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
4
.
1
. A monetary 6alue-based indicator set A common response to the controversies sur-
rounding cost-benefit analysis is to report costs and benefits for separate groups of the population
for example, Johansson, 1993. This may in prin- ciple solve the problem, but only for rather spe-
cific choices of groups. The problem, however, is that it may be impossible to know in practice
whether
the group
specification is
in fact
appropriate. Define a group of equal welfare weights as the
set of all individuals i, m N such that V
j
v
i j
n
j
x
i
, y; a
i
x
i
= V
j
v
m j
n
j
x
m
, y; a
m
x
m
4.1 for all j J, i.e. the social importance of a mar-
ginal income change is the same for everyone within the group, according to every decision-
maker.
19
Identifying such groups is certainly not a straightforward task since decision makers’ sub-
jective welfare weights may not be known to the researcher. Let us disregard this problem for a
moment, however. Let us also assume for the moment that every decision-maker accepts that
revealed choice provides an ordinal measure of individual i’s well-being condition 3.4. Then,
i’s net willingness to pay for the project, NB
i
b = x
i
b + [u
i
yu
i
x
i
] y b ,
is an ordinal measure of the project’s effects on i’s
well-being. Under these assumptions, Eq. 2.4 implies that the social welfare effects of a project
can be written as a weighted sum of net willing- ness to pay by groups, plus the effects of the
intrinsic value variable:
W
j
b,a =
G g = 1
b
g j
i g
NB
i
b
n
+ V
j
Z Z b
=
G g = 1
[b
g j
n
g
NB
g
b] + V
j
Z Z b
4.2 Here, g denotes an equal welfare weight group,
and G is the number of such groups. Further, b
g j
= V
j
v
i j
n
j
x
i
, where i g, is the social welfare weight attached by decision-maker j to
marginal income changes for any given individual in group g, n
g
is the number of members in group g, while NB
G
b = 1n
g i g
NB
i
b is the aver- age net willingness to pay in group g.
20
The above implies that if analysts provide in- formation about net willingness to pay for each
group, any decision maker can indeed evaluate the well-being effects of a project. Note, however,
that the intrinsic value variable must be evaluated separately since it enters the social welfare func-
tions directly; not, by definition, through effects on individual well-being. Provided that there are
not too many groups, i.e. G + 1 5 K,
21
then, aver- age net willingness to pay by groups, supple-
mented by separate information on the intrinsic value variable, constitutes a sufficient welfare in-
dicator set. In the following, let us call this indica- tor set Vb:
V b = {NB
1
b, . . . ,NB
G
b,DZb} 4.3
20
All i N are members of one and only one equal welfare weight group each. If there is no individual m i such that
4.1 holds, then individual i will be the single member of her group.
21
If y and Z are vectors with m and r elements, respectively, the corresponding inequality is G + r 5 K.
19
Note that decision maker j need not attach the same welfare weight to individual i as decision maker k; but if i and
m are members of the same group, j and k must agree that i should not be treated differently from m.
There is no reason to attempt to value changes in the intrinsic value variable in money terms, for
example by estimating individual willingness to pay for such changes. Since weighing of welfaris-
tic versus non-welfaristic concerns must be left to the individual decision-maker’s discretion, he or
she can evaluate this directly using hisher social welfare function, and for this purpose no common
measurement unit is required. For example, if a project involves a dispute over the right to land
used by, but not formally owned by, aboriginal people, information about this must be included
in a comprehensive project analysis, but a verbal description might be quite sufficient.
22
Note, however, that the indicator set Vb relies on equal welfare weight groups. If welfare weights
vary just as much within groups as between groups, reporting net benefits by groups is not
more informative than the aggregate number. Un- fortunately, knowledge of decision-makers’ wel-
fare weights is difficult to obtain. In practice, the choice of groups will probably have to rely quite
heavily on analysts’ subjective judgement.
In addition, the approach outlined here requires certain restrictions on decision makers’ welfare
weights. If there is too much disagreement on which individuals should be treated equally, the
number of groups may become exceedingly large. Finally, if some decision makers refuse to accept
willingness to pay as an ordinal measure of indi- vidual well-being condition 3.4, Vb is not a
sufficient welfare indicator set.
Although the indicator set suggested above is based on revealed or reported ordinal utility
information, the need for subjective judgements of other people’s well-being by no means disappears.
Decision makers must still subjectively assess and compare the marginal utility of income of the
various groups. The normative weights V
j
v
i
and V
j
Z must also be assessed subjectively — this should not be regarded as a problem, how-
ever, since leaving purely normative evaluations to decision makers was precisely the purpose of
the analysis.
4
.
2
. A physical-unit based indicator set The above analysis may be taken to indicate
that environmental valuation is, after all, vital to rational project evaluation. However, if we are
willing to assume that equal welfare weight groups can be identified, it is equally possible to
find indicator sets that do not rely on such valua- tion. The change in social welfare due to a project
b see Eq. 2.3 can be written as a weighted sum of the costs paid by each group, the change in the
environmental good measured in physical units, and the change in the intrinsic value variable:
W
j
b,a =
G g = 1
[b
g j
n
g
x
g
b] + g
j
Dyb + V
j
Z Z b
4.4 where g
j
=
i
[V
j
v
i j
n
j
x
i
, y; a
i
y] is the marginal welfare effect of increasing environmen-
tal quality, as judged by decision maker j. Fur- ther, −
x
g
b is the average cost paid by members of group g.
The weights, although presumably unknown to analysts, will be known to decision-makers them-
selves. Thus, if researchers provide information about the project’s environmental effects mea-
sured in physical units, in addition to information on the intrinsic value variable and the costs paid
by each group, any decision-maker is capable of evaluating the project. Hence, environmental val-
uation is not required. Stated formally, if G + 2 5 K,
23
the indicator set Pb, where: P
b = { x
1
b, . . . , x
G
b, y b , Z b }
4.5 is a sufficient welfare indicator set.
An obvious objection to the above is that the evaluation is made subjectively, without reference
to the affected individuals’ own reported prefer- ences. Recall that g
j
, the weight attached by decision-maker j to changes in the environmental
good, is comprised partly by normative elements, V
j
v
i j
, and partly by the decision maker’s attempts
to judge
others’ well-being,
22
Land rights to aboriginal people might, of course, affect their well-being, in addition to being an issue of rights as such.
Such effects are captured through the individual well-being variables in the social welfare functions.
23
If y and Z were vectors with m and r elements, respec- tively, the corresponding inequality would be G + m + r 5 K.
n
j
x
i
, y; a
i
y. As before, the fact that the former of these is judged subjectively is not a
problem here since the aim of the analysis was precisely to allow normative disagreement. How-
ever, it is more troublesome that decision mak- ers’ evaluations of others’ well-being may not be
too well-founded.
The main difference of assumptions between the monetary value-based indicator set Vb and
the physical unit-based indicator set Pb is the following. The former indicator set requires an
assumption that revealed or reported choice is an ordinal measure of well-being 3.4. In the
latter indicator set, this assumption is not re- quired. Instead, one more subjective evaluation
on decision makers’ part is needed g
j
. Both indicator sets require extensive subjective judge-
ment on both normative and descriptive issues; however, even in the indicator set based on
monetary values, subjective judgements on cardi- nal and interpersonal aspects of utility functions
are unavoidable.
In some situations, the assumption of ordinal equivalence between utility and well-being is
more troublesome than otherwise. If respondents to contingent valuation surveys perceive the val-
uation question as a political or moral question, rather than a question about their own personal
well-being effects, they might value projects in accordance with their view on social welfare
W
j
rather than their own well-being preferences v
j j
Nyborg, 2000. If so, their reported valua- tions will not generally reflect ordinal properties
of their own well-being. If the good to be val- ued is very different from a market good such
as biodiversity or wilderness, respondents might easily perceive the valuation question as political
or moral — while it seems more reasonable to interpret the sensitivity of housing market prices
to noise as an expression of individual well-be- ing effects. Hence, an indicator set like Vb
may be more useful when the environmental good is closely connected to markets. If deci-
sion-makers do not trust that willingness to pay reflects individual well-being, physical unit infor-
mation is required; so indicator set Pb would then be preferred to Vb.
24
In practice, groups with equal welfare weights may be very difficult to identify. One approach
might be to ask decision makers directly about this. The best one can hope for in practice,
however, is probably information allowing deci- sion-makers to arrive at approximate evalua-
tions. One could try to avoid the most severe errors, though, if some decision-makers’ welfare
weights are very different for two groups; aggre- gating those two groups into one may cause
severe mistakes in those decision-makers’ evalua- tions. Thus, the analyst should particularly look
for groups whose interests are known to be em- phasized by some decision-makers such as
groups who are especially badly off, or perhaps even
politically powerful
groups and
also groups whose marginal well-being of income is
regarded as particularly large by some decision makers for example, low income groups. This
does not imply that information about other groups is unnecessary, only that less disaggre-
gated information is required for those with more similar welfare weights.
Both indicator sets described in this section leave the researcher with the task of making ex-
tensive subjective judgements about decision makers’ welfare weights. This is troublesome for
two reasons. Firstly, it is not clear that the pro- fessionals who carry out project analyses — for
example, economists — are particularly well trained in judging the political or ethical impor-
tance of different aspects of projects’ conse- quences. Secondly, information may possibly be
manipulated by project analysts who want to pursue political or personal goals of their own.
To avoid such problems, indicator sets that rely less on the researcher’s judgements about wel-
fare weights might be preferable. The approach outlined in the next section does not require
such judgements, but is only applicable to a lim- ited class of projects.
24
If projects are non-marginal in the sense that subjective social welfare weights are changed, intra-group welfare weights
must be assumed to be equal both before and after the project is implemented. In the indicator set Vb the expression for
marginal net benefits should be replaced by the equivalent variation measure see, for example, Johansson, 1993.
5. Projects with simple income distribution effects
