper to the general equilibrium thesis against par-
tial analyses. Prices variations indeed modifies the budget constraint, hence
should entail a modification of the demand of other goods, and the prices
of other goods. This has but an effect on utility which is unduely neglected
by surplus analysis. Along the same line, Pareto (1892, 1896)[42] remarks
that surplus analyses implicitly assume that marginal utility of money is
constant. He shows that if this should hold, the price elasticity of all goods
should equal to -1, which is highly impossible. Third, Samuelson (1942)[49]
regrets the confusion between the assumption of constant marginal utility of
money – which may be considered as reasonable, though it is not properly at
stake in surplus analysis – and the assumption of constant marginal utility of
income – which is the relevant issue for surplus. In the latter case, Samuelson
insists that is very unlikely that this assumption holds.
It is fair not to consider the criticisms addressed at surplus just concern
the mere comparisons of utility. These criticism are more substantially led
to the interpretation of utility and the properties of the utility functions.
First the meaningfulness of comparisons derives from that the possibility ot
aggregate individual surpluses; and the latter relies on the heterogeneity or
homogeneity of the ability of different individuals to derive utility from the
same attributes, hence on the assumption of a plurality of utility functions in
the society. Second, the confusion between demand curve and utility function
relies on an interpretation of utility which would more or less directly led
to individual demand behavior, and to the relevance of computing utility
within an analysis of partial equilibrium rather than in of general equilibrium.
Third, assumptions on marginal utility of incomes have a direct consequence
on the possibility and interpretation of comparisons.
Let us now turn to the case of Pigou-Dalton transfers (Pigou 1920: chap. 8)[44].
They consist in this judgment. Let us say you want to compare two incomes
– or welfare, national dividend, or whatever – distributions. Consider the
following happens. (1) Individual p is poorer in x than in y of the amount
δ; (2) individual r is richer in x than in y of the amount δ; (3) individual
r is richer than p in state x, and at least as much richer than p in state y;
(4) all other individuals remain unaffected between x and y. This change
may result of a regressive transfer from the rich guy of the amount δ to the
poor guy from x to y. After such a transfer, called Pigou-Dalton transfers,
distribution y shall be judged less unequal than x. Pigou considers that the
economic welfare of the society shall be higher after transfers than before
10transfers if nobody’s welfare is decreased (Pigou 1920: 87-97)[44]. Of course,
such transfers imply interpersonal comparisons of utilities. Because social
welfare is higher when rich people are not so rich and poor people are not so
poor, it is socially better to transfer income or utility from certain people to
others: the latter shall produce more social welfare than the former. More
fundamentally, committing to the principle of transfers entails two implicit
and necessary assumptions on utilities: they imply value judgment hence
they are normative utilities, and they are objective.
First, utilities have an unavoidable normative status: any social welfare
judgment imply some values judgments. Pigou, as an economists of the old
welfare economics does not hesitate to explicitly recognize his a priori egali-
tarian position. Notice surplus may have a similar interpretation – although
Marshall does not make a similar confession, and even pretends his frame-
work is free from any utilitarian traces7 –, aggregation of surpluses of different
persons suppose a normative position8 . The assumption of homogeneity of
agents should make the trick. Let us say each time the tool is used when the
assumption does not hold, then the use of surpluses is value-loaded.
Second, utilities should be objective. Utility is objective when it is inter-
preted as a state of the world such that it can then be computed equally by
any observers. If utility is measured by the time to smile in a day, by the
amount of calories consumed per week, by a monetary assessment of hap-
piness, or any other uni-dimensional objective attributes of the same type,
then they are quantifiable under a common metric, whoever the observer is.
Comparisons of different utilities do not only make sense, they are possible
and easily tractable. Furthermore, in each of such cases, the sum of utilities
makes sense. Such computation are possible in Pigou’s framework since he
defines welfare economics as the study of a part of welfare which is quan-
tifiable with the measuring rod of money9 . More generally, the objectivable
nature of utility allows for this quantification and comparisons. Notice this
7
See Martinoia (1999)[35].
8
J. Schumpeter (1954: 415)[51] indeed considers that surplus is merely utilitarian.This
is just one reference defending this position, among many others.
9
“The range of our inquiry becomes restricted to that part of social welfare that can
be brought directly or indirectly into relation with the measuring-rod of money. This
part of welfare may be called economic welfare.” (Pigou 1920: 11)[44]. See also Hicks’s
interpretation (Hicks 1975)[28]. Quantification, in Pigou’s framework, is notably possible
thanks to the use of national dividend.
11analyses could also be applied to the surpluses analyses. Indeed surpluses
are being objectivized thanks to the computation of monetary measures on
the basis of the demand curve. I do not intend to say that objective utility is
a necessary nor a sufficient property to allow for any quantification and com-
parisons. Some scholars spent much effort to justify intra and interpersonal
comparisons of subjective utilities; conversely, objective utilities do not imply
the total absence of idiosyncrasy, and further work may be required before
making comparisons with such objective utilities (Bentham 1789[7], Baujard
2009[3]). What I put forward here is that a metric is much easier to find in
such context, such that inter-and intrapersonal comparisons are meaningful
with less difficulties –and no need for primary work – for objective utilities10 .
Let us conclude on the first welfare economics. What makes policy rec-
ommendations possible is the possibility of comparing utilities intra and in-
terpersonally. But such possibility is more fundamentally due to certain as-
sumptions on the homogeneity of utilities, and the objective and normative
properties of utilities.
3 The age of questioning comparisons: Com-
pensations between subjective utilities
From the thirties onward, interpersonal comparisons of utilities have been
strongly criticized. Most welfare economists then refrained from using any.
L. Robbins claims, in his famous essay of 1932, that any interpersonal com-
parisons of utility, and in particular the use of the (standard) assumption
of decreasing individual marginal utility in an interpersonal context, are,
subjective in the following sense: they cannot be the result of any scientific
demonstration11 . The intensity of satisfactions of two different individuals
10
A similar argument is the essence of the controversy between R. Cooter and P. Rap-
poport (1984)[12], Rappoport (1988)[45] one hand and P. Hennipman (1988)[24] another.
11
“They are in fact entirely unwarranted by any doctrine of scientific economics [...]
The proposition we are examining begs the great metaphysical question of the scientific
comparability of different individual experiences. [An interpersonal comparison] is a com-
parison which is never needed in the theory of equilibrium and which is never implied
by the assumptions of that theory. It is a comparison which necessarily falls outside the
scope of any positive science. To state that A’s preference stands above B’s in order of
importance is entirely different from stating that A prefers n to m in different order. It
12indeed cannot be measured nor compared, whichever by introspection or ob-
servation, i.e. by any scientific method. All assumptions about the equal
or unequal ability of individuals to transform purchasing power, goods or
attributes into utilities are inevitably based on value judgments or conven-
tions. Now, whereas science studies observable facts and is aimed at some
objectivity, the consideration of value judgments belongs to a normative dis-
cipline. It follows that they should be excluded from the scope of science. If
we rephrase, science just tackles positive facts, interpersonal comparisons of
utility are normative rather than positive; such normative issues can never be
considered as scientific. If economics is a science, it cannot rely on interper-
sonal comparisons.12 Here, the argument is clear: interpersonal comparisons
should be ruled out per se.
Let us consider what argument of intrinsic importance has contributed to
provide Robbins’ essay such a large echo, not only in welfare economics but in
economics in general, and which still rings today. The reason why Robbins
rejected comparisons is based on the will to contain economics within the
scientific method.13 Restoring the scientificity of economic study entails two
implications for welfare economics: a positive interpretation of individual
utility is required, and a neutral criterion of aggregation of these individual
utilities is needed.
The first implication becomes possible thanks to the emergence of the
new demand theory. R. G. D. Allen and J. Hicks (1934)[26] reconstructed
the theory of demand on the basis of marginal rates of substitution between
goods, and of elasticities of demand with respect to price and income. Util-
ity functions are used to account for the complexity of income effects and
involves an element of conventional valuation. Hence it is essentially normative. It has no
place in pure science.” (Robbins (1932: 130 ff )[46])
12
Notice other critics, on operationality, or on moral stakes (including the justification of
circus games, the number wins, and the question of separeteness of the person), have also
considerably weakened the popularity of interpersonal comparisons in welfare economics,
yet much later on.
13
Notice this is an old argument, which was already present in Pareto’s work. He
presents his projects of creating a pure economics as strictly scientific in the sense that we
can strictly on facts. This position entails his famous, yet too often forgotten distinction
between (subjective) ophelimity and (objective) utility (Pareto 1896)[42]. We even here
touch the limits of chronological presentation: Pareto who wrote in the late XIXth or very
early XXth century should be considered as the first author of this second period which
we artificially stated it started in the thirties.
13substitution effects between goods. Utilities yet only convey ordinal inter-
pretation related to each consumer’s behavior, and does not at all stand for
any normative notion of welfare. There is no reason, in particular, to choose
a common scale to capture individual’s i demand behavior in good x or y,
and to capture individual’s j demand behavior in those goods. Limited to
the theories of demand and exchange, such a concept of ordinal utility is
not compatible with any interpersonal comparisons of utility: they would be
meaningless.
Without any comparisons, it may seem difficult to assess which the best
policy is when the welfares of different individuals are concerned. As a sec-
ond consequence, finding another aggregation principle remains necessary. L.
Robbins, and many others, suggests to keep up with an attitude of minimum
attention to optimality criteria. Welfare economics should contend with find-
ing the optimal means to achieve a consistent end14 : this may at least avoid
inconsistent policies. Pareto criterion is a good candidate for this15 : if people
are unanimous to order a pair of options, this ordering should be reflected in
social preference, or, at least, the social preference should never contradict
the unanimity of preferences. This criterion can be translated as a condition
of effectiveness: a state is Pareto efficient if it is impossible to improve the
status of any individual in the society without damaging the situation of at
least one of them. The information used to apply this criterion is limited
to individual utility comparisons between pairs of options, hence to strictly
ordinal utilities. No other criterion would be able to avoid the need for inter-
personal comparisons, and these would not be meaningful. As a conclusion,
what explains the rejection of interpersonal comparisons is an evolution of
the properties of utility used in economics – i.e. ordinality –, which gathers
the overall project of doing a science with economics.
Let us go a step further in the historical overview. The Pareto criterion
alone does not allow to decide when there is a conflict of interest. A ranking
of social situation just based on the Pareto criterion in this case is incom-
plete: it merely cannot decide. Most of the time though, policies do entail
winners and losers. A criterion which just concern improvements that may
not affect negatively anybody is most likely mute to assess most policies. To
achieve a more complete ranking of social situations and be able to make
14
See Robbins (1932: 134)[46].
15
See also E. Barone’s works. See Samuelson (1947: 214-217 )[50] or Schumpeter (1954:
416)[51].
14policy recommendation, a trick consists in sticking to situations that are po-
tentially better in the sense of the Pareto criterion, rather than just better
in the sense of the Pareto criterion. Considering potential improvements
considerably extends the scope of this criterion. The principle of compensa-
tion criteria was introduced by Kaldor in 1939 and developed by Hicks and
Scitovsky, whose contributions are sometimes labelled as belonging to the
British approach to the new welfare economics. Potential transfers permit
to transform incomparable situations into comparable situations in the sense
of Pareto. The argument is the following. Going from a first situation x to
y may create winners and losers, so that the two situations are not compa-
rable. Yet, in the case where transfers from the winners to the losers would
increase the situation of the latter until a point where they do not strictly
prefer the status quo to the new situation, we can say the new situation
is better in the sense of Pareto.16 The actual decision of making transfers
or not is fundamentally a distributive issue, involving normative questions,
which are not in the scope of economic science. This decision is hence not
the role of an economist, and belongs to the decision-maker. This separation
of tasks guarantees that no normative issues are involved in the economist’
assessment of the situations. With such potential transfers, the situations
are ordered according to the Pareto criterion, yet still considering strictly
ordinal considerations, and a priori no interpersonal comparisons of utility.
These transfers have been both widely used and strongly contested. First,
they entail inconsistent rankings of social states. John Chipman and James
Moore (1978) showed that:
“The welfare criteria suggested by Kaldor and Hicks, even with
the qualifications added by Scitovsky and Kuznets, could not
escape the possibility of giving rise to an inconsistent sequence of
policy recommendations, unless either the distribution of income
and wealth or the forms and degree of dissimilarity of consumers’
preferences were assumed to be suitably restricted.”
16
Let x, y, z be social states. According to Kaldor’s criterion (1939)[29], x is preferred to
y, if, from x, it is possible to get to state z by transfers, and such that the potential state z
is better than y, Pareto-wise. According to Hicks’s criterion (1939)[27], x is preferred to y
if, from y, it is not possible that, by transfers, to obtain a state z that would be preferred
Pareto-wise to x. According to Scitovsky’s criterion (1941)[13], x is preferred to y if both
Kaldor and Hicks’s criteria are satisfied.
15In particular, there exist cases of intransitivities that cannot be eliminated
but if individual preferences are all identical and quasi-homothetic. In other
words, either the criteria entails inconsistency, either exaggeratedly restric-
tive assumptions on preferences or individual states must hold.17 . Further-
more, these criteria are not strictly equivalent to the Pareto principle. A
positive number of successive compensatory changes may not correspond to
a Pareto improvement. According to Boadway paradox (1974), a move from
of a Walrasian equilibrium to another may result from such compensatory
changes even if there were no gain of efficiency. In short, the words ’Pareto
criteria’ do not necessarily mean what they mean.
Second, even though interpersonal comparisons of utility are avoided,
the normative criticism linked to these comparisons still holds. On the one
hand, if transfers are eventually made, it is enough to observe ex post that the
new situation is better, Pareto-wise, than status-quo, so that these criteria
are redundant (Sen 1979:25). On the other hand, if transfers (hypothetical
compensation) are not done, it is trivial to say that losers do loose. The
mere idea that compensations could have been possible is little consolation.
As Marc Fleurbaey (2008: 3.1) said:
“Such criteria are then typically biased in favor of the rich whose
willingness to pay is generally high (i.e., they are willing to give
a lot in order to obtain whatever they want, and therefore they
can easily compensate the losers; when they do not actually pay
the compensation, they can have the cake and eat it too).”
Persons with the highest willingness to pay are the most advantaged, which
we can but recognize is a partial view. Last but not least, when you throw
interpersonal comparisons by the door, they may well come back by the win-
dows. Considering that compensations may be realized logically implies that
compensations are meaningful. Transfers allows to compare losses and wins
on monetary terms, which advantage is to be interpersonally comparable.
To devise the application of compensation tests, comparisons are basically
possible and necessary, implying that utilities are now reduced to their mere
proxy, i.e, willingness to pay (or to accept). These normative criticisms ba-
sically entails a standard assessment of the test of compensatory transfers:
17
Notice these restrictions are similar to those described above for Marshall surplus to
hold.
16it is utilitarian without saying his name, and pretending to be neutral and
scientific (Worland, 2005). Chipman et Moore (1978: 581, 584) conclude:
“When all is said and done, the New Welfare Economics has suc-
ceeded in replacing the utilitarian smoke-screen by a still thicker
and more terrifying smoke-screen of its own.’ [...] After 35 years
of technical discussions, we are forced to come back to Robbins’
1932 position. We cannot make policy recommendations except
on the basis of value judgments, and these value judgments should
be made explicit. [...] Judged in relation to its basic objective of
enabling economists to make welfare prescriptions without hav-
ing to make value judgments and, in particular, interpersonal
comparisons of utility, the New Welfare Economics must be con-
sidered a failure.”
In a nutshell, the actual banishment of interpersonal comparisons, fun-
damentally linked to the evolution of the concept of utility used in micreco-
nomics in order to make economics a science, comes with the impossibility of
welfare economics to make policy recommendations. The British approach
to the new welfare economics has developed an successful attempt to reestab-
lish the possibility of recommendations –successful in the sense that it soon
became widely used and inspiring for cost-benefit analysis. Yet we have
shown it supposes a silent reincorporation of comparisons, implying again a
reassessment of the interpretation and the properties of utilities.
4 Arrow’s theorem without comparisons
The history of welfare economics has been widely disrupted by the Arrovian
impossibility result.
At the very beginning of the fifties (1951[1]), Arrow explored whether a
rational social preference relation can be derived from the ordinal rational
individual preferences. Four conditions should hold18 . The condition of uni-
versal domain allowing for any profiles of individual preferences captures the
18
We here just briefly recall the theorem. See, e.g., Arrow 1963[2] or Gaertner 2006[19]
for a more detailed presentation and some proofs.
17sovereignty of individuals, who may have any preference without any restric-
tion. Pareto condition guarantees that the society should not contend with
an option that would be Pareto dominated by another; and if everyone prefers
one option to another, then the society prefers the former option to the latter.
The condition of independence to irrelevant alternatives (now denoted IIA)
requires that, if everything keeps the same except, the ranking between two
alternatives for two individuals, the social ranking of these two alternatives
does not depend on other alternative neither on the preference of the others,
neither of the names of these two individuals. Finally, a non-dictatorship
condition requires that there does not exist any decisive individual on every
options, i.e., an individual whose preference on any pairs of options always
replicates into the social preference. Arrow’s theorem establishes that there
does not exist any rational social preference relation that satisfies these four
conditions simultaneously.
The mathematical framework used by Arrow to tackle the problem of
aggregation is based on binary relations, unlike the analysis of continuous
functions standardly used in microeconomics. Within this framework, the
condition IIA imposes that the information on individual preferences is re-
stricted to binary information only, i.e., on pairwise comparisons over social
states only. This allows Arrow to remain faithful to ordinalism, not only
standard in the field of consumer’s demand theory but also in the analysis
of social welfare after Bergson. The main reason for attributing such an im-
portance to ordinalism is that the intensity of utilities cannot be observed
experimentally (at least easily), hence there is no way why such information
may seriously be considered as scientifically relevant for the computation of
social welfare.
This change shall have dramatic consequences. Let us say, for instance
xPi yPi z and yPj x hold.19 The only relevant information for the arrovian
19
For all i, Ri is the preference relation of individual i between two social states, such
that xRi y reads: “individuals i weakly prefers option x to y”, or, “according to individual
i, x is at least as good an option than y”. This individual preference Ri is a complete
preorder, i.e., it satisfies properties of reflexivity, transitivity and completeness. Relation
Ri is reflexive if and only if: ∀x ∈ X, xRi x. Relation Ri is transitive if and only if:
∀x, y, z ∈ X, xRi y and yRi z ⇒ xRi z. Relation Ri is complete if and only if: ∀x, y ∈
X, xRi y or yRi x. Individual preference Ri is defined by: ∀x, y ∈ X, xPi y ⇔ xRi y and
no-yRi x. It is asymmetric if: xPi y ⇒ no-yPi x, which corresponds to strict individual
preference. It is symmetric if : ∀x, y ∈ X, xIi y ⇒ xRi y and yRi x. The symmetric part
of the individual preference corresponds to indifference. Respectively the asymmetric and
18framework is: xPi y, xPi z, yPi z and yPj x. If we say beside that individual
i prefers more x to y than j does prefer y to x, it seems possible to compen-
sate the loss of utility of individual j by the increase of utility of individual
i. By comparing gains and losses, we could reach a social agreement, and
deduce that x is better than y for the {i, j} population, as in the analyses of
surpluses or potential transfers. IIA condition prevents any such conclusion
since no information on interpersonal comparisons is contained in the pair-
wise comparisons. IIA does not though require unanimity to infer a social
preference. There may well be disagreement between individuals and still a
solution. IIA does not exclude all kinds of interpersonal comparisons. In case
of disagreement between i and j over x and y, the social preference should
remain still when the names of the concerned persons i and j, and/or of the
options x and y, are permuted. Beside, the observation such that individual i
prefers more x to z than he does prefer x to y – as implicit in the first descrip-
tion of i’s preference – cannot be taken into account because of IIA. Rather
than an interpersonal information, IIA has here excluded an intrapersonal
information from of the consideration of social welfare, the characteristics
of individual trade-off between three social states, as fully described in the
usual indifference curves. “The social welfare function was to depend only
on indifference maps; in other words, welfare judgments were to be based
only on interpersonally observable behavior. The Condition of Independence
of Irrelevant Alternatives extends the requirement of observability one step
farther.” (Arrow 1963[2]: 109-110) In other words, there is here a sort of
confusion between two sorts of properties: comparability in the one hand,
ordinality in the other hand.
Let us make a retrospective analysis of Arrow’s justification of IIA. Ac-
cording to the principle “if you can move mountains you can move molehills”,
the focus on binary information was indeed a sufficient condition to rule out
interpersonal comparisons of utilities (Arrow 1963: 32). It is though not
necessary to rule out all but binary information to contend with ordinal pref-
erences. Although the restriction to binary information allows the exclusion
of interpersonal comparisons of utility but is not necessary to exclude them,
it is one possible explanation for Arrow’s negative result. Let us develop
this conclusion. With the sole information available in the binary framework
imposed by IIA, the comparison of any two options y and x is just based on
individual preferences over x and y, and no other options, i.e., the preference
symmetrical part of Ri are written Pi and Ii .
19profile is such that i prefers x to y and j prefers y to j. By the unrestricted
domain condition, this could be compatible with any preference profiles, in-
cluding xPi y or yPi x, yPi z or zPi y, and xPi z or zPi x. Knowing that xPi y,
imagine we had the following profile: yPi z and zPi x. Individual i’s pref-
erence is hence intransitive (or inconsistent since we get xPi y and yPi x).
Saari (1998)[48]’s interpretation is that the arrovian framework imposes no
objection to the consideration of irrational individual preferences, so that the
transitivity of the social preference is a plausible risk. In general words, the
arrovian framework induces the exclusion of some relevant description of the
individual ordinal preferences, from which the impossibility is derived.
An explanation for the impossibility was the poverty of information on
preferences, strictly reduced to binary comparisons. It aimed at avoiding the
computation on intensities of utilities or comparisons of utilities, but it went
much further. It totally prevented to use information on ternary comparisons
for instance. Whereas Arrow interprets the choice of IIA as necessary to avoid
comparisons, we see it as responsible for much further and unnecessary20
restrictions. Although a common reading of Arrow’s impossibility is that the
ban of interpersonal comparisons is responsible for the impossibility of social
choice, my demonstration shows that another property of preferences may
be held responsible for the impossibility, namely, the access to more than
binary information on ordinal preferences. I claim this is historically due to
the influence of revealed preference theory in Arrow’s vision of what a good
intepretation for preferences should be.
The Arrovian result may be considered as the death knell of social choice.
Some also derived another reason for the death of welfare economics in gen-
eral.
5 The need for enriching information on util-
ity
Two obvious distinct moves have resulted of the schock induced by Arrow’s
theorem. On the one hand, social choice theory, faithful to the arrovian
framework, developed in the area of binary relations to thrive to go be-
20
Unnecessary to be consistent with the reasons developed by Arrow.
20yond the impossibility. On the other hand and totally independently – and
indifferently–, welfare economics developed in a totally different framework:
the British approach, pretending not doing any interpersonal comparisons
of utility was at least succeeding in providing collective recommendations.
These two trends constitute important sub-disciplines of economics. I shall
however focus on two other evolutions, that took some time to establish as
relevant solutions for welfare economics.
The first evolution is based on the considerable influence of A. K. Sen
(1979)[54] in social choice theory and in normative economics in general. He
considers that the problem of social choice can be overcome by allowing com-
parisons interpersonal utility, and by enriching the information contained in
the utility that is to say, using post-welfarist evaluations of social states. An
assessment is welfarist if it is based exclusively on information on individual
subjective utilities; it is post-welfarist if it takes into account information of
other kinds (See, e.g., Sen 1970, 1979, 1985, 1991, 1999[52][53][54][56][57][58],
and Pattanaik 1994[43] or Sugden 1993[59]). The possibility of comparisons
critically depends on a renewal of interpretation of utilities (See Baujard
2003). This obvious link is not explicitely put forward by Sen to my knowl-
edge, but essential to understand the solution here provided. When utilities
are subjective, comparisons are not meaningful. A condition for restoring
the possibility of comparisons is to change in the intepretation of utilities. In
his essential role in the existence and the development of the debate against
welfarism, Sen indeed defended the use of more objective information on
individual welfare. This evolution has further consequences. The focus on
objective utilities may suppose multidimensional accounts for the quality of
life, it is necessary to identify these dimensions. All this process may be
best conducted by a team of multidisciplinary workers. In a nutshell, the
use of objective utilities (with comparisons indeed) is a solution for welfare
economics.
The second evolution is meanwhile older and more recent.
Older because it is inspired by ‘the American approach’ to welfare eco-
nomics since Samuelson and Bergson. Social welfare should there be inter-
preted as the view of the whole society (Bergson 1954: 242[8]; Arrow 1963:
107[2]). A problem is hence raised to identify which view should be retained
by welfare economists. At least should it respect three distinct conditions.
First, social welfare is based on individual preferences only —this condi-
21tion corresponds to what Samuelson calls individualism in his 1947 book
and Sen later called ‘welfarism’. Second, welfare economics does not pre-
tend to exclude interpersonal comparisons of utility, but it should contend
with a minimum number of normative criteria21 : the Pareto criterion and a
restricted number of redistributive criteria (typically the Pigou-Dalton prin-
ciple of transfers). Third, such criteria are transparently captured trough
a social welfare function. An important question is whether Arrow’s result
concerned or not the existence of any social welfare function. The debate
really was born in the 70s. Certain theorists defended this view: it is impos-
sible to find a “reasonable Bergson-Samuelson [function] based on individual
orderings” (Kemp and Ng 1976: 59). The explanation they provided was
that “the Bergson function must make interpersonal comparisons [of utility]
or be dictatorial” (Parks 1976: 450) Others, namely Samuelson, considered
the result had nothing to do with welfare economics.
We talk of a more recent than Sen’s rehabilitation of comparisons of util-
ities, because the evolution I want to put forward here is mainly conducted
by Marc Fleurbaey since the 1990ies. Firstly, they reinterpret Arrow’s im-
possibility. Rather than a restriction to ordinal information, Arrow restricts
information to binary comparisons. He went further than needed. As soon
as a possibility of social choice could be derived with non-binary yet ordinal
preferences, we will have shown that this over-zealous restriction of informa-
tion is alone responsible for the impossibility. That is what these economists
do. The restriction in Arrow’s theorem is not linked to the rejection of inter-
personal comparisons of utilities (see Mongin and Fleurbaey 2005, Fleurbaey
and Blanchet 2013). It rather derives from the negation of a substantial
amount of non-binary ordinal information on individual utilities, the kind of
information that would still be acceptable in the Hicksian view of utilities,
and basically consistent with the demand theory. Secondly, if restoring a
possibility of social choice does not in itself require to reintroduce interper-
sonal comparisons of utility, the reintroduction of normative criteria could
not be avoided for this purpose. They propose clear and transparent nor-
mative criteria in their use of utilities in welfare models, which make use of
all advances of social choice theory. As a result, they propose an microe-
conomic solution to welfare economics, in which comparisons of utilities are
not required, utilities are subjective, and they are embedded in a normative
framework.
21
Mongin (2006)[38] qualifies this approach ‘the containment claim’.
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