ANALYSIS
Project analysis as input to public debate: Environmental
valuation versus physical unit indicators
Karine Nyborg *
Di6ision for Resource and En6ironmental Economics,Statistics Norway,PO Box 8131,0033 Oslo, Norway Received 24 August 1999; received in revised form 16 March 2000; accepted 23 March 2000
Abstract
Monetary valuation of environmental change is useful if one aims to rank alternative projects according to some specific social welfare function. However, if the project analysis is intended as background information to a democratic debate, the advantages of monetary valuation are less obvious. This paper analyzes aggregation of information, taking normative disagreement explicitly into account. It is demonstrated that monetary valuation is not always more informative than a physical unit measure of environmental change. © 2000 Elsevier Science B.V. All rights reserved.
JEL classification:A11; D61; D78; D83; H43
Keywords:Cost-benefit analysis; Environmental valuation; Democratic decision-making
www.elsevier.com/locate/ecolecon
1. Introduction
Cost-benefit analysis of environmental change is a central topic in the environmental economics literature. For example, Michael Hanemann (1994, p. 19) argues as follows — ‘The ability to place a monetary value on the consequences of pollution discharges is a cornerstone of the eco-nomic approach to the environment. (...) Placing a value on [goods that cannot be bought and sold
in a market] can be essential for sound policy.’ Similarly, Navrud (1992, p. 37) claims that ‘we need to know the marginal value of environmen-tal goods to find the socially ‘right’ (optimal) quantity/quality of different environmental goods. On the other hand, skeptics have argued that traditional cost-benefit analysis is too ambitious, and simplifies too much, in its attempts to aggre-gate all relevant information into one single indi-cator of projects’ social desirability (e.g. Kelman, 1981; Sagoff, 1988; Bromley, 1990; Vatn and Bromley, 1994). And in fact, public debate and perhaps also applied decision-making frequently
* Tel.: +47-22-864868; fax:+47-22-864963. E-mail address:karine.nyborg@ssb.no (K. Nyborg).
seem to be framed more in terms of physical unit indicators than monetary value measures. Throughout publications such as OECD’s Envi-ronmental Performance Reviews (e.g. Organiza-tion for Economic Co-Operation and Development, 1996), OECD’s Environmental In-dicators (Organization for Economic Co-Opera-tion and Development, 1998), or in political documents (for example, Ministry of the Environ-ment, 1996), physical unit indicators are used extensively to describe and discuss environmental changes and their importance: the number of endangered species; The size of protected areas; or the ambient concentration of SO2 are merely a
few examples. To the extent that monetary unit indicators are discussed at all, the focus in the above-mentioned documents is on costs, such as spending on environmental R&D, or required funding for environmental clean-up. Monetary benefit estimates based on individuals’ willingness to pay for environmental changes are surprisingly rare, considering economists’ emphasis on such information as a basis for sound policy. More-over, some analyses indicate that even when mon-etary benefit estimates are indeed available, their impact on policy may be very limited (Fridstrfm and Elvik, 1997; Nyborg, 1998; Kuik et al., 1992). Monetary valuation is obviously useful when the goal of a cost-benefit analysis is to provide a final ranking of policy alternatives. However, a very common goal of economic analysis is to
pro6ide background information to a public debate.
The latter aim differs from the former in a funda-mental way — while a final ranking requires that the policy-maker’s normative views are taken into account (for example, formalized as a social wel-fare function), democratic debate requires, in-stead, that citizens have access to factual information which can, as far as possible, be distinguished from normative judgement.1 In this
context, the advantages of monetary valuation and cost-benefit analysis are much less obvious.
Although a cost-benefit analysis can, in theory, be performed according to the normative views of
any citizen, it cannot simultaneously be based on the normative views ofe6erycitizen, except in the
absence of normative disagreement (see Dre`ze and Stern, 1987, pp. 955 – 958). This represents a prob-lem when cost-benefit analysis is used as informa-tional background to public debate. The question is, however, whether the alternatives, such as rely-ing on physical unit indicators or other informa-tion, are any better.
Below, I will use a simple formal model to analyze the information requirements for demo-cratic environmental policy-making and debate. My aim is to characterize information sets which enable any individual decision-maker to arrive at well-founded project evaluations in accordance with his/her own ethical or political views. I will assume that the amount of information an indi-vidual can perceive about each project is limited, and that each individual gets exactly the same information. The main conclusion is that when there is normative disagreement, valuing environ-mental changes in monetary terms is not necessar-ily more informative than a physical unit measure of the environmental change. In some cases, mon-etary values will actually be less useful than phys-ical unit measures. The widespread use of physphys-ical unit indicators in the public debate on environ-mental issues may thus have a quite rational explanation.2 Perhaps surprisingly, the above
re-sult may hold even if lump-sum transfers are feasible. Further, when normative disagreement is present, one cannot solve the problem by assum-ing that the income distribution is socially optimal.
Throughout the paper, the termdecision-maker
denotes any individual participating in the politi-cal process (a politician, a voter, or any citizen taking part in public debate). The decision-mak-ing process is assumed to be of the followdecision-mak-ing stepwise type.
1. The alternatives are specified and described. 2. Each decision-maker subjectively evaluates the
alternatives.
3. Decision-makers’ individual judgements are aggregated to yield a collective choice.
1For an extensive discussion of requirements for democratic
decision-making, see Dahl (1989); see also Nyborg and Span-gen (2000).
2For a general discussion of environmental indicators, see
The paper focuses attention on step 1 and 2, while step 3 is disregarded. Hence, I do not study how the final collective decision is reached, or what the final decision is; the paper is concerned with the individual evaluation of projects before
processes such as bargaining, voting, lobbying, etc., begin. One might object that an individual may want to support a project for strategic rea-sons, so that the collective decision procedure does indeed matter for individuals’ ranking of projects. However, if strategic behavior is to make any sense, the individual must first know which project(s) he really prefers. Hence, his evaluation in step 2 does not necessarily correspond to infor-mation he reveals to others in step 3.
In Section 2, I present a model where several individuals participate in a decision-making pro-cess. Each decision-maker uses available informa-tion and her own normative views to judge the welfare effects of alternative projects. In Section 3, the model is used to discuss the performance of cost-benefit analysis as informational input to public debate. It is demonstrated that aggregate net willingness to pay information is too aggre-gated for this purpose, in the sense that only decision-makers who accept certain controversial assumptions can use this information to evaluate projects in accordance with their own ethical views. Section 4 shows that net willingness to pay by groups may be useful as information for all participants in the debate, but this requires that groups are chosen in a particular way — within groups, welfare weights must be equal for every group member, according to every decision-maker. This is clearly difficult to achieve in prac-tice since decision-makers’ welfare weights are usually not known. If such groups are identified, however, it turns out that individual welfare judgements can alternatively be based on physical unit measures of environmental change. Hence, monetary valuation of environmental change is not essential in this case.
Section 5 demonstrates that for projects with particularly simple income distribution effects, it is possible to provide sufficient information to the public debate without making assumptions on decision-makers’ welfare weights. This requires, however, that environmental changes are
de-scribed using physical unit indicators, not mone-tary values. Thus, for such projects, monemone-tary valuation is less useful as input to democratic debate than physical unit indicators. Section 6 concludes.
2. Normative disagreement in public debate: A simple model
Below, I will use a simple mathematical model to formalize my argument. Since parts of the presentation may seem somewhat technical to those not inclined to mathematical rigor, note that the whole model set-up can be summarized by two equations (Eq. (2.1) and Eq. (2.2)), repre-senting, respectively, decision makers’ ethical views and their judgements of individuals’ well-being.
Let N={1, . . . ,n} be the set of all members of society, whileJ¤Nis the set of decision-mak-ers. Each decision-maker jJ has his or her own ethical or political views, which for the case of simplicity, I will regard as exogenously given.3
Assume further that for eachj, these ethical views can be expressed as a social welfare function
W j
=Vj( v1
j, . . . , vn
j,
Z) (2.1)
where W jis social welfare as judged by
individ-ual j, vi
j is person i’s well-being as judged by j,
andZallows for inclusion of non-welfaristic con-siderations.4 This may, for example, be the view
that certain rights and duties should be respected, the view that nature has an intrinsic value, or religious concerns. For simplicity, Z will be treated as a single variable. Eq. (2.1) does not necessarily describe the ethical views of a purely benevolent decision-maker: It could also be inter-preted as a representation of j’s political views, which may be motivated, for example, by
re-elec-3The model presented here is a further development of a
model developed by Brekke et al. (1996).
4Sen (1979) defines a value system as welfaristic if ‘social
tion concerns, or by regarding oneself as a repre-sentative of some subgroup of the population.5
To be able to assess and compare the social welfare effects of different projects, decision-mak-ers must compare welfare effects for different people; formally, they need a cardinal and inter-personally comparable concept of well-being.6
The neoclassical concept of utility functions, defined as numerical representations of binary revealed choices, is neither cardinal nor compara-ble between individuals. Still, in everyday life people appear to repeatedly make their own sub-jective judgements on individual well-being in an informal way. Thus, assume that any decision-makerjis capable of making an informal, subjec-tive judgement of any other individual i’s well-being:7
vij=nj(xi,y;ai) (2.2)
where vij is j’s judgement of i’s well-being, xi is
i’s income, and y is environmental quality (mea-sured in physical units), which is assumed to be a pure public good.8Further,a
iis a vector
describ-ing i’s characteristics, such as age, sex, socioeco-nomic class, or health. Characteristics are regarded as fixed and observable, but ai is not
allowed to contain full identification of i.9
Also,
prices are assumed to be fixed throughout the analysis, implying that thenjfunctions bear much
resemblance to indirect utility functions. Note, however, that while the latter represent con-sumers’ own revealed choices, the former repre-sent beliefs about others’ well-being; moreover, while indirect utility functions are usually taken to be ordinal, thenjfunctions will typically be both
cardinal and interpersonally comparable from j’s point of view.10
Let X denote the vector of individual incomes for all iN. Assume that the set of alternative, feasible projects,B, is clearly defined. Any project
bB, including the status quo ‘project’b=0 (do-ing noth(do-ing), leads to a social state (X,y,Z); hence,X,yandZcan be regarded as functions of
b. This implies (Eq. (2.1) and Eq. (2.2)) that both
W j and v
i
j will be functions of (a,b), where a=(a1, . . . ,an). The model is static and
deter-ministic. For analytical simplicity, costless lump-sum transfers are aslump-sumed to be infeasible. However, as will be discussed below, the latter assumption is not crucial to the results.
To compare the social welfare effects of alterna-tive projects, each participantjin the debate must identify W
j
(b,a)=W j
(b,a)−W j
(0,a) for every project bB. Assume that b is a marginal project.11 Define
X(b) as the vector of income
differences between the status quo and the situa-tion after the project is implemented, that is,
X(b)=X(b)−X(0). This corresponds to the
negative of individuals’ monetary costs associated with the project. Accordingly, define y(b) and
Z(b) as the differencesy(b)−y(0) andZ(b)−
Z(0), respectively. Then, when choosing between any two projects, each decision makerjwill prefer the project which yields the largest increase in her social welfare function:
5However, when interpreting ‘decision-makers’ as
‘politi-cians’, note that if voters are concerned with social welfare, politicians who maximize their chances of being re-elected will behave as if they too were concerned with social welfare (Mueller, 1987). Further, in a representative electoral system where voters have different normative beliefs, it may be opti-mal for a vote-maximizing politician to behave in accordance with a different normative view than his competitors.
6Arrow (1951); for a thorough discussion of the
impossibil-ity theorem, see Sen (1970).
7See Brekke et al. (1996).
8For simplicity,ywill be treated as a single variable rather
than a vector, and phenomena such as altruism and envy are disregarded. The model may be extended to cover publicly provided private goods, such as health care or education.
9I assume anonymity of social welfare evaluations in the
sense that if anyvi jandv
l
jare interchanged in Eq. (2.1), then
if ai=al , this is not allowed to affect Wj. This anonymity
assumption is less strict than others frequently used in the social choice literature (see Sen, 1977b). Here, using character-istics as a determinant when deciding what weight to give to someone’s well-being (e.g. by letting the well-being of small children count more than the well-being of adults) is allowed.
10Judgements are not necessarily correct in the sense thati
would agree to j’s judgement, i.e. one may have vi
i"v
i j.
Indeed, judgements made by two different persons may not be comparable at all, but individualjmust be able to comparevij
andvkj for anyi"k.
11This means that general equilibrium effects can be
b]jb0 iffW
Eq. (2.3) can alternatively be written
W
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 (Vj
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 ofKpieces of information regarding each project,
where 1BKB .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 jJ. 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 jJ 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?
13Kmay 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.
14Here, 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.
15In 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.
12Alternatively, 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 (Vj/(v
ij, for example, utilitarianism; however, some
knowl-edge may still be required to determine(nj/(x
To analyze this formally, define
Ui(b)=ui(xi(b),y(b)) (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
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 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:
(Vj
where Cj is a monotonously increasing function,
and
(Vj
(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 whoiis. 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 countless 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
17In the present model, every decision-makerjactually has two preference orderings, represented by Wj(b) and vjj(b).
These preferences may conflict in the sense that W
i(b)\
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.
16If one only requires arankingof projects, not a cardinal
measure ofDW j, then it is sufficient thatDW j=fj(DWCB),
wherefjis a monotonously increasing function. However, a
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 jJ). 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 his/her own views, and that this explained his/her 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.
18The survey was based on in-depth interviews with all 16
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,mNsuch that ginal income change is the same for everyone within the group, according to every decision-maker.19Identifying 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,
NBi(b)=xi(b)+[((ui/(y)/((ui/(xi)]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:
Here, gdenotes an equal welfare weight group, and G is the number of such groups. Further,
bg
j=((Vj/(v i
j) ((nj/(x
i), where ig, is the social
welfare weight attached by decision-maker j to marginal income changes for any given individual in groupg,ngis the number of members in group
g, while NBG(b)
=(1/ng)igNBi(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+15K,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 V(b):
V(b)={NB1(b), . . . ,NBG(b),DZ(b)} (4.3)
20AlliNare members of one and only one equal welfare
weight group each. If there is no individual m"i such that (4.1) holds, then individualiwill be the single member of her group.
21IfyandZare vectors withmandrelements, respectively,
the corresponding inequality isG+r5K.
19Note that decision maker j need not attach the same
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-welfariswelfaris-tic concerns must be left to the individual decision-maker’s discretion, he or she can evaluate this directly using his/her 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 setV(b) 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)), V(b) 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 (Vj/(v
i
and(Vj/(Zmust 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
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, ifG+25
K,23 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 gj
, the weight attached by decision-maker j to changes in the environmental good, is comprised partly by normative elements, ((Vj
/(v
i
j), and partly by the decision maker’s
attempts to judge others’ well-being,
22Land 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.
23Ify andZwere vectors withm andrelements,
((nj(x
i,y;ai)/(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 othmak-ers’ well-being may not be too well-founded.
The main difference of assumptions between the monetary value-based indicator set V(b) and the physical unit-based indicator set P(b) 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 (gj). 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 interpersocardi-nal 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 vj
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 V(b) 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 P(b) would then be preferred to V(b).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.
24If projects are non-marginal in the sense that subjective
5. Projects with simple income distribution effects
If the effects of a project are particularly sim-ple, aggregation of information becomes easier. Assume that a project is such that some individu-als pay exactly the same amount of money to implement the project. A group of people who pay the same (but who may be different in any other respect) will be called an equal payment
group.25
In that case, the change in social welfare due to projectb can be written as a weighted sum of the costs borne by each equal payment group, the change in environmental quality in physical units, and the change in the intrinsic value variable:
W
j(b,a)
= %
H
g%=1
[ng%x
g%
(b)bgj%]+gjDy(b)+
(Vj
(Z Z(b)
(5.1) Here, −x
g%
is the cost paid by each individ-ual in the eqindivid-ual payment group g%, b
g%
j
=
(1/ng%)ig%((V
j
/(v
i j) ((
nj
/(x
i) is the average
wel-fare weight attached by decision-maker j to indi-viduals in g%,n
g% is the number of members in g%,
while H5N is the number of equal payment groups.
Consequently, if the number of equal payment groups is small enough, then any decision-maker can evaluate the project based on knowledge of the costs paid by members in each group, physical unit data on the environmental change, and re-ports of changes in rights or any other intrinsic value variable. Formally, if H+25K, then the physical unit based indicator set
P%(b)={Dx1%
(b), . . . ,DxH%
(b), y(b),Z(b)}
(5.2) is a sufficient welfare indicator set for project b.
This indicator set is very similar to the indicator set P(b) described above. The main difference between them is the way groups are identified.
The criterion used in P%(b) is straightforward to
observe, and no restrictions on decision-makers’ social welfare functions are required. Moreover, all subjective judgements concerning welfare weights are left to the decision makers themselves.26
As a particularly simple example, assume that everybody pays an equal amount of moneyDx(b) to increase the supply of the public good, meaning that H=1. In this case, the information set {Dx(b),y(b),Z(b)} is a sufficient welfare
in-dicator set for the project, consisting of only three information items. Based on this simple informa-tion, any decision maker can evaluate the project, even if there is substantial disagreement concern-ing welfare weights.
Can we also find a sufficient welfare indicator set, using the equal payment groups approach, based on monetary valuation? The answer ap-pears to be no: Under the equal welfare weight approach, monetary valuation could be used pre-cisely because of the restrictions imposed on wel-fare weights. Under the equal payment group approach, however, no such restrictions are im-posed, which implies that willingness to pay data cannot be aggregated without losing information that may be important for some decision-makers. Different welfare weights will generally imply that the marginal social value of the public good dif-fers between decision-makers. Hence, aggregation of environmental benefits measured in monetary units requires restrictions on welfare weights.
To illustrate this, consider the simple example above in which everybody pays the same amount to finance an increase in the public good supply. Assume further that there is no intrinsic value variable, that all decision makers accept willing-ness to pay as an ordinal measure of individual well-being, and that all decision-makers are utili-tarian. Thus, in this example, welfare weights may differ only to the extent that decision-makers have different beliefs about individuals’ marginal well-being of income. The welfare change due to such a project, according to j (see Eq. (2.4)), is:
26Note that althoughP(b) andP%(b) are said to be based on
physical units, this relates to the measurement of environ-mental effects; costs are measured in monetary units in both sets.
25Formally,iandmare members of the same equal payment
W
j(b,a)=% iN
(nj(x
i
!
x(b)+(nj
(y/ (nj
(x
i
y(b)
"
n
=%
iN
(nj(x
i
(NBi)
n
(5.3)This expression reveals that individuals’ net benefits cannot be aggregated without restrictions on welfare weights. Thus, without such restric-tions, a sufficient welfare indicator set reporting the environmental change in monetary units would have to include net benefit estimates for every single individual. This would presumably far exceed decision-makers’ information process-ing capacity. The indicator setP%(b), on the other
hand, would consist of only two information items ({x(b),y(b)}).
A common view seems to be that the economist should clarify the costs of proposed projects, while the task of judging whether the project is actually worth this cost should be left to policy makers. In the case of projects with simple income distribution effects as discussed above, all subjec-tive welfare judgements can indeed be left to policy makers. This requires, however, that infor-mation about the public good is reported in phys-ical units. If monetary valuation of the public good is to be used, the analyst cannot avoid making non-verifiable and possibly controversial assumptions about welfare weights.27
An example may help to clarify matters. In the interview survey among Norwegian Members of Parliament by Nyborg (1998) and Nyborg and Spangen (1996), respondents were asked to evalu-ate a hypothetical road investment project. One of the described effects of the project was a slight reduction in the bird population of a nearby protected bird habitat, but this effect was not valued in monetary terms. For simplicity, assume that this was the only environmental issue affected by the project, and that the benefits of the invest-ment project mainly concerned firms’ and work-ers’ earnings and thus could be counted along
with the project’s costs as part of individuals’ income change. Then, to calculate the indicator setsV(b) andP(b), one would first have to define equal welfare weight groups (in practice, the best one can hope for is probably to identify groups with substantially less than average differences between welfare weights). For example, one may use criteria such as low, high or middle income, age, and geographical residence. The monetary-based indicator set V(b) would then consist of average net willingness to pay for the project for each of these groups, i.e. their income gain from having the road built, minus their share of the costs to build and maintain the road, minus their willingness to pay to avoid the reduction in bird population. In addition, if some policy-makers are concerned about future generations’ right to a pristine environment, the fact that a protected area is disturbed should be reported in addition. Regarding the physical unit-based indicator set
P(b), this would consist of average cost for each of the groups, i.e. their income gain from having the road built, minus their share of the costs to build and maintain the road. In addition, it would contain a physical unit measure of the expected reduction in the bird population, such as the number of species or the number of nesting birds; and here, too, the fact that a protected area is affected should be mentioned. The indicator set
P(b)% will be similar to P(b) except that one
would report monetary costs by equal payment groups rather than equal welfare weight groups. Again, one must probably in practice be satisfied with approximations. If the road is financed through general taxation, for example, it is difficult to know who really pays; the project may not necessarily lead to higher taxes, but can alter-natively lead to a reduction in other public con-sumption or transfers. As a rough approximation, one might assume that everyone pays the same small share of investment and maintenance costs, and then use estimated increased earnings due the new road to identify approximate equal payment groups. One may then report costs for several small groups particularly affected by the project, while most of the country’s population could be defined as one large equal payment group for which only a single average cost figure would be reported.
27If projects are non-marginal in the sense that welfare
Respondents of the Nyborg and Spangen (1996) survey reported different views on mone-tary valuation of the environment. Eight of the 16 interviewed politicians expressed skepticism to-ward monetary valuation of environmental changes, while two were clearly positive. The re-maining six did not express specific views on this issue. However, throughout the interview, valua-tion of other non-market goods was also dis-cussed (leisure time, statistical lives). Fourteen of the 16 respondents expressed skepticism towards monetary valuation of at least one non-market good. Two of these doubted that sufficiently accu-rate value estimates could be obtained, but nine had quite fundamental objections, for example, that certain goods ought not to be measured in monetary units at all, or that such money values appeared meaningless or just confusing.
6. Summary and concluding remarks
Providing input into a public debate is a funda-mentally different task than ranking projects ac-cording to a well-defined objective function. While the theory of cost-benefit analysis is mainly focused on the latter, there has been remarkably little focus in the economics literature on how to analyze public projects with the explicit purpose of contributing to a democratic decision-making procedure, taking normative disagreement explic-itly into account. The analyst’s problem in such contexts is to aggregate project information enough to make it understandable, but not so much as to convey information that is important to some decision makers’ welfare evaluations.
Aggregate net willingness to pay is definitely too aggregated information when there is norma-tive disagreement. Participants in a political de-bate cannot be expected to rank projects in accordance with this indicator, and it is quite possible that such estimates cannot assist them in their evaluations at all. This holds even if deci-sion-makers are both benevolent and rational, and even if they systematically judge individuals’ well-being in accordance with each individual’s ordinal preferences. Moreover, it might hold even if costless lump-sum transfers were feasible.
Valuing the environment in monetary terms is not essential for sound project evaluation. Of the three aggregated indicator sets identified in the present paper, two are based on environmental indicators measured in physical units rather than monetary values. Using physical unit information requires extensive subjective judgement by deci-sion-makers concerning effects on individuals’ well-being. However, this problem is only very partly solved by using the monetary value-based indicator set since this too requires judgement by decision-makers on cardinal and interpersonally comparable aspects of utility.
People sometimes worry about aspects of projects not directly related to individual well-be-ing, for example, religious concerns or fundamen-tal moral norms. Parts of what is frequently called existence value may fall into this category. A description of projects’ effects on such issues is part of any sufficient indicator set, but there is no reason to value this in monetary terms.
In general, it is impossible to rank projects without choosing which welfare weights to use. An important prerequisite for democratic debate, however, is that citizens are provided with infor-mation that is relevant even if they do not share a particular normative view. The need to separate positive from normative judgement may explain why physical unit indicators (such as m2 of
wilderness, or the ambient concentration of pollu-tants) appear to be more popular as tools for public debate about environmental policy than monetary benefit estimates.
If a decision is made through a political pro-cess, it is the decision mechanism itself, not the economic analysis, that gives its participants their power to judge and make decisions. If the as-sumptions of the analysis are incompatible with a decision-maker’s ethical or political views, she can simply choose to ignore it; and in that event, the economic analysis will certainly have little influ-ence. By taking care that the project analysis is relevant to individuals with a variety of normative views, one can at least give decision-makers the opportunity to base their political judgements on a sound factual basis.
ex-ample, one might want to calculate social benefits according to a wide range of social welfare func-tions (Dre`ze and Stern, 1987). Then, if the rank-ing of projects turns out to be robust to the choice of welfare weights, but some politicians still insist on another ranking, one can ask them to explain their choices publicly, which might facilitate voters’ evaluation of their performance. There is no inconsistency between such an approach and the framework presented above. However, before extending the analysis like this, one should make sure that politicians have been provided with sufficient project information to, at least, be able to make a well-founded evaluation.
Finally, a caution is in order. In this paper, I have considered conditions under which it is feasi-ble to provide sufficient welfare indicator sets. Some projects’ effects are undoubtedly too com-plex for this to be the case, for example, a whole range of environmental variables may be affected, not just one. The above analysis does not provide a recipe for what to do in such cases. Subjective judgement by analysts might then be unavoidable, and aggregate net willingness to pay cannot at the outset be excluded as a valuable indicator in such instances. A formal analysis of this, however, remains to be done.
Acknowledgements
I am grateful to Kjell Arne Brekke and Pras-anta Pattanaik for their helpful comments on earlier versions. Thanks also to Aanund Hylland, Rolf Aaberge, Jørgen Aasness, Victor Fuchs, Kenneth Arrow, Peter Hammond, and many oth-ers for discussions and comments on earlier drafts. Financial support was provided by the Norwegian Research Council.
Appendix A. Ranking of projects when welfare weights are not known
The proposition below and its proof was out-lined to me by to Prasanta Pattanaik. The respon-sibility for any errors is mine alone.
Assume that all decision-makers accept that utility, defined as revealed (or stated) choices, is an ordinal measure of well-being, so that condi-tion (3.4) applies. For simplicity, assume also that there is no intrinsic value variable. The super-script j is suppressed below since it is not needed for the argument.
Assume that the only information the analyst has is Dy(b),Dxi(b), as well as each individual’s
marginal rate of substitution between the public good and income, i.e.
(n(xi,y;ai)/(y]/[(n(xi,y;ai)/(xi
for all i=1, . . . , n. Define the relative welfare weight attached to i’s income,ti, as
ti=
((V/(vi) ((n(xi,y;ai)/(xi) %
n
m=1
[((V/(v
m) ((n(xm,y;am)/(xm)]
and i’s net monetary benefits of implementing project b as
NBi(b)=Dxi(b)+
(n(x
i,y;ai)/(y
(n(x
i,y;ai)/(xi
Dy(b)
for all iN and bB. The weighted sum of indi-vidual net monetary benefits, D, is then a mone-tary measure of project b’s effect on social welfare:
D(b,t)= %
n
i=1
tiNBi(b)
where t is the vector (t1, . . . ,tn).
A projectais said to weakly dominate a project
c if and only if NBi(a)]NBi(c) for all iN
(a,cB). Let us further assume that ti\0 for all
iN.
Proposition A.1. Assume that the only thing that is known about the social welfare weights is that
ti0,1 for all iN. Then, two projects a and c
can be ranked if and only if a weakly dominates c
or c weakly dominates a.
Proof: Assume that a weakly dominates c. Then,
NBi(a)]NBi(c) for every iN, which implies
n
i=1tiNBi(a)] n
i=1tiNBi(c), so D(a,t)]
To prove the ‘only if’ part, assume that neither of the two projects weakly dominates the other. Then, for some i,mN, NBi(a)\NBi(c) and
NBm(a)BNBm(c). Consider (t0
1, . . . ,t0n) such
thatt0i=1 and, for all k"i, kN, t0k=0 (that is,
all weight is given toi’s interests). Also, consider (t&1, . . . ,t&n) such that t&m=1 and, for all k"m,
kN, t&k=0. (Note that by assumption, neither
(t01, . . . ,t0n) nor (t&1, . . . ,t&n) are allowed as
vectors of social weights.) Then, it is clear that n
ists a vector of allowable social weights (t.1, . . . ,t.n) arbitrarily close to (t0
weights, project a is better than project c. Simi-larly, we can find a vector (t(1, . . . ,t(n) of social
weights which is arbitrarily close to (t&1, . . . ,t&n),
but such that t(i\0 for all iN, iNt(i=1, and
for which kNt(kNBk(c)\kNt(kNBk(a). For
such a vector of social weights, project cis better thana. Thus, if neither project weakly dominates the other, it is impossible to rank them without knowing anything about the relative social weights beyond their positivity. (Q.E.D.)
A special case is when for each project b,
Dxi(b)=Dxk(b) for all i,kN(costs are equal for
everyone). However, it is still perfectly possible to have two individuals i and ksuch that:
NBi(a)=Dxi(a)+
In that case, neither of the two projects is weakly dominated by the other, and the ‘only if’ part of the above proposition applies.
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