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A Rational Approach to Governmental
Decision Concerning Air Pollution
by
Howard M. Ellis
and
Ralph L. Keeney
OR -005-71
August, 1971
Rev. June, 1972
Abstract
This paper addresses a problem common to many government
agencies--trying to specify a regulatory policy that is in some sense
best for a given situation.
Such questions demand the consideration of
multiple conflicting objectives, non-repeatable uncertainties,
costs
and benefits accruing to various individuals, businesses, and
organizations, and effects which extend far into the future.
Here a
systematic approach--known as decision analysis--appropriate for
analyzing such problems, is illustrated.
The specific problem
involves determining the maximum legal sulfur content of fuels
burned in New York City.
From the point of view of a city administra-
tor, seven major objectives are identified for this problem.
These
include physical and psychological health effects on residents,
economic consequences to both residents and the City, and political
implications.
Measures of effectiveness are specified for each
objective, and the possible consequences of lowering the legal sulfur
content of fuels from one to 0. 37 percent in terms of these measures
of effectiveness are assessed.
Finally, the impact of this application
of decision analysis are described.
3.
1.
Introduction
In New York City, the mayor must decide whether to approve a pro-
posed major addition to Consolidated Edtison's electric-power generating
station in Astoria, Queens.
If this addition is approved,
City residents,
over the next several years, would be reasonably assured of receiving at
fair economic cost the growing quantity of electricity which they demand.
However, approval of the addition would lead to a further worsening of the
city's air quality, particularly in terms of the air pollutants sulfur dioxide,
particulates,
and nitrogen oxides.
Should this addition be approved?
In both Boston and New York City, the respective City Councils must
decide whether to pass legislation that would place stringent limits on the
sulfur content of fuels burned in the city.
If passed, the legislation would
lead to a definite improvement in the city's air quality--especially in terms
of the air pollutant sulfur dioxide.
However, passage of this legislation
would require residents to incur added annual costs for heating and electricity
to pay for the more expensive low-sulfur-content fuels.
Should these City
Councils pass such legislation?
In Washington, D. C., the U. S. Congress must decide whether to
establish very stringent emission standards for carbon monoxide, hydrocarbons, and nitrogen oxides for all motor vehicles manufactured and sold
in this country after January 1, 1975.
Establishment of these standards
would contribute toward improving our air quality.
On the other hand, they
would require the public to pay significantly more money for new automobiles.
Should Congress adopt these stringent standards?
4.
Each of these decision problems is faced presently or has been faced
recently by public officials.
Moreover, they are representative of a host of
similar problems that public officials are increasingly being asked to confront-namely, should government adopt a specific, proposed program intended to
improve the air quality.
With each, there is the additional question "What
should the air quality standard be?"
Due to the complex nature of these problems,
an individual finds it difficult to decide which, if any, of a series of proposed
air pollution control programs to support.
The purpose of this work is to describe how a public official, by using
the concept of decision analysis, :*' can obtain help in choosing an air pollution
control program.
To illustrate the method of analysis we focus on one specific
problem faced by one particular individual, namely the Mayor of New York City.
Obviously, we would not expect the Mayor of New York to spend his time working
on details of the air pollution problem.
It would be reasonable to expect members
of the Mayor's staff in the Environmental Protection Administration and the
Department of Air Resources to work on this problem.
These individuals and
the Mayor might then review the results and implications of such analyses in
formulating and supporting air pollution control programs for New York City.
Before beginning, we should make clear our views on the contribution of
this paper.
We do not claim to have the solution to any of the current air pollu-
tion problems, nor do we think decision analysis is the panacea for analyzing
*A brief introduction to decision analysis is given in the appendix.
details, the reader may refer to Howard[8] or Raiffa[18].
For more
proposed solutions to all of these problems.
However, when it is worthwhile
to examine the proposed policies in more detail than is currently done, we
think decision analysis is a useful approach.
Our work here is meant to be somewhat exploratory--an attempt to find
out if in fact decision analysis is useful for certain problems.
And as such,
our results and conclusions must be interpreted as preliminary.
We believe
they do represent a good basis upon which others can comment and critically
review.
This will hopefully begin a process of modification and improvement
of the work presented here.
1.1
Motivation for this Work
Three of the main reasons for the difficulty experienced by public
officials in selecting an air pollution control strategy are as follows:
1.
The official has several conflicting objectives,
such as improving air quality and limiting total
program costs, which he wishes to satisfy.
These
objectives must be identified and clearly defined.
2.
The extent to which any alternative program will
achieve these objectives cannot be precisely specified.
Said another way, there are inherent uncer-
tainties in the effectiveness of any proposed program.
3.
Because of conflicting objectives, the official is faced
with the complex task of deciding how much achievement on each objective he is willing to forego in order
to achieve specified amounts on other objectives.
That
_____I__
(O.
is,
the trade-offs between the conflicting objectives
must be considered.
Notwithstanding these complexities,
must still be evaluated.
air pollution control programs
However, it seems unreasonable to assume that a
busy public official has the facility or the time to process rationally all the
relevant information informally in his mind and then to come up with a responsible decision.
The alternative we suggest, decision analysis, is designed
to assist the official in examining proposed programs and analyzing their overall implications.
One would like the analysis to aid the public official in dealing with the
particularly difficult aspects of choosing an air pollution control program
identified earlier.
1.
The approach we suggest involves the following steps:
Structuring the decision problem.
This includes
identifying all objectives and selecting, for each
of these, a measure of effectiveness which can be
used to indicate the degree to which the objective
is met.
2.
Describing the possible consequences of each alternative program in terms of the effectiveness
measures.
Thus, the uncertainties associated with
the proposed programs are specified.
I ---_
11
7.
3.
Prescribing the relative preferences of the public
official for each possible consequence.*
Here, the
trade-offs among the conflicting objectives are
precisely identified.
4.
Rationally synthesizing the information from the
first three steps to decide which of the proposed
programs to support.
One will note that the first three steps correspond with the three main
difficulties identified in choosing among alternative air pollution control
programs.
This basic idea is then to break the problem into parts, which by
themselves are still quite complex but presumably easier than the entire
problem tackled as a whole; separately work on these parts; and then put the
parts together to make implications about the best course of action for the
public official.
Looking at the four steps above, a public official might say "But that's
the way I make all my decisions."
It may well be.
However, the distinction
between our approach and more traditional procedures is the degree of formality of each step.
For instance, with decision analysis, the uncertainties
are quantified using the subjective or judgmental probabilities and the official's
preferences are represented by utilities.
In step four, the best alternative
is that which has the greatest expected utility.
The difference between decision
*The public officials preferences are used since he or she usually has responsibility for the decision. In this paper we skip the issue of whether the
official's preferences are appropriate for accounting for the public's
preferences. Presumably, they are influenced in part by the perceived
preferences of the constituency which the public official serves.
____
___1_
-LIIIII_-__-_--·
^___
n^___l
_-------L--·--CI-I
_I
_II_
__
1
111
1
_
8
analysis and the current approaches for choosing an air pollution control
program are discussed in more detail in section three.
1.2
Outline of the Paper
A brief overview of the air pollution control problem in New York
City is given in section two.
The specific problem which we use for our
discussion in the rest of the paper is also introduced.
Section three is concerned with identifying objectives and selecting
an adequate measure of effectiveness for each of these.
The end result is a
set of objectives and associated effectiveness measures for the analysis of
our decision problem.
These concern the physical (health), economic, and
psychological well-being of the residents of New York City as well as costs
to the government and the political implications of each program alternative.
In section four, the methods which were used to describe the possible
consequences of each alternative program in terms of a probability distribution over the measures of effectiveness are discussed.
Then, in the fifth
section, we indicate how the public official can decide with some conviction
which of the program alternatives he prefers.
A few remarks on the impacts of the results of the study on which this
paper is principally based are given in section six.
Our conclusions are
presented in section seven.
2.
The Air Pollution Control Problem of New York City
A general model of the process by which air pollution control programs
are designed and evaluated is shown in Fig. 1.
This main problem with the
control process as it is now practiced is that the outputs are not considered
much in choosing air pollution policy.
The reason is,
of course, the complexities
19,
___
INPUTS
_
_
_
POLLUTION PROB LE M
OUTPUTS
Air Pollution
Emissions
Adverse effects
on residents
Standard of living (e. g.,
demand for electric power)
~~~~~.,
N/
weathe r
Air Pollution
Concentrations
air pollution control
technology
Adverse effects
on the City's
economy
I
Current air pollution programs and legislation
_
____
_
.
_
_
.
_
Measurement
of Air Pollution
Concentrations
.J
4
CONTROL .
Proposed Air
Pollution Control
Legiiation ardA
Programs
,I
-l
lation a
prorow
.-
_
1
K
i
existing air pollution control legis-
C-
)
availability of government funds
direct program costs
--
priority of an air
pollution control program relative to other
government programs
Fig. 1.
Note:
.
the arrow
symbol ---reads
I"influence s"
A General Model for Evaluating
Air Pollution Control Programs
1-11111_1-
1
-_
.
lo.
indicated in the introduction:
the difficulty in defining output measures,
establishing the relationships between pollution concentrations and these
measures, and specifying preferences for the various possible outputs.
As a
substitute for this information, the public official must rely on the measured
air pollution concentrations.
In a sense., the process can be thought of as
Thus, the current deci-
being short-circuited at the dashed line in Fig. 1.
sion-making process excludes the most important information necessary for
rational control.
Our efforts are meant to eliminate the short-circuit and
bring the outputs into the decision-making process.
The Sulfur Decision Problem
A survey of air pollution problems and current air pollution control
programs in New York is given in Eisenbud[3].
In 1970 major decisions still
to be made in New York City's air pollution control program included those
concerning the control of sulfur dioxide.
Table 1 presents a breakdown of the
estimated 1972 emissions of sulfur dioxide from sources within the City.
These estimations account for all provisions of existing laws enacted through
mid- 1971.
Table 1: Estimated 1972 Emissions of Sulfur
Dioxide in New York City[1 6 ]
Source of Emissions
Emissions of Sulfur Dioxide
(per cent of total)
tons
Incineration of refuse
Motor vehicles
Industrial processes
Space heating
Power generation
2,500
20,400
9,900
195,300
169,500
TOTAL
397, 600
(0.6%0/0)
(5.15)
(2.5%)
(49.2%)
(42.6%0)
(l00. 0%)
II.
Since over ninety per cent of these emissions arise from the burning
of fuels for space heating and power generation and since the only current,
practical way to reduce emissions from these sources is to lower the sulfur
content of the fuels burned, clearly one major decision still faced by the City
with regard to its air pollution control program is the "sulfur decision problem."
That is,
the decision on whether and how much to lower the legal limit on the
sulfur content of fuels burned in the City below the present legal limit of one
per cent.
In what follows we will use the sulfur decision problem to illustrate
the proposed methods for analysis.
3.
Specification of Objectives and Measures of Effectiveness for the Analysis
In this section we specify what we believe is a reasonable set of objec-
tives and measures of effectiveness for an air pollution control program in
New York City.
The discussion begins with a presentation of objectives
currently in common use by public officials.
These are rejected as inadequate,
and an alternative set of objectives are suggested.
The final result is seven
objectives and measures of effectiveness which are used to describe the consequences of each of the alternative courses of action.
3.1
Inadequacy of the Objectives Currently Used by Public Officials
One might understandably ask why so much effort is being devoted to
specifying objectives for an air pollution control program.
Surely with all
the experience certain public officials have had with such problems, the
objectives must be well known ......
mustn't they?
Table 2 indicates the
kinds of objectives and measures of effectiveness principally used in making
policy relating to air pollution control programs.
12.
Table 2: The Objectives and Measures of
Effectiveness Currently Used by
Public Officials in the Analysis
of Air Pollution Decisions
Objective
Associated Measure of Effectiveness
1.
Improve air quality
Citywide concentrations of air
pollutants
2.
"Minimize" the costs to
the City government of
improving the air quality
Direct costs to the City government
3.
"Minimize" the costs to
City residents of improving the air quality
Direct costs to City residents
The main problems with this set of objectives and effectiveness
measures can be illustrated by the following.
Almost any public official
will state his primary objective in decisions relating to air pollution is to
improve air quality.
Of course, air quality per se is of very little, if any,
concern to the official.
What is of concern are the fundamental human
benefits to his constituency and the direct and indirect costs that result from
a given air quality.
Air quality, as measured by pollutant concentration
levels, merely serves as a convenient, but inadequate,
fundamental benefits and costs.
proxy for these
And only when the public official begins
grappling with such basic questions as "How much should we improve air
quality?" or "Should we spend $X of government money to reduce emissions
of air pollutants by Y per cent?" does the inadequacy of the traditional objectives and their associated measures of effectiveness become
__________11_1_1l1l____lll._L-_1111
__
-1·11111-
1-_11
1_
apparent.
Il^_--CIII II
I --CIIII
_
13,
What the public official needs for choosing among air pollution control programs is a much clearer understanding of how each of these alternatives affects the fundamental human benefits and costs of concern to him.
Whether he uses this understanding explicitly or implicitly in the subsequent
analysis is not important at this point.
What is important is that he under-
stands as clearly as possible the package of fundamental benefits and costs
associated with each alternative in his decision problem so that he has a
meaningful basis for making a responsible decision.
To provide this meaningful basis, it is necessary to move behind the
traditional objectives used by public officials and ask what really is of concern to the official.
In other words, what are his true objectives related to
the air pollution problem.
3. 2
Identification of Major Objectives
in almost every decision problem faced by the Mayor of New York
City, his most fundamental objective is to improve the well-being of his
constituents.
However, one must spell out in more detail what is meant by
this objective as it pertains to air pollution.
Precisely what would the Mayor
like to accomplish by his actions in the air pollution area?
After some
serious thought, and evolutionary process led us to divide the overall objective
into five major objectives:
1.
Decrease the adverse effects of air pollution
on the health of New York City residents.
2.
Decrease the adverse economic effects of
air pollution on the residents.
____
--------1_111
tAD
3.
Decrease the adverse effects of air pollution
on psychological well-being of the residents.
4.
Decrease the net costs of air pollution to the
city government.
5.
Achieve as desirable a political "solution" as
possible.
These objectives require little justification.
However, it should be
noted that the second objective is meant to include costs of the air pollution
control program in addition to the costs due to the pollution.
Concerning the
fourth objective, net costs include all the direct costs, such as the costs of
an air pollution control program, as well as indirect costs such as those due
to migration of businesses and industry from the city, less tourism, and tax
revenue losses due to workers in the city who miss work, etc., due to sickness
caused by air pollution.
A problem remains as to whether these five include all the issues of
importance to the Mayor.
For instance, nothing has been said about the
economic consequences of the various alternatives on New York State, on the
Federal government, on businesses, or on non-residents of New York City.
Furthermore, no mention is made about the benefits of improved air quality
to non-residents.
Should these factors be included in a complete analysis of
proposed air pollution control programs?
I5.
The Mayor is certainly not indifferent about the varying impact of
alternatives on such factors.
However, note that some aspects of these
consequences, such as economic effects due to tourism and businesses
moving to the city, are included in the objective "decrease the net costs of
air pollution to the city government."
In view of this, it seems unlikely that
explicit consideration of any of these in the analysis would alter the optimal
strategy.
Therefore, based on our judgment, they are excluded from the
list of objectives.
Again we must mention that after a preliminary analysis,
the reasonableness of such exclusions needs to be re-examined.
The same type of considerations lead us to exclude from the analysis
an objective concerned with the benefits to non-residents from any air
pollution program.
The case can also be made that since these benefits are
probably highly correlated to the benefits to residents, in some sense the
interests of non-residents are implicitly taken into account via the benefits
to residents.
3.3
Assigning Measures of Effectiveness to Each Objective
In this subsection, we identify measures of effectiveness for each of
our objectives.
Each measure of effectiveness takes on values or amounts,
often numerical, which should unambiguously indicate the degree to which the
associated objective is achieved.
Health Effects on Residents
Several possible measures of effectiveness immediately come to mind
for the objective "decrease the adverse effects of air pollution on the health
of residents."
These include the annual number of deaths attributable to air
pollution, the annual number of man-days of morbidity attributable to air
pollution, and some subjectively assessed health index that includes consideration of both morbidity and mortality.
Important objections can be raised against each of these.
The annual
number of deaths attributable to air pollution does not account at all for what
is believed to be the more prevalent effect of air pollution on health--namely,
its effect on morbidity.
Similarly, the annual number of man-days of morbidity
does not account at all for the extremely serious effect of air pollution on health
in terms of mortality.
Thus, it seems clear that no single measure of effectiveness, aside
from possibly a subjective health index, can be identified for this objective.
However, because such an index lacks a physical interpretation, we chose the
alternative of specifying the major objective in more detail.
Thus, health con-
siderations were divided into two detailed objectives, "decrease mortality" and
"decrease morbidity."
For the first of these, two of the possible measure of effectiveness are
the "annual number of deaths attributable to air pollution" and the "per capita
increase in the number of days of remaining lifetime due to improved air
quality."
The first equally weighs the death of an old person and the death of a
child, whereas the second measure weighs the death of a young person more
heavily.
Since we believe this latter more adequately describes the impact of a
program alternative with respect to "decrease mortality," the latter measure
was chosen.
For the objective "decrease morbidity," the "per capita decrease in the
number of days of bed disability per year due to improved air quality"
...-..--l__ilXII1---s---_11·--·(·-
1-1_11 -----·
-
17.
was chosen as the measure of effectiveness.
Obviously, this does not in-
clude such effects as sore eyes which would not render one to a bed.
Part
of the consequences of sore eyes is psychological, which can be accounted
for by the third major objective.
However, the physical aspects of sore eyes
intuitively seem important enough to be formally included in the analysis.
To
do this we would suggest calibrating a number of days of bed disability per
year which one would feel is equivalent to having sore eyes for one day.
Then for each program alternative, the effects due to sore eyes would be
included in the analysis by either adding or subtracting an "equivalent number
of bed-days disability" to our measure of the degree to which "decrease
morbidity" is met.
Economic Effects on Residents
No single measure of effectiveness could be identified for the objective "decrease the adverse economic effects of air pollution on residents of
New York City," because the Mayor would likely differentiate between the
economic impact on low-income residents and the economic impact on other
residents.
But from the preceding discussion a solution to this problem should
be evident.
Clearly, a breakdown of the economic effects on low-income and
other residents is required.
This is done and "per capita annual net cost to
residents" is used as the measure of effectiveness for each group.
Psychological Effects on Residents
There seems to be no direct measure of effectiveness for the objective "decrease the adverse effects of air pollution on the psychological
8.
well-being of the residents."
One way to handle this problem would be to
define some subjective index.
It might be possible to interview residents
and ascertain their feelings toward various levels of air quality.
But a
simpler approach, which seems reasonable, would be to use the daily concentration of sulfur dioxide as the measure of effectiveness for "psychological
well-being.""
Since this pollutant can easily be detected both visually and by
breathing, it seems reasonable to assume "psychological well-being" is
closely related to the concentration levels.
Economic Effects to the City
The fourth objective,
"decrease the net costs of the air pollution
control program to the City government," has the obvious measure of effectiveness "annual net costs."
direct and indirect costs.
As mentioned previously, this includes both
Although, for some decisions, annual net costs
may vary from year to year, these variations are not likely to be significant.
If a large year-to-year variance is expected, the Mayor or his staff might
need to synthesize something like an equivalent net annual cost.
Political Implications
The fifth objective, "achieve the best political solution to the air
pollution problem," has no nice objective index which indicates the degree to
which this objective is met.
In fact, the index for this objective will have to
be a subjective index if it is to be at all realistic.
be included in measuring the index,
Many considerations must
such as the possibility of court suits
*It is important to emphasize that this concentration level is to be viewed as a
proxy for psychological well-being only and not for the other objectives.
I9.
brought by landlords or home-owners who are forced to pay higher fuel
prices for heating, the Mayor's relations with the City Council and with
Con Edison and with any of the political groups in the city, and the support
of the general public for various program alternatives.
These will all have
a potential effect on the Mayor's political future which also should be taken
into account.
Obviously, many political factors not mentioned here are also
impo rtant.
The analyst can arbitrarily scale the subjective index in any convenient way.
He could choose three levels of political implications such as good,
bad, and in-between.
these.
Then each program would be associated with one of
Or he could arbitrarily scale the index from zero, representing the
worst political solution, to ten, indicating the best political alternative.
Each program alternative would then be assigned a number from zero to
ten, the higher numbers indicating better political implications.
A discus-
sion of subjective indices and subjective scaling techniques can be found in
Green 7].
3.4
The Final Set of Objectives and Measures of Effectiveness
As a result of the process spelled out in this section, a set of objec-
tives and their associated measures of effectiveness for choosing an air
pollution control program for New York City were identified.
These are
presented in Fig. 2.
Of course, there may be important objectives of which we are unaware, and consequently omitting from the analysis.
However, if one cannot
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identify such omissions before utilizing the implications of the analysis, it
is safe to assume the same omissions would have occurred if any less formal
procedure for guiding the decision making process were followed.
And thus,
at least-in this respect, we can conservatively conclude that we are no
worse off using decision analysis than not.
But, as we mentioned at the
beginning of this paper, our intent is to provide a first step toward investigating the usefulness of decision analysis in governmental decision-making.
The results are meant to provide a basis for further discussion, modification, and improvement.
2z.
4.
Describing the Consequences in Terms of a Probability
Distribution Over the Effectiveness Measures
As we discussed at the beginning of this paper, one cannot specify
precisely the effects of any of the program alternatives.
There are un-
certainties about the degree to which each objective will be achieved by any
particular program at the time the choice of an alternative must be made.
Thus for each alternative strategy, one must assess a probability distribution
over. the seven measures of effectiveness which quantifies the decision maker's
judgment about the extent to which the objectives will be met by that particular
program.
His final decision then involves choosing which probability distri-
bution represents the preferred situation.
Since we will be discussing a probability distribution over seven
effectiveness measures, we must define some notation.
A small letter x.
will represent a specific amount of effectiveness measure X., which are
defined as follows:
X 1 - per capita increase in the number of days of
remaining lifetime,
X2
per capita decrease in the number of days of
bed disability per year,
X3
per capita annual net costs to low-income
residents,
X
4
-per
capita annual net costs to other residents,
X 5 =daily sulfur dioxide concentrations in parts per
million,
23.
X 6 -total annual net cost to the City government,
X 7 -subjective
index of political desirability.
The joint probability distribution which we wish to assess will be designated
as fX (x)
fX (
x 2,
. . ,
X7)' where the Xi can be thought of as random
variable s.
4. 1
The General Assessment Scheme
The basic strategy for assessing any probability distribution is to
fully utilize all the relevant information available to the decision maker.
In
the case of air pollution control, a growing body of literature exists on the
subjects of
1.
the relationship between air pollution emissions and air pollution concentrations [12, 131,
and,
2.
the relationship between air pollution concentrations over time and its adverse effects on
the physical, economic, and psychological
well-being of people
1, 2, 6, 14, 15].
Because this information is available and because the levels of air
pollution emissions conditional on any program alternative can be predicted
with almost complete certainty, the following steps are suggested as the
assessment scheme:
1.
Predict the certain level of air pollution
emissions conditional on each particular
program alternative.
24.
2.
Assess the probability distribution of air pollution concentrations Q conditional on the given
level of emissions.
3.
Call this fQ ().
Assess the probability distribution for X conditional on each level of air pollution concentrations.
4.
Label this fQ
(x/q).
Calculate the joint probability distribution
f (x,g), from which you get the marginal distribution fX' (x) conditional only on a particular
program alternative.
Techniques to make this scheme operational are considered in the following
subsection.
4. 2
Simplifying the Assessment Procedure
It is a fact that the difficulty of assessing a probability distribution
increases rapidly as the number of variables increase.
And also, not
surprisingly, the amount of work required in an assessment scheme is
directly related to the number of separate assessments required.
With this in mind, there would appear to be three major obstacles in
the general assessment scheme which was suggested.
First of all, the
quantity Q has not yet been specified and could involve several variables.
Secondly,
step three above could possibly involve the assessment of an
infinite number of conditional probability distributions since there may be
an infinite number of Q levels.
And finally, each function fXQ is itself a
seven-variable probability distribution.
Let us consider these obstacles
one at a time.
We have defined Q as air pollution concentrations.
In the sulfur
decision problem, the only pollutant whose concentrations depend on the
program alternative is sulfur dioxide.
Hence the quantity Q need only
summarize sulfur dioxide concentrations, and Q can be defined as the daily
concentration of sulfur dioxide.
Recent research has indicated that the log
normal family of probability distributions--a two-parameter family--provides
an excellent fit to empirically observed cumulative frequency distributions
for daily concentrations of sulfur dioxide.[12,13]
Concerning the problem that there may be an infinite number of conditional distributions f/Q
it appears reasonable to organize the possible
values of Q into approximately ten regions such that it is appropriate to
assume fX/Q does not vary over any particular region.
To simplify the assessment of the seven-variable distribution fX/Q
we would exploit the properties of probabilistic independence that exist
among the effectiveness measures X conditional on any particular Q.
Based
on reasoning which is discussed in great detail in Ellis[4], it was concluded
that the groups of effectiveness measures {X1}, {X}, {X7}, and {X2X3,X4,X 6 }
would be conditionally mutually probabilistically independent.
Thus fX/Q can
be evaluated using
fX/Q (x/q) = f(x
1 /q)
f(X
5 /q)
f 7 (x 7 /q) fo(X2 ,x
3 ,x 4
,x
6
/q)
where fi, i = 1,5, 7 are conditional probability distributions over Xi given q
and where f
q.
is a joint probability distribution over X 2,X
3 ,X 4 ,
and X 6 given
The single variable distributions can be assessed using techniques such
as those described in Pratt, Raiffa, and Schlaifer[17].
Then f
0
is assessed
using
f (2'x
3
x
4
x6/q) = f2(x 2 /q) fe(X3 x 4X
6 /q2.
To obtain f , which has three economic variables, the factors, such as fuel
e
prices and sick days, which would influence these economic variables are
first identified.
Then the relationships between X3,X
influencing factors are specified.
4
, and X 6 and these
Finally probability distributions over the
influencing factors are assessed, and a Monte Carlo simulation used to obtain
f
e
4.3
Results of the Assessments
To briefly indicate one of the results of the assessment of fx, we
present an upper bound and lower bound on the possible values of each effectiveness measure for the program alternative in the sulfur decision problem
of lowering the legal limit on the sulfur content of all oil and coal burned in
New York City to 0.37 and 0.7 per cent, respectively.
These values are
measured relative to the alternative of continuing the current situation which
permits burning fuels with a maximum of one per cent sulfur content.
The
results are given in Table 3.
As one illustration of how these results were calculated, consider the
upper bound on effectiveness measure X 2 .
As Table 3 indicates, this measure
specifically represents the .99 or larger fractile of the probability distribution
Z7
Table 3:
Range of Possible Effects of Reducing the
Maximum Legal Sulfur Content of Oil and
Coal Used in New York City from the
Present 1.0 Per Cent to 0.37 Per Cent for
Oil and 0.7 Per cent for Coal
Effectiveness Measure
Upper Bound':
74.2
Lower Bound*'
Unit of
Measurement
0.0
days
0.0
days
X1:
per capita increase
in the number of
days of remaining
lifetime
X2:
per capita decrease
in the number of
days of bed disability per year
X3:
per capita annual
net cost to lowincome residents
+$3.83
- $8.42
dollar s
X4:
per capita annual
net cost to other
residents
+$3.83
-$9.57
dollars
X:
daily sulfur dioxide
concentrations in
the city
0.33
0.01
X 6:
total annual net cost +$4,499,000
to the City government
X7:
subjective index of
political desirability
0. 224
10
-$2,000,000
0.0
parts per
million
parts of air
dollars
--
':The upper bound was assessed as the 0. 99 or Larger fractile conditipnal on
having the best possible. The lower bound air quality was used as the 0.01
or smaller fractile conditional on having the worst possible air quality. This
upper and lower bound in effect provide a practical range of possible values
for each effectiveness measure in the sulfur decision problem.
28.
for X 2 conditional on having the best air quality possible in the sulfur decision
problem.
The best and worst possible air qualities are described by log normal
cumulative frequency distributions of daily SO2 concentrations.
These fre-
quency distributions are in turn determined from the predicted SO 2 emissions
conditional on having 0.3770 and 0.7% legal limits instead of 1.0% legal limits
on the sulfur content of oil and coal burned.
The best possible air quality in
the sulfur decision problem has a log normal frequency distribution with the
following parameters:
0.5 fractile = 0.049 parts SO 2 per million parts air (ppm),
0.99 fractile = 0.153 ppm.
The worst possible air quality has a log normal
frequency distribution with the following parameters:
0.5 fractile = .096 ppm,
0.99 fractile = 0.355 ppm.
The research literature indicates that five groups of New York City
residents are candidates for decreased bed disability from having this best
instead of worst air quality. For each of these groups, the relationship between
daily SO 2
concentrations and morbidity leading to bed disability was reviewed
to develop assessments of the decrease in bed disability days. A summary of
results is presented in Table 4.
Assessment of the upper and lower bounds for the other effectiveness
neasures involve extensive assessment schemes that are discussed in detail
in [41.
Table 4: Upper Bound on X
Population Group
Chronic bronchitis and
over 54 years old
Chronic asthma and
over 14 years old
Emphysema and its
outward symptoms
Chronic heart disease and over 18
years old
Those who may be
subject to acute
respiratory illness
Total
Population of N.Y.C.
Upper Bound
on X 2
Estimated
Number of
N. Y.C.
Residents in
This Group
-9
2
Upper Bound on DeMain Research crease in Annual Bed
Results Used
Disability by Having
to E stimate
Best Instead of Wor st
Increased Bed Possible Air Quality
Disability
(in man-days)
33,891
a,b,c
74,618
d,e,
50,194
f,g
259,503
813,070
h,j
823,233
7,781,981
175,200
93,275
k,m,n
(1,741,958)/(7,781,981)
=
390,747
1,741,958 man-days
7,781,981
0.224 days
a.Carnow,B.W.,M.H.Lepper,R.B.Shekelle,and J.Stamler, "Chicago Air
Pollution Study," Archives of Environmental Health, Vol. 18,No. 5,May, 1969.
b. Petrilli,F.L.,et al., "Epidemi ologic Studies of Air Pollution Effects in Genoa,
Italy," Archives of Environmental Health, Vol. 12, June, 1966.
c.Glasser,M.,Greenberg, L.,et al.,"Mortality and Morbidity During a Period of
High Levels of Air Pollution, New York, Nov.23-25,1966," Archives of Environmental Health, Vol. 15,pp. 195- 198, December, 1967.
d.Booth, S., et al.,"Detection of Asthma Epidemics in Seven Cities," Archives of
Environmental Health, Vol. 10, No. 2, pp. 152- 155,1965.
e.Greenberg,L ., and Field, F., "Air Pollution and Asthma," Journal of Asthma
Research,pp.195-198,1965.
f.Motley,H.L., Smart,R.H.,et al.,"Effects of Polluted Los Angeles Air on Lung
Volume Measurements ,"J .A.M.A., Vol. 171, No. 1, pp. 1469- 1477,1959.
g.Ishikawa,S.et al.,"The Emphysema Profile in Two Midwestern Cities in North
America,"Archives of Environmental Health,Vol.18, No.4,pp.660-666, 1969.
h.Greenberg,L.,et al.,"Air Pollution and Morbidity in New York City,"J.A.M.A.,
Vol .182, October 13,1962.
j.Shephard,R .J ., et al., "Correlation of Pulmonery Function and Domestic Microenvironment,"Journal of Applied Physiology, Vol. 15,pp.70-76,January, 1960.
k.Winkelstein,W., et al.,"Respiratory Symptoms and Air Pollution in an Urban
Population of Northeastern U.S. ,"Archives of Environmental Health, Vol. 18,
May, 1969.
m.Douglas,J.W.B.and Waller,R.E., "Air Pollution and Respiratory Infection in
Children,"British Journal of Preventive and Social Medicine,Vol.20,No. 1,
pp.1-8,1966.
n.Lunn,J.E.,et al.,"Patterns of Respiratory Illness in Sheffield Infant Schoolchildren," British Journal of Preventive and Social Medicine,Vol.21,No. 1,
pp.7-16,1967.
5.
Assessing Preferences for the Program Alternatives
Once the consequences of each program alternative are described in
terms of a probability distribution over X, the decision of choosing an air
pollution control program consists of determining which of these probability
distributions is preferred.
With multiple effectiveness measures, there is
little chance that the decision maker can make this choice directly with any
degree of conviction.
The problem is systematized using utility theory,*
which requires the decision maker to quantify his preferences with a utility
function assessed over the measures of effectiveness and then to use expected
utility as the criterion for choosing among program alternatives.
To simplify
the assessment of the utility function over the seven effectiveness measures,
the concept of utility independence, discussed in Keeney[9, 10], was exploited.
Based on the utility independence assumptions--made in the manner in which
we would expect the Mayor of New York to make them, based on discussions
with staff members in the Department of Air Resources--the assessment of
the complete utility function over X was reduced to the following:
1.
Assessing seven one-attribute utility functions,
one over each effectiveness measure, and
2.
Assessing eighteen scaling constants to insure
the seven utility functions are properly scaled.
*A brief introduction to multiattribute utility theory is in the appendix.
Fishburn[5] and Raiffa[9] have more details.
1.
Appropriate techniques for performing each of these tasks are found in
Schlaifer[20].
No assessments of the utility function have yet been completed, although
details of the assumptions made and the procedure to follow in these assessments are given in Ellis[4].
6.
Impact of this Work
A summary of the end results of applying the above methodology
follows.
Because of the preliminary nature of this effort, we cannot report
any dramatic impacts which are clearly consequences of this work.
However,
we believe the ideas and results expressed in this paper have had some influence on the thinking of individuals responsible for air pollution control
programs in New York City.
The following events have occurred; however,
no claim is made concerning causality.
The results of this work including Table 3 concerning the range of
possible effects of a program which lowered the legal limits of oil and coal
used in the city from the present one per cent to 0.37 and 0.7 per cent respectively, were made available to the New York City Environmental Protection
Administration, which was in the process of preparing a new air pollution
control code for the City.
This group included, as one of the key provisions
in its recommended code to the City Council, a program which is essentially
the same program as the one we discussed.
32.
These same results, as well as the methods of analysis upon which
these results are based, were presented in testimony before the New York
City Council in its legislative hearings on the proposed new air pollution
control code.
Finally, the basic methods of analysis developed in this study--especially
those concerned with identifying objectives and effectiveness measures and
assessing probability distributions--were discussed with program planners
at the Environmental Protection Administration, and it is believed these
discussions will have some impact on the way programs for environmental
protection are planned and evaluated.
7.
Conclusions
Based on the above experiences with applying the methods of analysis
proposed in this study, we believe the following conclusions can be reached:
1.
To determine which course of action he really
prefers in decisions concerned with air pollution and other aspects of environmental quality,
the public official requires a much better description than he now receives of the consequence of each course of action in terms of
the fundamental human benefits and costs of
real concern to h.m in these decisions.
2.
Decision analysis is a potentially useful concept which would likely improve aspects of the
-- -----
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e-
33,
governmental decision-making process.
It could
be implemented in many areas, of which air pollution control is one example.
One important con-
tribution of decision analysis is that it often serves
as a learning experience for those attempting to
utilize it.
If the analysis is well documented, one
could expect that flagrant errors would be eliminated as critical experience is accumulated.
3.
Because the decision analysis approach for choosing
program alternatives differs so much from traditional
approaches, a great amount of effort and positive results will be needed to convince public officials of the
virtues of decision analysis.
It is especially important
to gain experience with using this approach.
As support for the first two conclusions, we can refer to section 6.
However, one should not erroneously think decision analysis is the panacea
to our governmental decision problems, but the approach is promising and it
could significantly contribute to improve decision-making.
And it should go
without saying that a poor analysis will lead to poor results.
Therefore, the
consumer of decision analysis must appropriately scrutinize the assumptions,
the analysis, the results, and the implications of any such studies.
Concerning our third conclusion, the public official finds the decision
analysis process foreign, and is thus skeptical of its implications.
--1111_111---·1111
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X
34-.
are many reasons for this.
However,
since these reasons apply to essen-
tially all public decision-making rather than specifically to decisions involving air pollution control, we will not discuss them here.
One point of
view on the role of decision analysis in public decision-making and problems
inhibiting its use is given in Keeney and Raiffa [11].
It remains that public officials need to be convinced of the validity of
the decision analysis approach.
The best way to accomplish this is likely to
involve both an educational program on the foundations of decision analysis
and participation in decision analytic projects where a program alternative
must be chosen.
But, at the same time, a serious attempt must be made by
decision analysts to modify the procedures of decision analysis to conform
more to the traditional methods of decision-making now used.
As one sugges-
tive example to illustrate our point, rather than assess multiattribute utility
functions directly, the decision-maker may find it more intuitive to consider
trade-offs under certainty among effectiveness measures to reduce the
dimensionality of the problem down to one.
Then a utility function could be
assessed over this one measure of effectiveness.
This should not change
any of the results of the subsequent analysis, but it may result in the
deci-ioi,-maker feeling more comfortable with the approach.
8.
Acknowledgment
We thank Professors Richard Meyer and Howard Raiffa of the
Harvard Business School who made substantial contributions to the dissertation [41 on which much of this work is based.
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References
1.
Brasser, L., P. Joosting, and D. von Zuilen, "Sulfur Dioxide-To What
Level I, II Acceptable," Research Institute for Public Health
Engineering, Report G-300, Delft, The Netherlands, July, 1967.
2.
Carnow, B. W., M. H. Lepper, R. B. Shekelle, and J. Stamler,
"Chicago Air Pollution Study," Archives of Environmental Health,
Vol. 18, No. 5, May, 1969.
3.
Eisenbud, Merril, "Environmental Protection in the City of New York,"
Science, Vol. 170, November 13, 1970, pp. 706-712.
4.
Ellis, Howard H., "The Application of Decision Analysis to the Problem
of Choosing an Air Pollution Control Program for New York City,"
unpublished doctoral dissertation, Graduate School of Business
Administration, Harvard University, 1970.
5.
Fishburn, Peter C., Decision and Value Theory, John Wiley and Sons,
New York, 1964.
6.
Glasser, M. L. Greenberg, and F. Field, "Mortality and Morbidity
During a Period of High Levels of Air Pollution, New York,
Nov. 23 to 25, 1966," Archives of Environmental Health,
Vol. 15, No. 12, December, 1967.
7.
Green, B. F., "Attitude Measurement," Chapter 9 in Handbook of
Social Psychology-Volume I: Theory and Method, ed. by
G. Lindzey, Addison-Wesley Publishing Co., Cambridge,
Massachusetts, 1964.
8.
Howard, Ronald A., "The Foundations of Decision Analysis," IEEE
Transactions on System Science and Cybernetics, Vol. SSC-4,
(September, 1968), pp. 211-219.
9.
Keeney, Ralph L., "Utility Functions for Multiattributed Consequences,"
Management Science, Vol. 18, No. 5, January 1972,pp.276-287.
10.
, "Multidimensional Utility Functions:
Theory,
Assessment, and Application," Technical Report No. 43,
Operations Research Center, M.I. T., October, 1969.
11.
, and Howard Raiffa,
"A Critique of Formal Analysis
for Public Decision Making," Chapter 5 in Analysis of Public Systems,
ed. by A. W. Drake, R. L. Keeney, and P.
v Morse, M.I.T. Press,
Cambridge, Massachusetts, 1972.
-'---1'1111111-1--111_
3(-
12.
13.
Larsen, Ralph I., "A New Mathematical Model of Air Pollutant
Concentration Averaging Time and Frequency," Journal of the
Air Pollution Control Association, Vol. 19, No. 1, January, 1969.
,
and Charles E.
Zimmer,
"Calculating Air Quality
and Its Control," Journal of the Air Pollution Control Association,
Vol. 15, No. 12, December, 1965.
14.
Lave, Lester B. and Eugene P. Seskin, "Air Pollution and Human
Health," Science, Vol. 169, August 21, 1970, pp. 723-733.
15.
Lawther, P. J., "Compliance with the Clean Air Act: Medical Aspects,"
Journal of the Institute of Fuel, Vol. 36, No. 271, August, 1963.
16.
New York City Department of Air Resources, "Emissions Inventory,"
1969.
17.
Pratt, John, Howard Raiffa, and Robert O. Schlaifer, Introduction to
Statistical Decision Theory, McGraw-Hill, New York, 1965.
18.
Raiffa, Howard, Decision Analysis: Introductory Lectures on Choices
Under Uncertainty, Addison-Wesley, Reading, Massachusetts,
1968.
19.
, "Preferences for Multiattributed
RM-5868-DOT/RC,
20.
Alternatives,"
the RAND Corporation, April,
1969.
Schlaifer, Robert O., Analysis of Decision Under Uncertainty,
McGraw-Hill, New York, 1969.
Appendix
Theoretical Concepts of Decision Analysis
This appendix will briefly discuss the basic concepts of decision analysis.
It is assumed that the decision maker must choose among alternative courses
of action. As a result of this choice, some consequence will eventually occur.
The approach assumes the desirability of any course of action should depend
on
(1)
the likelihoods of the various possible consequences resulting from that course of action, and
(2)
the decision maker's preferences for the various possible
consequences.
Both the likelihoods and the preferences are quantified in a manner which provides us with an operational mathematical method of choosing the best alternative using a logical calculus.
To be more concrete, suppose there are multiple objectives with
associated measures of effectiveness X1,X2, ..
X
Specific amounts of these
measures will be designated by xi, so using this notation, a consequence can be
designated by a vector (x I ,x 2 , .. .
,x ).
To quantify the likelihoods of the con-
sequences, for each alternative A., we need to obtain a probability density
function pj(x ,xZ, . .. ,x ),
(x,x
2,
u(x 1 ,x
2
.. .,x)
which indicates the probability any consequence
will occur given alternative A. is chosen.
The decision maker's preferences are quantified with a utility function
... ,x) indicating the desirability of any consequence (x i ,x2, ... ,x).
The utility function,which is assessed by asking the decision maker questions
about his preferences, has two important properties:
(1)
(x 1 ,x2, ... ,x ) is preferred to (x ,x, ... ,x' ) if and
1 2
n
n
only if u(x 1, ,
. ., x ) > u(xl, '
. . x), and
2
n
x
2'
n
(2)
A 1 is preferred to A2 if an only if E 1[U ] > E 2 [u],
of
where the notation E.[x] indicates the expected utility alternative A., which is
evaluated from
^
Ej[u] =
21u]
u(xx
1'
2
x
p (
'
,x ,
1( 2
.. x ) dxl dx
X nl
1'
.
dx
n
2.
Thus, once the probability density functions for each alternative and
the utility function are assessed, the expected utility of each alternative can
be calculated. The decision maker then should choose the alternative with
the highest expected utility. Note that decision analysis prescribes the best
course of action consistent with the decision maker's preferences and the
likelihoods of consequences occurring. It does not describe what in fact the
decision maker will do.