b ]
j
b 0 iff
W
j
b, a ] W
j
b 0 , a.
where W
j
b, a =
i N
V
j
v
i j
n
j
x
i
x
i
b + n
j
y y b
n
+ V
j
Z Z b
2.3 for all a and all b B.
Eq. 2.3 can alternatively be written W
j
b, a =
i N
V
j
v
i j
n
j
x
i
x
i
b + n
j
y n
j
x
i
y b
n
+ V
j
Z Z b
2.4 which, under certain conditions, corresponds to a
weighted sum of individuals’ net willingness to pay willingness to pay minus costs, plus the
welfare effect of the intrinsic value variable rights, religious considerations. This expression
will be useful below.
Throughout the paper, I will assume that deci- sion-makers have sufficient a priori knowledge of
society to determine their subjective welfare weights V
j
v
i j
, n
j
x
i
, n
j
y and V
j
Z.
12
What they do not know, and need information about, are the impacts of alternative projects.
However, we have to take into account that peo- ple have a limited ability and time to receive and
understand information. Project reports from an- alysts cannot contain an unlimited amount of
detailed information. Formally, assume that each decision-maker is capable of handling a maximum
of K pieces of information regarding each project, where 1 B K B .
13
A piece of information is defined as a single number with an interpretation
attached to it. For example, the statement ‘the average increase in the income of single mothers
will be 2’ is a piece of information according to this definition.
14
If decision makers are presented with too much detailed information, they are
assumed to be unable to distinguish the data they need,
and are
thus unable
to determine
W
j
b,a. The aim of the analysis below is to identify sets
of information which enable any decision-maker to evaluate a project in accordance with her own
normative views, provided that the same informa- tion must be given to all j J. Such information
will be termed a sufficient welfare indicator set Brekke et al., 1996.
Definition 2.1: a sufficient welfare indicator set for project b is information that enables any decision
maker j J to determine W
j
b,a, for b B.
3. Cost-benefit analysis and disagreements
In a traditional cost-benefit analysis without explicit welfare weights, projects are ranked in
accordance with aggregate net willingness to pay. I will disregard the substantial practical problems
of eliciting individual willingness to pay for environmental goods, and simply assume that
marginal willingness to pay is observable.
15
This section discusses the conditions under which aggre-
gate net willingness to pay is a sufficient welfare in- dicator set — in other words: When can partici-
pants in the debate form their own judgements on the basis of aggregate net willingness to pay?
13
K may be exogenously given as a natural limit to people’s cognitive capacity, or it may be the result of an optimizing
process which for our purposes must be regarded as made ‘once and for all’, not being revised for every new decision
problem if perceiving information is costly.
14
Here, one must exclude the possibility of using codes, like using the first digit of a number to indicate the value of one
variable and the second digit to indicate another.
15
In practice, measurement problems caused by misunder- standings, strategic responses, and other factors are substan-
tial. Taking these problems into account would make the analysis below even less favorable to monetary valuation.
12
Alternatively, status quo information may be provided to decision-makers before the discussion of alternative projects
starts this description may have to be more thorough than that of the projects. Some social welfare functions do not
require knowledge of the status quo to determine the weights V
j
v
i j
, for example, utilitarianism; however, some knowl- edge may still be required to determine n
j
x
i
andor n
j
y.
To analyze this formally, define U
i
b = u
i
x
i
b,yb 3.1
as a numerical representation of individual i’s revealed or, in the case of contingent valuation,
reported choices. Then, net benefits as estimated by the unweighted cost-benefit analysis can be
formalized as
W
CB
b, a =
i N
x
i
b + u
i
y u
i
x
i
y b 3.2
where u
i
y u
i
x
i
is individual i’s marginal willingness to pay for the environmental good.
The cost-benefit test will generally evaluate projects in accordance with decision maker j’s
individual judgements
only if
W
j
b = m
j
DW
CB
b for all b B, where m
j
is a positive constant.
16
From Eq. 2.4 above, we can see that this will be the case if and only if each of the three
following conditions is fulfilled: V
j
v
i j
n
j
x
i
= V
j
v
k j
n
j
x
k
for all i, k N 3.3
n
j
x
i
, y; a
i
= C
j
[u
i
x
i
b, yb] 3.4
where C
j
is a monotonously increasing function, and
V
j
Z Z b = 0
3.5 These conditions may need some explanation.
The essence of the first is that the marginal effect on social welfare when i’s income increases is
judged to be the same, regardless of who i is. This holds for a utilitarian decision-maker who be-
lieves that everybody has the same marginal well- being of income. If a decision-maker believes that
the marginal well-being of income varies between individuals, condition 3.3 requires that an indi-
vidual well-being is weighted inversely propor- tional to that individual’s marginal well-being of
income. Thus, if an extra dollar is more important to poor people than to the rich, the interests of
the poor must count less in social welfare evalua- tions than those of the rich. Emphasizing income
effects for low-income individuals is hence incon- sistent with 3.3, unless one believes that the
marginal well-being of income is increasing in income.
The second condition says that the decision- maker accepts revealed choice as an ordinal mea-
sure of an individual’s well-being. Nobel laureate Amartya Sen 1977a, 1985 has repeatedly pointed
out that revealed preferences may reflect other concerns than the individual’s own well-being.
Sen maintains that individuals may act out of what he calls commitment: They may sometimes
sacrifice personal well-being concerns to do what they believe is morally right, even if they never get
any monetary or other compensation that is, even in the form of a good conscience for this.
Thus, the second condition is also controversial.
17
The third condition means that non-welfaristic concerns must not be relevant for the decision-
maker. Many relatively common political or ethi- cal views appear to be at odds with this criterion;
for example, the belief that loss of well-being resulting from self-induced events should count
less than losses that the individual had no oppor- tunity to avoid, or the view that animals have
rights.
It follows from the above discussion that aggre- gate net willingness to pay,
W
CB
b, does not constitute a sufficient welfare indicator set, except
under the very strong assumption that all three of the above conditions hold for every single deci-
sion-maker. If a decision-maker disagrees with at least one of the conditions, the cost-benefit analy-
sis will not in general evaluate alternative projects in accordance with her own views, and she cannot
17
In the present model, every decision-maker j actually has two preference orderings, represented by Wjb and v
j j
b. These preferences may conflict in the sense that
W
i
b \ W
i
b 0 does not necessarily imply v
i i
b \ v
i i
b 0 . In a con-
tingent valuation study, some respondents may respond using their social rather than personal preferences Sagoff, 1988;
Vadnjal and O’Connor, 1994; Nyborg, 2000, in which case WTP will not generally be an ordinal measure of personal
well-being.
16
If one only requires a ranking of projects, not a cardinal measure of DW
j
, then it is sufficient that DW
j
= f
j
DW
CB
, where f
j
is a monotonously increasing function. However, a cardinal measure may sometimes be needed, for example,
when considering whether to strategically support another project than the most preferred.
determine W
j
b on the basis of the net benefits estimate alone. Thus, only some decision-
makers can be expected to use the net benefit estimates to rank projects. Note that this result
holds even in the case of purely benevolent deci- sion-makers who act rationally to maximize social
welfare, taking no other political or personal con- siderations
into account
in their
objective functions.
Using explicit distributional welfare weights does not solve the problem when there is norma-
tive disagreement, unless one performs a separate analysis for every normative view — regardless of
which weights one applies, some individuals will disagree with the choice of weights.
It is frequently claimed that unweighted cost- benefit analysis can be defended on the basis of
any welfaristic social welfare function, provided that the status quo income distribution is socially
optimal see Johansson, 1993. When many indi- viduals participate in the decision-making process,
however, this would require that e6ery decision- maker regards the income distribution as optimal
i.e. 3.3 holds for all j J. In addition to being implausible,
this may
even be
a logical
impossibility. Further, it is often pointed out that if costless
lump-sum transfers were available, undesired dis- tributional consequences could be compensated ex
post. However, consider a decision-maker who supports a project with to her unacceptable dis-
tributional consequences, because she believes these effects can be dealt with ex post. If other
decision-makers disagree with her distributional preferences, however, they may choose not to
support her ex post redistribution proposals. With normative disagreement, it will not generally be
possible to redistribute income according to every decision-makers’ judgement. Knowing this, ratio-
nal decision-makers will have to take distribu- tional concerns into account in the project
evaluation itself, even if lump-sum transfers are technically feasible.
Note also that the above results were derived for marginal projects, implying that distributional
effects need not be dramatic for the above results to hold. Even if costs are marginal and equal for
everyone, and with no intrinsic value variable, the ranking of projects will generally depend on the
chosen welfare weights. Formally, it can be demonstrated that if one knows nothing about the
social welfare weights, then two projects can be ranked, if and only if project one strictly Pareto
dominates the other. This claim is stated as a proposition and proven in Appendix A.
The above results are supported by the inter- view survey among Norwegian Members of Par-
liament by Nyborg and Spangen 1996 and Nyborg 1998.
18
We found that cost-benefit ra- tios were rarely used to rank projects; most re-
spondents said they needed more information. Moreover, leftist politicians were considerably
more skeptical of cost-benefit analysis than those farther to the right one leftist respondent stated
explicitly that the weighing of interests implied by cost-benefit analysis did not match hisher own
views, and that this explained hisher skepticism. If left-wing politicians are less content with the
current income distribution than other politicians, their skepticism may be quite reasonable.
Most politicians in the survey did find cost- benefit analysis useful, but not as a device for
ranking projects. A large number of road invest- ment projects were under consideration, and while
politicians had to depend on the road administra- tion’s judgement to some extent, they looked for
indications of projects requiring closer political attention. Cost-benefit ratios were used as such a
signal; if a very unusual cost-benefit ratio high or low was reported for a project, some politicians
would ask for more details. When given addi- tional information, however, they appeared to
make up their minds quite independently of the cost-benefit ratio itself. Moreover, the cost-benefit
ratio was clearly not the most important of such warning signals; in particular, indication of local
disagreement was used almost universally as a trigger for closer political attention.
Fortunately, most cost-benefit analyses report more than just aggregate net willingness to pay.
18
The survey was based on in-depth interviews with all 16 members of the Norwegian Parliament’s Standing Committee
for Transport and Communication, and the interviews focused on the Committee’s treatment of a long-term national road
investment plan.
Nevertheless, the way such additional information is organized is extremely important. If it is too
disaggregated, decision-makers may not be able to understand its implications i.e. the limit of K
informational items is exceeded, and if the addi- tional data reported is too aggregated, some deci-
sion-makers recieve insufficient information. The next sections are concerned with characterizing
conditions under which information can be aggre- gated without losing important information, and
also how information can be aggregated. In par- ticular, I will focus on whether it is desirable to
value the public good and the intrinsic value variable in monetary terms.
4. Groups of equal welfare weights
