Full text of DOI:10.2165/00019053-200119040-00001

Pharmacoeconomics 2001; 19 (4): 323-335
1170-7690/01/0004-0323/$22.00/0
LEADING ARTICLE
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On Individual Preferences and
Aggregation in Economic Evaluation
in Healthcare
Bengt Liljas1,2 and Björn Lindgren1,3,4
1
2
LUCHE (Lund University Centre for Health Economics), Lund, Sweden
Program on Economic Evaluation of Medical Technology, Department of Health Policy and
Management, Harvard School of Public Health, Boston, Massachusetts, USA
Department of Economics, Lund University, Lund, Sweden
3
4
Department of Community Medicine, Lund University, Malmö, Sweden
For practical reasons, in order to carry out economic evaluations of collective
decisions, total costs will generally be compared with total benefits; hence, indi-
viduals’ willingness to pay (WTP) or quality-adjusted life-years (QALYs) have
to be estimated at an aggregate level. So far, aggregation has usually been done
by taking the individuals’mean WTPor the unweighted number of QALYs. Since
the aggregation process is closely related to the way that income, health and/or
utility of different individuals are compared and weighted, it also has significant
equity implications. Thus, the explicit (or, more often, implicit) assumptions be-
hind the aggregation process will largely affect how health and welfare are dis-
tributed is society. The aggregation problem in economic evaluation is certainly
not trivial, but is seldom addressed in current practice.
Abstract
This paper shows the underlying assumptions of aggregate cost-benefit anal-
ysis (CBA) and cost-effectiveness analysis/cost-utility analysis (CEA/CUA), and
it emphasises the particularly strong assumptions which have to be made when
QALYs are interpreted as utilities in the welfare economics sense. Naturally, the
appropriate method to choose depends on what is to be maximised: welfare or
health. If decisions of resource allocation are to be based on economic welfare
theory, then CBA should be preferred. However, if QALYs are interpreted as
measures of health, rather than as utilities, then CEA/CUA would be appropriate.
Every time an individual purchases a good pro-
ably be prohibitively expensive. Thus, for practical
reasons, in order to carry out economic evaluations
of collective decisions, total costs will generally be
compared with total benefits. Hence, individuals’
willingness to pay (WTP) or quality-adjusted life-
years (QALYs) have to be estimated at an aggre-
gate level.
The aggregation problem in economic evalua-
tion is not trivial; however, it is seldom addressed
in current practice. Since the aggregation process
duced for the market, he or she informs the market
that he or she is willing to pay at least the price of
the good. Such information is repeatedly produced
by the day-to-day behaviour of large numbers of
consumers. It would certainly be possible, of course,
at least in principle, to make evaluations of collec-
tive decisions in the same type of manner, calculat-
ing gains and losses for every individual affected
by the collective decision. However, it would prob-

324
Liljas & Lindgren
is closely related to the way that income, health
and/or utility of different individuals are compared
and weighted, it also has significant equity impli-
cations. Thus, the explicit (or, more often, implicit)
assumptions behind the aggregation process will
largely affect how health and welfare are distrib-
uted in society. The aim of this study is therefore
to survey the underlying assumptions of aggregate
cost-benefit analysis (CBA) and cost-effectiveness
analysis or cost-utility analysis (CEA/CUA). Do-
ing so, we especially examine the interpretation of
QALYs as preference-based utility measures. With
this delimitation we do not, however, imply that
economic evaluations and QALYs need to be based
on economic (welfare) theory. However, when such
claims are being made, we strongly believe that it
is important to be aware of the underlying assump-
tions of those claims. Other foundations than eco-
nomic welfare theory exist, such as the extra wel-
farist approach and the decision-maker’s approach,
but these will not be discussed at any great length
here. The readers are instead referred to the articles
by, for example, Culyer,[1] Nord et al.,[2] and the
review by Brouwer and Koopmanschap,[3] and the
references therein. We concentrate on the principle,
theoretical issues involved rather than the practical,
empirical problems. Although this is a somewhat
technical area, we have attempted to keep the pre-
sentation as nontechnical as possible, even though
we thereby risk losing some exactness.
1. Historical Development of
Willingness to Pay (WTP) and
Quality-Adjusted Life-Years (QALYs)
CBA was introduced as a tool for improving de-
cision-making in situations where markets fail, e.g.
because of the existence of public goods, external
effects or natural monopolies, and/or where mar-
kets have become politically excluded as instru-
ment for the allocation of scarce resources i.e. in
the public sector.[4,5]
Large scale projects, such as
the building of bridges or airports, were among the
first investments to be assessed (see, for example,
the survey presented in Warner and Luce[6]). The
purpose in these analyses was to simulate market
information by calculating all expected benefits of
a project and all expected costs. In principle, the
CBA is based on economic theory, and benefits are
typically being estimated in monetary terms (di-
rectly or indirectly) as the individuals’ maximum
WTP. Societal welfare is maximised by undertak-
ing those interventions only where the net present
benefits minus the net present costs are larger than
zero.[7]
WTP as a measure of the benefits of a project
has a long history and is used in many other fields
of applied economics, especially in the environ-
mental field (see Mitchell and Carson[8] for a re-
view of empirical WTP studies). In the health area,
pioneering work was undertaken by, inter alia,
Weisbrod[9] and Klarman.[10] However, many non-
economists seem to have resisted placing monetary
values on the benefits of healthcare, and relatively
few WTPstudies have been performed in the health
area.[11-13] Thus, in order to be able to communicate
with the healthcare community, alternative meth-
ods of evaluating benefits have been derived, the
most prominent one being QALYs. The QALY ap-
proach typically produces a summary measure of
the length of life and the quality of life for each year
of life, where quality of life, ranging from 0 to 1,
is assumed to be independent of when and where
the relevant life-year is placed in the individual’s
life span. This concept was developed in the late
1960s and early 1970s.[14-16] In their much cited
paper, WeinsteinandStason[17] argued that theQALY
Section 1 outlines the historical development of
WTP and QALYs. In section 2, WTP and QALYs
are related to individual preferences and, by sum-
marising existing literature, it is shown under what
assumptions QALYs can be interpreted as an indi-
vidual utility function. Section 3 is devoted to prin-
ciples for aggregating individual WTPs and QALYs;
it introduces the concept of the social welfare func-
tion (SWF) and derives the necessary conditions
behind aggregating WTPs and QALYs. Section 4
holds a closing discussion, also containing some
remarks on the empirical problems.
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Pharmacoeconomics 2001; 19 (4)

Individual Preferences and Aggregation
325
was the most relevant outcome measure for evalu-
ating healthcare interventions. Economic evalua-
tion using QALYs as an outcome measure is now-
adays mostly known as CUA in Europe, while in
the US it has remained a subset of CEA.[18]
aluations, this subjective interpretation of QALYs
would then focus on the maximisation of economic
welfare rather than total health gains. The solution
of the 2 maximisation problems (i.e. QALYs inter-
preted as welfare versus health) will yield the same
solution only under rather implausible assumptions.
As long as there is a trade-off between health and
other components of the individual’s utility func-
tion (which there is according to economic theory),
these assumptions are violated, and the solutions
are thus different.
Early researchers do not seem to have been very
concerned with the relation between the outcome
measure and economic (welfare) theory or individ-
ual preferences. Instead they seem to have used a
rather straightforward operations research or system
analytical approach. In fact, several of the early
papers on the QALY concept were typically pub-
lished in operations research journals such as Man-
agement Science or Operations Research rather than
in economic journals. Changes in health were con-
sidered to be the output of the healthcare sector,
and scarce healthcare resources were to be alloca-
ted in order to maximise total health gains. In prin-
ciple, the necessary condition for optimum would
then be that the marginal cost per QALY gained is
the same in all healthcare activities.[19] An excep-
tion would be when there are some restrictions, for
instance the total number of kidney donors in renal
disease.
2. WTP, QALYs and
Individual Preferences
2.1 Ordinal and Cardinal Utility
In neoclassical economic theory, individual pre-
ferences are assumed to be completely subjective.
Furthermore, for most analytical purposes, prefer-
ences only have to be ordinal. Thus, the individual
is assumed to be able to rank bundles of goods
according to their desirability, but not to express
how much more he or she prefers one bundle to
another. An individual’s preferences can then be
represented by an ordinal utility function.
Naturally, health and welfare are related con-
cepts, but for most people health is but one factor,
although an especially important one, influencing
the welfare of the individual. Furthermore, the im-
pact on welfare from a change in health may de-
pend, inter alia, on the income, age, gender, family
situation, attitudes to risk-taking and time prefer-
ences of the individual. Moreover, individuals may
not be indifferent between healthcare measures pro-
ducing the same health gain, because of other char-
acteristics of the healthcare services that the indi-
vidual may find positive or negative.[20] However,
even though the early researchers did not claim that
the concept had any clear theoretical basis, but con-
sidered QALYs to be a rather practical measure of
health, suitable for planning purposes,[19] several
writers since then have had the ambition to derive
under which assumptions QALYs might be inter-
preted in terms of individual preferences for health
rather than as an ‘objective’ measure of health per
se (see section 2.3). When used in economic ev-
However, when the individual’s decision, for ex-
ample, involves risk, which is one of the funda-
mentals for the QALY model (see section 2.3), a
stronger assumption than ‘ordinality’ is needed.
When preferences are cardinal, the individual is
assumed to not only be able to state which bundle
of goods that he or she prefers, but also how much
more desirable one bundle of goods is in compa-
rison with another (i.e. differences in desirability).
A cardinal utility function meets these require-
ments.[21,22] Still, preferences are assumed to be
subjective and utilities not comparable among in-
dividuals (a condition which will be relaxed in sec-
tion 3.3 on aggregating individuals’ QALYs).
2.2 WTP and Individual Preferences
From the very beginning the concept of WTP
was derived from economic welfare theory and,
hence, from the assumptions about individual pref-
erences usually made in the economic theory of
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Liljas & Lindgren
individual behaviour. The underlying assumptions
of the individual’s preferences (see Varian,[23] for a
formal presentation) require that they are: (i) com-
plete (any commodities can be compared); (ii) tran-
sitive (if x is preferred to y, and y is preferred to z,
then x is also preferred to z); (iii) continuous (if y
is preferred to z and x is close enough to y, then x
is also preferred to z); (iv) monotone (at least as
much of every commodity, and more of one, is bet-
ter); and (v) convex (averages are preferred to ex-
tremes i.e. the more the individual has of x, the less
willing he or she is to give up y for additional x).
The individual’s utility function based on indi-
vidual preferences can be defined broadly here, and
is in this context usually assumed to depend on
the prices of commodities, income and the level of
health. In this case, the welfare change of a new
policy (that, for example, affects the individual’s
level of health) is simply the difference in the (or-
dinal) utility between the state before and after the
policy change. If this difference is positive, the
change in policy has been beneficial to the individ-
ual. This is, of course, a very general measure and
does not give decision-makers a very useful guide.
A monetary measure of this change would be more
helpful. One such measure is the compensating var-
iation, which is defined as the maximum amount
of money that can be taken from an individual (or
the maximum amount that he or she would be will-
ing to pay) after such a change, while leaving him
or her as well off (i.e. having the same utility) as
before the change.
they first accepted the assumptions of expected
utility theory.[25] These assumptions, called the von
Neumann-Morgenstern axioms (see, for example,
Baumol[26] for a formal presentation), are: (i) inde-
pendence (lotteries with indifferent prizes are in-
different); (ii) desire for high probability of success
(the lottery with the greater probability of a favour-
able outcome is preferred); and (iii) compound prob-
abilities (whether an outcome of a lottery results
in the participation in yet another lottery does not
matter – only the net probabilities of receiving prizes
matter). The expected utility function resulting from
these assumptions is a linear combination of the
uncertain outcomes and the associated probabili-
ties of achieving them.
Pliskin et al.[24] then assumed that health states
worse than death do not exist. Several empirical
studies have shown, however, that for many people
there are, indeed, health states worse than death
(see, for example, Kind et al.[27]). Utility was assu-
med to only depend on health and the number of life
years. Furthermore, health status was constant over
time (Broome,[28] however, generalised the model
to include variable health states without further re-
strictive assumptions), and there was no discounting
of QALYs (even though Broome[28] and Johannes-
son et al.[29] later showed how discounting could
be entered into the model).
Three assumptions regarding the shape of the
utility function were identified by Pliskin et al.[24]
to make QALYs a valid cardinal utility function.
First, for a given number of life-years, the individ-
ual’s preferences over health states are independent
of the constant number of life years, and vice versa.
For example, if the individual is indifferent between
living 5 years in moderate health, and having a 50%
likelihood of living 5 years in either perfect health
or poor health, then he or she should also be indif-
ferent between these choices for all other durations.
Secondly, the proportion of remaining life-years
the individual is willing to give up for an improve-
ment in health does not depend on the absolute num-
ber of remaining life-years involved. This can be
illustrated by the case when the individual is in-
different between 5 years in perfect health and 10
2.3 QALYs and Individual Preferences
As emphasised previously, the QALY approach
was introduced in a rather pragmatic way, without
any formal deduction from reasonable assumptions
of individual preferences. Ever since it was devel-
oped in the late 1960s, several attempts have been
made to examine under which assumptions about
individual preferences QALYs may be based in com-
mon neoclassical economic utility theory.
Using some simplifying assumptions, Pliskin
et al.[24] derived under which conditions QALYs
are a valid cardinal utility function. In doing so,
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Pharmacoeconomics 2001; 19 (4)

Individual Preferences and Aggregation
327
years in moderate health. If so, he or she should
also be indifferent between 10 years in perfect health
and 20 years in moderate health. Thirdly, the indi-
vidual must be risk-neutral over life-years (for all
health states). Risk neutrality implies that, for in-
stance, 5 additional years in perfect health with
certainty is perceived by the individual as giving
equal utility as a 50% likelihood of either 10 or
zero additional years in perfect health. The first
2 assumptions are technically known as mutually
utility independence and constant proportionally
trade-off. Bleichrodt et al.[30] recently showed that,
given risk neutrality, utility functions starting from
the origin in the QALY weight/time space implies
that these 2 assumptions automatically are satis-
fied.
With the assumptions outlined above, risk-neutral
QALYs are then simply defined as the product of
the utility of health and the number of life-years.
There also exists a risk-adjusted QALY model in
which constant proportional risk posture (or con-
stant relative risk-aversion) must hold instead of
risk-neutrality. This model has, however, empiri-
cally not gained as much attention.
individual behaviour, and is not affected by the
choice of utility framework. In practice, there are
a number of problems in the eliciting of individual
preferences, following the WTP approach (see, for
example, Mitchell and Carson[8]). Also, how well
hypothetical WTP corresponds with real WTP is
debated (but is not limited to CBA, as similar prob-
lems are present also for CEA/CUA), and the de-
velopment of calibration techniques for hypothet-
ical WTP is a current research area.[31]
When it comes to QALYs, however, a number
of rather restrictive assumptions, that normally are
not made when analysing individual behaviour in
economic theory, need to be made. The utility of a
given health status, for instance, is most often as-
sumed to depend on many other circumstances,[32]
rather than just the number (and quality) of the
individual’s remaining life-years (e.g. consumption
of other goods, income, age, gender, family situa-
tion). Hence, if QALYs were based on individual
preferences, the individual would behave in ways
which would be considered as exceptions to the
rule in other fields of economics in general – or
health economics in particular – or not in accord-
ance with empirical evidence (see section 4). The
different assumptions of WTP and QALYs are pre-
sented in table I.
2.4 Comparing Individual Preferences
Measured as WTP and QALYs
So, what measure of individual preferences in
economic evaluations invoke the most limiting as-
sumptions? In principle, the individual WTP mea-
sure rests on a rather limited set of assumptions of
3. Aggregating WTPs and QALYs
If all the restrictions and assumptions of WTPs
and QALYs outlined previously were met, then in-
Table I. The different assumptions needed when measuring individual preferences as either willingness to pay (WTP) or quality-adjusted
life-years (QALYs) in economic evaluations
WTPa
QALYs
Type of utility function
Other assumptions
Ordinal
Cardinal
1. The individual’s preferences are: (i)
complete; (ii) transitive; (iii) continuous; (iv)
monotone; and (v) convex
1. The individual’s preferences are: (i) complete; (ii) transitive;
(iii) continuous; (iv) monotone; and (v) convex
2. Acceptance of the axioms of expected utility theory: (i)
independence; (ii) desire for high probability of success; and (iii)
compound probabilities
3. Health states worse than death do not exist
4. Utility is only dependent on health and the number of life years
5. Risk neutrality or constant relative risk-aversion
6. Mutual utility independence
7. Constant proportional trade-off
a
For WTP assessed under risk, the axioms of expected utility theory must also hold.
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Pharmacoeconomics 2001; 19 (4)

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Liljas & Lindgren
dividual preferences would be correctly measured
by WTPs and QALYs. If this were the case, then
under what additional conditions would it be mean-
ingful to aggregate individual WTPs and individ-
ual QALYs to some total measure of the benefits
of a healthcare programme? This issue is addressed
in sections 3.1 to 3.4.
ities are weighted equally and, hence, reduced in-
equality does not increase social welfare. Harsan-
yi[42] showed that a SWF based on utilitarianism
can be formed only if the individual utility func-
tions as well as the SWF satisfy the von Neumann-
Morgenstern axioms, and that individual indif-
ference between 2 alternatives also implies social
indifference. At the other end of the spectrum is the
Rawlsian SWF.[43] In this case, social welfare de-
pends only on the lowest individual utility. Between
these 2 extremes lies the case where some weight
is attached both to all the individual utilities and to
its distribution.[44] Here, both efficiency and equity
aspects are taken into account. Empirically, the SWF
can be evaluated at a number of different levels for
the efficiency-equity trade-off in order to assess
the sensitivity of the decision-maker’s concern for
equity. Typical, but arbitrary, indifference curves
for these 3 versions of the SWF are illustrated in
figure 1.
It should be observed, however, that the SWF
does not have to be individualistic in the sense that
social welfare is a function of individual utilities.
The concept is more general than this. It could be
any ordering of alternative social states; in partic-
ular, it could be defined over individual charac-
teristics such as individual incomes, health, etc.,
without reference to individuals’ utilities.
3.1 The Social Welfare Function
In order to aggregate individual WTPs or indi-
vidual QALYs to a total measure of benefits, some
rules for aggregation have to be adopted. Several
options are available, but in current practice the
chosen rule is seldom explicitly stated. There has
been quite a bit of discussion in the economic lit-
erature in general, however, about the aggregation
of individual utilities. The SWF, a concept intro-
duced by Bergson,[33] Lange[34] and Samuelson,[35]
has played an important role in the discussion, and
it is also applicable in this particular context.
The SWF specifies the rules for aggregating in-
dividuals’utilities into social welfare. The problem
of maximising social welfare, in general, is to max-
imise the utility functions of all the individuals
in society, subject to the society’s budgetary con-
straint. The solution of this maximisation problem
can easily be proven to be Pareto efficient i.e. being
an allocation of resources in which no individual
can be made better off without anyone else being
worse off.[23] However, making some logical re-
quirements on the underlying social preference re-
lation, Arrow[36,37] showed that the only possible
way to use the SWF is to assume that the individual
utility functions are cardinal. In general, however,
the higher the ability (and information) of the de-
cision-maker to measure and compare individuals’
welfare and utilities, the larger the set of feasible
SWFs.[38-41] Furthermore, the optimisation problem
is very general and does not specify the functional
form (i.e. the aggregation process of the individu-
als’ utility functions) of the SWF.
3.2 How to Aggregate Individuals’ WTP
Much attention has been devoted to the issue of
aggregating WTP in CBA (see Johansson[45] for a
formal presentation). Basically, the change in so-
cial welfare is calculated by the weighted sum of
the individuals’ compensating variation (or maxi-
mum WTP), adjusted for their marginal utility of
income (i.e. the individual’s value, or utility, of
the last unit of income). If a new policy increases
the individuals’ health, the welfare measure of this
change is thus the sum of the individuals’ maxi-
mum WTP (adjusted by their relative marginal util-
ity of income) multiplied by the society’s (equity)
weights placed on these individuals’ respective mar-
ginal utilities. Hence, the welfare change is the in-
dividuals’ maximum WTP multiplied by the social
A large number of different SWFs exist. At one
end of the spectrum is the utilitarian SWF. This is
the classical SWF, and is most often the basis for
WTP and QALY aggregation. In this case, all util-
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Pharmacoeconomics 2001; 19 (4)

Individual Preferences and Aggregation
329
without worrying about these assumptions. Thus,
it might be possible to convert a potential Pareto
improvement (i.e. an investment that meets the
Kaldor-Hicks’ welfare criterion) to an actual Pareto
improvement (i.e. an investment that leads to at
least 1 individual becoming better off without any-
one else being worse off).
a
3.3 How to Aggregate Individuals’ QALYs
There have been few attempts to explicitly in-
corporate QALYs (interpreted as utilities) in an
SWF.[46-49] An exception is Bleichrodt,[50] who dis-
tinguished between the conditions for aggregation
(i) within the utilitarian framework and (ii) in SWFs
in which equity in the utility of health is of concern.
For the utilitarian SWF, changes in individual
QALYs (or utilities) must be cardinally compara-
ble among individuals (cardinal unit comparabil-
ity) but not absolute levels of individual QALYs
(or utilities). Furthermore, anonymity (meaning that
the social preferences are independent of who gets
the ‘final’QALY) must also hold. Ahealthcare pro-
gramme would then be preferred from the societal
point of view if the total gains in utility of those
who would gain utility from the programme are
larger than the total losses of those who would lose
utility from the programme – no matter who the
winners or losers might be, or whether those who
gained most were the better off also without the
programme. Thus, changes in utilities are not given
any distributional weights. It should be observed
that there is no requirement that individual QALYs
should be measured on a scale between 0 and 1.
For SWFs in which equity in the utility of health
is of concern, absolute levels of individual QALYs
(utilities) must be cardinally comparable (cardinal
full comparability). A healthcare programme would
be preferred from the societal point of view if the
sum of equity weighted gains in utilities among the
winners is greater than the sum of equity weighted
losses in utilities among the losers. In this case, a
cardinal measure of differences in utility is not suf-
ficient. Since the distribution of the utility of health
is of concern in the aggregation procedure, meas-
urement also requires that absolute (the initial) lev-
c
45˚
b
0
Individual i's utility
Fig. 1. Typical, but arbitrary, indifference curves for 3 versions
of the social welfare function (SWF). (a) stands for the Rawlsian
SWF, (b) for the utilitarian SWF and (c) for a SWF that lies in
between these 2 extremes and, thus, reflects some trade-off
between efficiency and equity.
marginal utility of individual income. Thus, as long
as society weighs all individuals equally (i.e. the
distribution of income is of no concern), and the
individuals’marginal utility of income is the same,
unweighted WTP is a correct measure of changes
in economic welfare.
If these assumptions do not hold, an investment
that meets the Kaldor-Hicks’ welfare criterion[23]
[defined as a change that makes the gainers so much
better off that they can at least (hypothetically) com-
pensate the losers], usually (assuming no transac-
tion costs) will increase the economic welfare to
society. This is so because, for example, an invest-
ment in which individual i gains $2 and individual
j loses $1 might not be indifferent to society if the
marginal utility of income and/or the equity weight
placed on the individuals’ utilities, is higher for
individual j, and the compensation actually never
takes place (i.e. it remains hypothetical). However,
if the government could redistribute incomes over
individuals so that the social marginal utility of
income became equal for all individuals, then it
would be possible to maximise the social welfare
by aggregating the individuals’ maximum WTPs
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Pharmacoeconomics 2001; 19 (4)

330
Liljas & Lindgren
els of individual utility of health can be compared.
It should be observed that this does not necessarily
mean that individuals must have identical prefer-
ences over health states. Individual preferences may
differ, but they should be measurable in such a way
that, for instance, the utility of perfect health for
individual Ais cardinally comparable with the util-
ity of perfect health for individual B.
individual preferences really are but as normative
statements about how individual utilities of health
states should be treated. Thus, the utility of perfect
health and the utility of immediate death, respec-
tively, should be treated as if they were the same
for everyone. For other health states, individual util-
ities are assumed to be cardinally measurable, but
not necessarily identical. In the aggregation proce-
dure they are simply summed and averaged in the
utilitarian SWF, but weighted before summation in
the SWFs in which equity is of (special) concern.
However, since some regard has already been taken
to equity by giving the same utility to everyone for
the health states immediate death and perfect health,
the former is not quite a utilitarian SWF and should,
hence, perhaps be referred to as a semi-utilitarian
SWF. To assign predefined real values to 2 out-
comes, X and Y, such that everyone prefers X to Y
in order to create a consistent scaling procedure for
social welfare judgments based on von Neumann-
Morgenstern utilities, was first suggested by Hil-
dreth.[56] Obviously, the QALYapproach as usually
practised, is a special case of this general idea.
The necessary conditions for the aggregation of
individual QALYs are very restrictive in compari-
son with what is being considered reasonable as-
sumptions in mainstream economics. This is true
in particular for the SWF in which equity in the
utility of health is of concern. At the same time,
there is evidence that people do care about equity
in the health area. An experimental attempt to in-
vestigate individuals’ willingness to trade efficiency
for equity of QALYs between 2 hypothetical groups
was done by Johannesson and Gerdtham.[51] They
found that the respondents’mean marginal willing-
ness to trade was significant (they were, on aver-
age, willing to give up 1 QALY in the group with
more QALYs to gain 0.5 QALYs in the group with
fewer QALYs), but that the size of the difference
in the number of QALYs between the 2 groups was
insignificant. In an experiment of similar design,
Andersson and Lyttkens[52] found an even higher
inequality aversion; the respondents were here
willing to give up 1 QALY in the group with more
QALYs, to gain 0.11 to 0.35 QALYs in the group
with fewer QALYs. They also found, contrary to
Johannesson and Gerdtham,[51] that the size of the
difference in the QALY distribution had a signifi-
cant impact on the trade-off.
The aggregation problem would, of course, be
slightly easier if all individuals valued each arbi-
trarily chosen health state in exactly the same way.
Still, absolute levels of utility must be cardinally
measurable even in this case. Furthermore, there
is ample empirical evidence that individuals differ
considerably in their preferences for specific health
states.[53-55] To be fair, when the utility of immediate
death is assigned the value zero and perfect health
the value 1 in QALY-based CEA/CUA, this should
not be interpreted as positive statements about what
3.4 Comparing the Aggregation of WTP
and QALYs
So, which aggregation process imposes the most
restrictiveassumptions–theoneforWTPorQALYs?
When making this comparison we will leave the
assumptions of the underlying SWF out, as they are
the same for both WTP and QALYs.
For WTP, we have seen that the underlying as-
sumptions are relatively few. Taking a Paretian per-
spective, the ‘only’assumption that needs to be made
is that the marginal utility of income has to be the
same for all individuals. However, if society is to
maximise potential Pareto improvements, not even
this assumption is needed. The issues involved in
aggregating individual QALYs have recently gained
some attention, and it has been shown that individ-
ual utilities need to be both cardinal and compara-
ble across individuals. It is completely clear that
the conditions for aggregating individual QALYs –
in addition to the conditions for individual QALYs
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Individual Preferences and Aggregation
331
Table II. The assumptions needed [on top of those for measuring individual preferences as willingness to pay (WTP) or quality-adjusted
life-years (QALYs)] for aggregating WTP and QALYs in a utilitarian framework, as well as in other social welfare functions (SWFs)
WTP
QALYs
Utilitarian 1. If a Paretian perspective: equal marginal utilities of income
1. Cardinal unit comparability (i.e. changes in individual
QALYs must be cardinally comparable among individuals)
2. Anonymity (i.e., that the social preferences are
independent of who gets the ’final’ QALY)
SWF
2. If a potential Pareto perspective: no further assumptions
Other
SWFs
1. The individuals’ marginal utilities of income have to be
estimated (which is not an assumption per se)
2. The society’s equity weights of the individuals’ utilities have
to be estimated (which, again, is not an assumption per se)
1. Cardinal full comparability (i.e. absolute levels of
individual QALYs must be cardinally comparable)
to be consistent with individual preferences – are
very restrictive (see table II for a comparison).
trade length of life for quality of life if the remain-
ing years of life was less than 5. When the remain-
ing years of life were less than 5, it was only length,
rather than quality, of life that affected the individ-
ual’s utility. Sackett and Torrance[66] noticed that
the value that individuals attach to different health
states is highly affected by the duration they would
have to remain in that health state.
4. Discussion
Individual WTPs in CBA are based, at least in
principle, on exactly the same, fairly weak, assump-
tions about individual preferences which are com-
monly made in economic theory. In contrast, some
very strong assumptions about individual prefer-
ences have to be made in order for QALYs to be
interpreted as utilities.[57,58] The reason for the dif-
ference in assumptions between WTP and QALYs
is (partly) that income (from which the individual’s
WTP is deducted from) is just one argument in the
individual’s utility function, whereas the number
of QALYs is a utility function by itself. Mutual
utility independence, constant proportional trade-
off and risk neutrality are assumptions not normally
made in economic theory and they are also often
contradicted by experimental evidence. See, for ex-
ample, Bleichrodt and Johannesson[59] and Krabbe
and Bonsel[60] for experimental tests of the first 2
assumptions, Stiggelbout et al.[61] for an experi-
ment on the third assumption, and Shoemaker[62]
for a review of experimental tests on expected util-
ity theory. Moreover, it should be mentioned that
other economic foundations than expected utility
theory have been tested. In the study by Bleichrodt
and Quiggin,[63] the prospect theory (which can be
seen as a generalisation of the expected utility model)
of Kahnemann and Tversky[64] was applied as an
alternative. This was proven to increase the descrip-
tive validity of the model. Furthermore, McNeil et
al.[65] found that individuals were not willing to
In our view, rather than examining under what
strong assumptions QALYs can be interpreted as
utilities, it would be more interesting to examine
whether there exists a health index based on plaus-
ible assumptions about individual preferences. How-
ever, accordingtotheanalysisofHougaardand Keid-
ing,[67] such an index quickly runs into the same
issues, and is thus not easily achievable. In a Lan-
caster or Grossman framework (in which health
and other commodities are produced by using own
time and market goods), Hougaard and Keiding[67]
show that the health index (or QALY) must be com-
pletely individual-specific, or preferences have to
be identical, production technologies the same, and
the initial endowments of health and wealth equal.
Furthermore, while the consistent aggregation
of individual WTPs boils down to an assumption
regarding the individuals’ marginal utilities of in-
come, the aggregation of QALYs requires an as-
sumption of cardinal unit comparability of indiv-
idual utilities. Bleichrodt and Quiggin[68] showed
under what conditions CEA/CUA is consistent with
CBA for the more general (and realistic) utility func-
tion consisting of both consumption and health sta-
tus. It turns out that very restrictive assumptions
have to be made, e.g. that: (i) the individual’s util-
ity is multiplicative in the utility of consumption
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Pharmacoeconomics 2001; 19 (4)

332
Liljas & Lindgren
and the utility of health status (implying that im-
provements in health are valued higher at high levels
of consumption, which has obvious distributional
implications); and (ii) the utility of consumption is
constant over time (which in this case implies that
consumption is constant). The latter assumption is
a much stronger assumption than the former one.
In fact, since Robbins’ methodological criti-
que,[69,70] disputing the scientific status of inter-
personal comparisons of utilities, many economists
seem to have come to the conclusion that no inter-
personal comparisons whatever are allowed or rec-
ommended. Others, such as Sen,[71,72] have criti-
cised their fellow economists for avoiding one of
the most important political issues i.e. inequalities
in individuals’ opportunities. Sen has instead ar-
gued for moving away from a utility-based SWF to
interpersonal comparisons based on non-utility in-
formation, such as functionings and capabilities.
Taking all these problems into consideration, the
cautious economist may feel that he or she could
just as well leave the tricky normative issues in
health and healthcare to others and concentrate on
the issues of positive health economics. However,
decisions about allocating scarce healthcare re-
sources will be made whatever the economist de-
cides for him or herself. The challenge to provide
decision-makers with information for improving the
allocation of resources, both in terms of efficiency
and equity, would still be there. Portney[73] recently
raised a similar argument as a response to several
critics of the contingent valuation method in the
environmental field (who argued that it was flawed
and thus should be abandoned by economists, rather
than further developed).
This approach does not necessarily completely re-
solve the issue of equity considerations, however.
In practice, most CBA done so far have taken the
unweighted mean of the concerned individuals’
WTPs as a measure of health benefits (i.e. a utili-
tarian approach). From an economic welfare per-
spective, the procedure rests on the assumption that
the marginal utilities of income for all individuals
in question are equal. So, few (if any) cost-benefit
studies have in reality tried to take equity into ac-
count.
If you are concerned with individuals’ health and
the distribution of health among individuals rather
than just the utilities which individuals may derive
from their health (or the distribution of utilities),
you may choose to treat QALYs as an ‘objective’
measure of health in its own right, or at least as a
commonly accepted way of measuring outcomes
in healthcare. Maximising the number of equity-
weighted QALYs would then be quite an appro-
priate goal for the healthcare sector (or society at
large). This is in line with Sen’s[71,72] advocacy for
interpersonal comparisons in the non-utility space,
for which there is very much to be said, in our opin-
ion. For instance, according to the Swedish Health
Care Act of 1984, the main objectives of the Swe-
dish healthcare system are the health of individuals
and the distribution of health in the population. This
trade-off between efficiency and equity has recent-
ly been confirmed in a survey to Swedish politi-
cians.[75] Furthermore, see Olsen[76] for a discussion
on the priority-setting in the Norwegian healthcare
system (which is based on severity level and the
capacity to benefit).
Sen’s view is also shared by many health econ-
omists (see, for instance, Culyer,[1] Wagstaff,[47] and
Williams[77]). Since this view is obviously not found-
ed in economic welfare theory, it has been called
the ‘non-welfarist’ (or ‘extra-welfarist’) view on
economic evaluation in healthcare.
In principle, it would be possible to take equity
considerations into account in ‘extra welfarist’CEA/
CUA, e.g. using a SWF in which utilities are re-
placed by health states.[47] In practice, however, ag-
gregation has (implicitly) applied a utilitarian ap-
What options would then be left for economic
evaluation? If you are a traditional Paretian welfare
economist, claiming that all decisions about resource
allocation should be based on individual utilities,
the obvious answer would be to increase the use of
WTP-based CBA. This idea was recently promoted
by Kenkel,[74] who argued that the customers of
economic evaluations should be given (what he per-
ceives to be) the correct economic evaluation (i.e.
CBA) rather than what they demanded (CEA/CUA).
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Pharmacoeconomics 2001; 19 (4)

Individual Preferences and Aggregation
333
proach, with the same weights given to all indiv-
iduals’ health states (or rather, changes in health
states), as measured by QALYs. Thus, so far, there
exist few, if any, published CEA/CUA studies that
have taken equity in health into account.
abound,[18,82,83] and the need for future research
and development is substantial, indeed.
Acknowledgements
Financial support for this study was provided in part by
grants from the Swedish Medical Research Council and the
Swedish Council for Social Research. The funding agree-
ment ensured the authors’ independence in designing the
study, interpretingthedata, writingand publishing the report.
We would like to thank Fredrik Andersson, Sören Höjgård
and Carl Hampus Lyttkens (Lund University), and Magnus
Johannesson (Stockholm School of Economics) for their
comments on earlier versions of this paper.
Another issue of debate, which concerns both
methods, is how to deal with altruism i.e. how (and
if) should the values individuals place on other in-
dividuals’health and/or utility be incorporated into
the analysis. This has been touched upon in the
case of CBA in healthcare a number of times,[78-80]
but is still an interesting topic for further research
within CEA/CUA. Labelle and Hurley[81] discuss-
ed this issue within the CEA/CUA framework, and
stated that which externalities to include depends
on what should be maximised: the SWF or the com-
munity’s health (i.e. what interpretation of QALYs
that should be made; as utilities or as health).
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