Hydrological Sciences-J'ournal-des Sciences Hydrologiques, 42(4) August 1997
531
Distributive fairness considerations in sustainable
project selection
SAM MATHESON
Department of Civil and Geological Engineering, Room 342 Engineering Building,
The University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6
BARBARA LENCE
Department of Civil Engineering, 2324 Main Mall, University of British Columbia,
Vancouver, British Columbia, Canada V6T1Z4
JOSEF FÛRST
Institute for Water Management, Hydrology and Hydraulic Engineering, University of
Agricultural Sciences, Muthgasse 18, A-1190 Vienna, Austria
Abstract This work develops general fairness measures that may be used as criteria
for sustainable project selection. Sustainable development, fair allocation objectives
and empirical distance-based measures of fairness, and their evaluation are discussed. Generalized fairness measures are developed and extended for both
intratemporal and intertemporal fairness comparisons. A preliminary application of
the extended distance based fairness measures is then performed for a case study of
the selection of an electricity supply project. The case study involves selecting
between a dispersed diesel energy supply and centralized energy supply with land
line energy distribution. Due to data limitations, the perceived fairness is measured
in terms of the annual energy costs per megawatt-hour that result from implementing
each alternative. The applied fairness measures indicate that intratemporal fairness,
in terms of the distribution of user unit costs, may be increased by choosing the land
line alternative and that there is no significant difference among alternatives with
respect to intertemporal fairness. These results provide limited insight into the
energy supply problem, however, and it is suggested that further analyses should be
conducted when information regarding the environmental impacts and reliability of
power supply for each of the alternatives becomes available.
Considérations d'allocation équitable dans la sélection de projets
durables
Résumé Ce travail définit des quantificateurs généraux d'équité pouvant être utilisés
comme critères de sélection de projets durables. Le développement durable, les
objectifs d'allocation équitable et des mesures empiriques d'équité fondées sur une
notion de distance ainsi que leur estimation y sont discutées. Des mesures d'équité
généralisée sont définies et étendues en vue de comparaisons d'équités tant
synchroniques que diachroniques. Une application préliminaire de ces mesures
d'équité généralisée a été réalisée dans une étude de cas concernant un projet
d'alimentation en électricité. L'étude de cas consiste à choisir entre une production
décentralisée utilisant des générateurs diesel et une production centralisée impliquant
un réseau de distribution. En raison du peu de données disponibles, la perception de
l'équité a été mesurée par les coûts d'énergie annuels par mégawatt-heure produit de
chacun des termes de l'alternative. Les mesures d'équité utilisées indiquent que la
meilleure équité synchronique, exprimée en termes de coût unitaire pour
l'utilisateur, est obtenue en choisissant la solution centralisée et qu'il n'existe pas de
différence significative entre les deux solutions en ce qui concerne l'équité
diachronique. Ces résultats ne fournissent toutefois qu'une vision limitée du
problème d'alimentation en énergie et des analyses plus approfondies devront être
réalisées lorsque des données concernant les impacts environnementaux et la fiabilité
des deux termes de l'alternative seront disponibles.
Open for discussion until I February 1998
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Sam Matheson et al.
INTRODUCTION
In the process of project selection and implementation, a best compromise solution
for a problem is often achieved by considering conflicting criteria, or objectives, and
after the project is implemented it may be modified as appropriate based on initial
impacts and additional information as this becomes available (United Nations, 1988).
Project selection criteria may consider economic, financial, biophysical and social
impacts of a given project alternative. Project-related impacts may be either benefits
or costs. Simonovic et al. (1995) recently identified three additional criteria for
including sustainability in project selection. These are: intergenerational equity,
project and impact reversibility and risk management over time. While common
project selection criteria such as economic efficiency are widely applied, applications
of project selection based on equity, or fairness, are less common. This paper
develops intratemporal and intertemporal fairness criteria for project selection. These
criteria are examined in a preliminary application to a case study that evaluates
alternative electrical power supply technologies required to meet the 40-year load
forecast for seven northern Manitoba communities.
In civil engineering, in general, a project may be seen as an allocation of
different impacts that may originate during the construction and operational phases of
a project's design life, and may affect the biophysical, social and economic subsystems of a region. Impacts may persist after the project has been dismantled and
may also affect other subsystems in different regions and thus may be seen to act on
a local, regional, or global scale. An example in water resources engineering is the
construction of a structure which controls both spatial and temporal quantities of
surface water in order to harness the biophysical system's potential energy. The
spatial and temporal manipulation of surface water from its natural state may
distribute social, economic and biophysical impacts within the region that may be
seen as unfair by affected or interested groups of people.
Examples of project selection and evaluation, based in part on a fair distribution
of project related impacts, in water resources engineering and management science
include Brill et al. (1976), Cohen (1978), Sampath (1991) and McAllister (1976).
Brill et al. (1976) examine both efficiency and equity aspects of waste discharge
water quality management programmes for the Delaware Estuary. They define equity
as the equality of removal efficiencies among dischargers and use three different
distance-based fairness measures: absolute deviation from the mean waste treatment
level, the range between the maximum and minimum waste treatment levels and the
maximum of the waste treatment levels. Cohen (1978) discusses a multiobjective
river basin development plan for the Rio Colorado River in Argentina in which a
regional allocation objective function is formulated in addition to an efficiency
objective function. The regional objective function is to minimize the mean absolute
deviation of water withdrawals among four provinces in a region. Cohen (1978) also
mentions that, for this case study, the decision makers did not agree with a perfect
equality allocation objective nor did they reveal their preference for an alternative
fair allocation objective. Sampath (1991) employs Theil's Entropy Coefficient (Theil,
1967) to examine fairness in the distribution of access to irrigation water between
Distributive fairness considerations in sustainable project selection
533
agricultural groups in India. McAllister (1976) presents a theoretical framework to
evaluate fairness and efficiency for both delivered and nondelivered urban public
services to examine the implications of service size and service spacing alternatives.
He defines fairness as the degree of equality of service and operationalizes it by
comparing the standard deviations of the distances between service centres and
demand points.
Authors such as the Brundtland Commission (WCED, 1987), Young (1992),
Jacobs (1993) and Weiss (1995) state that sustainability requires consideration of the
fairness of impacts both on the present generation and on future generations.
Therefore, serious investigation of sustainable project selection should examine issues
related to the distributional fairness of project-related impacts both within and between
generations as perceived by groups of individuals. The intratemporal and intertemporal
distributional fairness criteria presented in this paper may be used in conjunction with
other criteria in a multiobjective framework to determine the relative desirability of
competing project alternatives. Although not considered in this work, other project
selection criteria that may be considered in such analyses include economic efficiency,
effectiveness, risk and reversibility. In the next section, basic concepts of sustainability
are discussed. This section focuses on elements of sustainable development that are
relevant to equity. In the third section, fair allocation objectives, empirical distancebased fairness measures, and the previous application of these measures to case studies
are presented in order to provide a foundation for the development of intratemporal and
intertemporal distributive fairness measures. This section also describes how fair
allocation principles may be related to empirical fairness measures found in the
literature. Impact assessment and other approaches for measuring fairness are beyond
the scope of this work. The fourth section presents measures of distributive fairness
that account for the major issues outlined in sections two and three. Following this, a
preliminary application of the distributive fairness measures to a case study involving
the choice between two different power supply technologies for a number of northern
Manitoba communities is discussed. The alternatives for this problem are dispersed
diesel generation and hydropower generation with land line distribution, which must
meet a 40-year load forecast for the communities. For each alternative, this work
considers the forecasted annual average cost per megawatt-hour, in 1993 Canadian
dollars, to consumers within the communities. The limited data for this case study
restrict the analysis to an investigation of only one issue related to the fair allocation of
project impacts. Indeed, further comparisons of other biophysical, sociocultural and
economic impacts that result from each alternative would be required for this problem
before a sustainable alternative may be selected. However, the measures presented here
may be applied should further meaningful impact forecasts become available. Finally, a
discussion of the application and the conclusions are given.
SUSTAINABILITY AND DISTRIBUTIVE FAIRNESS
While equity, or distributive fairness, has long been discussed by management
scientists regarding the provision of public services (Savas, 1978), interest in this
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Sam Matheson et al.
topic has increased in the last 10 years due to the introduction of the concept of
sustainable development. According to the Brundtland Commission (WCED, 1987),
a sustainable development meets the needs of the present generation while still
allowing future generations to meet their own needs. The Brundtland Commission's
definition of sustainable development stresses the consideration of the needs of the
present generation and of future generations, and has prompted others (Young, 1992;
Nachtnebel et al., 1994; Beltratti, 1995; Munasinghe & Shearer, 1995; Simonovic et
al., 1995) to promote equity as one of a number of objectives required for
sustainability. At this point, two issues need to be addressed if intratemporal and
intertemporal distributive fairness criteria are to be defined.
First, the notion of fairness within and between generations implied by the
Brundtland Commission's definition of sustainable development is vague and needs
to be examined in greater detail. In the context of project selection, for example,
several questions related to fairness within and between generations are: (a) how long
should equity be a concern?; (b) among whom should equity be a concern?; (c) what
is a generation?; and (d) what impacts should be evaluated in terms of equity?
Matheson (1997) proposes that equity should be a concern in project selection for as
long as project-related impacts affect groups of similarly situated individuals.
Similarly situated individuals are individuals that are affected by similar project
related impact magnitudes, which may be considered as a group, in order to simplify
the analysis. Marsh & Schilling (1994) suggest that individuals may be aggregated
into groups on several bases such as: spatial, demographic, physical and temporal.
An example of segregating a population into groups on a spatial basis may be to
divide a population into countries, provinces, or municipalities. A population may be
divided into groups demographically according to, e.g. age, gender, ethnic background, occupation, social class, or income. A population could be segregated into
groups on a physical basis according to different drainage basins or different
bioregions. Finally, a population may be segregated on a temporal basis, perhaps in
terms of generations as was mentioned by the Brundtland Commission (WCED,
1987). While the exact grouping basis is case specific, it should also be noted that a
grouping strategy may be a combination of more than one of the above bases.
In addressing temporal considerations while evaluating the sustainability of a
project, the affected groups over time must be compared. McKerlie (1989) discusses
temporal aspects in fairness evaluations. In comparing impacts on two people, he
considers whole life, simultaneous segments of lives and corresponding segments of
lives comparisons. The whole life approach compares the total impact acting on each
person's life. This approach may not reflect differences that occur during the same
time period (e.g. mid-life) of the different lives. The simultaneous segments
approach compares the impacts acting on the individuals in some mutual time period
in both lives, i.e. impacts that both parties experience at the same point in time
(e.g. 1991-1995). The corresponding segments approach compares the impacts
acting on each life in the same stage of the respective lives, i.e. impacts that both
parties experience at the same time period in their lives (e.g. in mid-life). Regarding
the question of generations, Matheson (1997) suggests the use of time steps might be
a more flexible approach because project-related impacts are project specific and may
Distributive fairness considerations in sustainable project selection
535
not have a duration that exceeds a generation or may exhibit high variability within a
generation. Comparisons based on a generational time step may be too coarse to
account for this variability and in such cases, a smaller time step (e.g. 1-5 years)
may be more appropriate than a generational time step.
The second issue related to the formulation of intratemporal and intertemporal
distributive fairness criteria is that, defining fairness as merely equity may be
avoiding a more important question, that is: what is fairness in a distributive context?
This question must be addressed if a measurement approach for sustainable project
selection is to be formulated. This question has been studied at least since the
writings of Aristotle (Thomson, 1985), but the answer remains elusive. The next
section addresses the question of how fairness may be measured empirically so as to
provide the groundwork for the formulation of fairness measures for sustainable
project selection. Here, a project alternative is considered to result in an allocation of
impacts that are distributed among different groups of similarly situated people.
FAIR ALLOCATION OBJECTIVES, DESIRABLE CHARACTERISTICS AND
EMPIRICAL MEASURES OF DISTRIBUTIVE FAIRNESS
Blalock (1991) proposes that, when considering the reactions of groups to any
allocation process, the analyst should consider their perceptions and interpretations
concerning the fairness of both procedures and the outcome of the allocation.
Procedural aspects are also important, in terms of public participation and awareness,
as they help to make distributive outcomes more socially acceptable. In general,
groups evaluate the fairness of their outcome by a social comparison process between
the perceived project-related impacts and the impacts which these groups feel are
fair.
Aristotle (Thomson, 1985), Deutsch (1975), Arthur & Shaw (1978), Blalock
(1991) and Almond (1995) identify simple fair allocation objectives that groups may
view as representing a fair allocation of project-related impacts: perfect
proportionality, perfect equality and satisfaction of need. Young (1994) provides an
excellent overview of these and other approaches to fair allocation. The first
allocation objective, known as perfect proportionality, focuses on differences among
groups and requires that each group should receive goods in proportion to what that
group deserves. Achieving this objective may be problematic if the amount each
group deserves cannot be assessed or if what is being distributed cannot be divided
among groups. An equal distribution may be seen as fair when there is no reason to
differentiate among groups. However, situations may arise where groups are
different and one group may need more or less of what is being distributed than
another depending on if what is being distributed is perceived to be a benefit or a
cost, respectively. For this reason, the distribution of impacts according to the
amount each group needs or can tolerate is often proposed as an alternative to perfect
proportionality and perfect equality. Although that which constitutes a group's need
is not well defined, Almond (1995) states that this problem may be overcome if basic
needs were determined using statistics such as infant mortality or life expectancy.
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Sam Matheson et al.
The relative importance of each fair allocation objective is discussed by Deutsch
(1975) and Blalock (1991). They identify underlying factors that affect preferences
for these objectives, for example, the time and information available for the allocator
to make a decision.
While a number of desirable characteristics and principles have been proposed to
evaluate fair allocation measures, a consensus in the literature does not exist
regarding which characteristics and principles are required for evaluating measures
of the various fair allocation objectives. Young (1994) states that all acceptable
measures of fairness should satisfy the principles of impartiality and consistency
because these principles are fundamental to fairness considerations. Impartiality
requires that a fairness measure be applied to that which is being distributed and not
based on some other ordering or ranking, such as a group attribute that is not
considered to affect the distribution. Consistency requires that the fairness measure
be applied across groups in the same manner for all groups. Marsh & Schilling
(1994) mention three principles that are most commonly found in the literature on the
evaluation of fairness measures. These are the principles of impartiality, transfers
and scale invariance. The principle of transfers, proposed by Pigou (1912), requires
that when a unit amount of positive (negative) impact is transferred from a better-off
group to a worse-off group, an acceptable equality-based measure should reflect an
improvement in fairness. The principle of scale invariance requires that only relative
differences in impacts should matter not absolute differences. Thus, for two impact
distributions, one distribution being a multiple of the other, a scale invariant fairness
measure would calculate the same deviation from perfect fairness for both
distributions.
In addition to impartiality and consistency, measures based on a perfect proportionality fair allocation objective are required to satisfy the fundamental principle
(Harris, 1983) and thus exhibit an ordinal relation between a group's impact and a
group's reference distribution. Measures based on a perfect equality are also required
to satisfy the principle of transfers and the principle of scale invariance (Matheson,
1997). As no distance-based measure of need, nor any literature relating to satisfaction of need are available, for need there are no additional requirements suggested in
the literature. Matheson (1997) suggests that, for need, satisfaction of the principles
of impartiality and consistency are required. Other principles and desirable characteristics may be required to evaluate a need-based distance measure when this
concept is further developed.
Marsh & Schilling (1994) review 20 empirical distance-based fairness measures
that have been applied and propose a generalized framework for their classification.
A distance-based fairness measure is a weighted sum of the distances between the
ideal values for a distribution of impacts among groups of individuals and the actual
values of these impacts. The authors' generalized framework for classification and
future evaluation of distance-based fairness measures consists of examining three
factors: the reference distribution, scaling and distance exponent of the measure. The
authors describe a reference distribution as being a specified or desired effect level
for each group. Possible types of reference distributions are peer, mean, or attributebased distributions. Peer and mean reference distributions are based on perfect
Distributive fairness considerations in sustainable project selection
537
equality as the objective for fair allocation where peer reference distributions refer to
comparisons among all peers and mean reference distributions refer to comparisons
with the mean of the impacts for all peers. For the purposes of this paper, measures
of this type are referred to as based on a perfect equality fair allocation objective.
Marsh & Schilling (1994) also describe an attribute-based reference distribution
as being specific to each group and being based on, for example, the level of social
need, desire, demand, social merit, or population. An attribute-based reference distribution may be referred to as being based on the fair allocation objectives of perfect
proportionality or satisfaction of needs. In this manner, Marsh & Schilling's
framework is analogous to that of the fair allocation objectives discussed above.
Thus, from this point on, measures of this type are referred to as measures based on
proportionality or need.
Scaling is described as being commonly used when group sizes differ to account
for large differences in the size of the distances measured. If scaling is performed, it
is typically based on a normalization of distances or as a weighting based on the
different attributes of the groups. Commonly used distance exponents are either one,
two, or infinity. As the magnitude of the distance exponent increases from one to
infinity, a greater weight is placed on deviations from the reference distribution.
Thus, distance-based fairness measures with different distance exponents may indicate different levels of fairness when applied to the same impact distribution.
The review by Marsh & Schilling (1994) reveals that when the 20 common
distance-based fairness measures found in the literature are applied to the same data
set, different measures give different results. Matheson (1997) evaluates the 20
measures reviewed by Marsh & Schilling (1994), based on how well each measure
satisfies the desirable principles associated with each fair allocation objective. He
shows that potentially appropriate proportionality-based measures are Walsters
Formula and the Equal Excess Formula because these measures satisfy the impartiality, consistency and fundamental principles. The Relative Mean Deviation
Measure and the Gini Coefficient (Gini, 1912) are potentially appropriate equalitybased measures because these measures satisfy the impartiality, consistency, transfers
and scale invariance principles. Six potential need based measures are proposed that
are variations on common proportionality-based measures. In the following section,
the Equal Excess Formula (Heiner et al, 1981), Gini Coefficient (Gini, 1912) and a
proposed need-based fairness measure (Matheson, 1997) are discussed and expanded
for intratemporal and intertemporal fairness considerations.
The distance-based fairness measures discussed by Marsh & Schilling (1994) are
either proportionality-based or equality-based fairness measures. This distinction is
not made explicit by Marsh & Schilling (1994) and need-based fairness measures are
not given in the literature. As the literature indicates that fairness may be a combination of one or more of the fair allocation objectives, a generalized fairness measure
based on a combination of proportionality, equality and need fair allocation objectives may be a more useful approach than an approach based on either perfect
proportionality or satisfaction of need fair allocation objectives. Furthermore,
allowing the present generation to meet its needs while allowing future generations to
meet their own needs indicates that a need-based fair allocation objective may be an
Sam Matheson el al.
538
important consideration if one applies the Brundtland Commission's definition of
sustainable development. Generalized measures for intratemporal and intertemporal
fairness are developed in this paper for use as criteria for sustainability. Such
measures may be applied for comparisons between groups located at a given time and
between groups located in different times. As described above, individuals and
groups tend to view fairness from more than one perspective. Such differences in
value systems may be even more pronounced between groups in different time
periods. Therefore, in this work it is proposed that generalized fairness measures
represent a composite or weighted sum of objectives that may describe a fair
allocation. The fairness measures presented here, then, are composite measures that
describe how much a project's impacts deviate from being distributed in proportion
to each group's contribution, being distributed equally and being distributed such that
each group's needs are satisfied.
OPERATIONAL DEFINITIONS OF DISTRIBUTIVE FAIRNESS
Consider a situation in which there is a total of / groups where group i is affected by
some impact with a magnitude E(i) that results from some action. In this situation,
define A(i) as the impact magnitude that group / feels it deserves and Z(i) as the
impact magnitude required to meet the needs of group i. Measures identified by
Matheson (1997) that satisfy the desirable principles of impartiality, consistency,
transfers and scale invariance, and the fundamental principle are given in equations
(l)-(3). These equations are based on the fair allocation objectives of perfect
proportionality, perfect equality and satisfaction of needs respectively. They are:
Bt=t\E(i)-A(i)\
/ /
\m-EU)\
2I2Ë
B3 = tjE(i)-Z(i)\
(1)
(2)
(3)
where 5, = deviations from a proportional impact allocation; B2 = deviations from
an equal impact allocation; B3 = deviations from an impact allocation that exactly
satisfies the needs of all groups; / = number of groups being considered; i and j =
group indices; E(i) = impact magnitude acting on group i; A(i) = impact magnitude
that group i deserves, or group fs contribution towards receiving E(i); Z(i) =
amount of E(i) that group i requires to satisfy its needs; and E = average impact
magnitude that acts upon the / groups being considered.
Equation (1) is known as the Equal Excess Formula and represents the magnitude
of fairness resulting from impacts which deviate from an allocation that is
proportional to each group's contribution. Equation (2), known as the Gini Index or
Distributive fairness considerations in sustainable project selection
539
Gini Coefficient, is commonly used by economists to measure deviations from
perfect equality, and is presented in the form given in Marsh & Schilling (1994). The
two group indices, i and j , are required for equation (2) as the numerator of this
equation is the sum of all possible pairwise comparisons of impact magnitudes
between groups. The magnitude of the Gini Coefficient represents the decrease in
fairness resulting from impacts that deviate from being allocated equally among all /
groups. Equation (3) is presented in this work as one way to measure the fairness in
an allocation of impacts that deviate from meeting each group's need for that impact.
It should be noted that other methods of operationalizing a need fair allocation
objective, such as a binary expression of whether or not a need is met, may be
possible. Equations (l)-(3) have values that may increase in magnitude from zero,
where zero corresponds to complete fairness as defined by each fair allocation
objective.
If equations (l)-(3) are to be used in the context of sustainable project
selection, the equations must be expanded to address four major concerns. First,
these measures are not currently formulated in a way that accounts for the
dimensions required for both intratemporal and intertemporal comparisons.
Second, projects are likely to distribute more than one impact among groups and a
measure of fairness should account for this in some way. Third, equations (l)-(3)
represent three different aspects of fairness evaluations and a fairness measure
should incorporate all of these objectives because, for example, not all people
evaluate fairness by proportionality alone and may employ one or more fair
allocation objectives. This may gain more significance when considering the
extended temporal horizons associated with intertemporal fairness evaluations.
Finally, as evaluations of fairness are case specific, a measure should reflect the
variability in the emphasis placed on the different fair allocation objectives by the
groups who are affected by a project.
Consider a situation in which there are X project alternatives, each distributing G
different impact types to / groups over T time steps. Thus, each project alternative
may be thought of as having a G x / x T impact matrix. While it may be possible for
each project impact matrix to have different magnitudes for G, I and T, this work
assumes for simplicity, that each project alternative impact matrix is the same size.
Therefore, the matrix that represents the impact magnitude accruing to group /, of
impact type g (i.e. either a benefit or cost), during time step t, resulting from project
alternative x may be written as E(i, g, t, x). For each group, /', its contribution
toward receiving a certain impact type, g, or the impact it deserves, may vary with
time step t and is written as A(i, g, t). Additionally, a group's need for a particular
impact may also vary with time and is written as Z(i, g, t). Equations (l)-(3) may be
rewritten to correspond to this generalized problem. Equations (4)-(6) represent the
three fair allocation objectives expanded for the intratemporal case with any number
of impacts and equations (7)-(9) represent the three fair allocation objectives
expanded for the intertemporal case, with any number of time steps.
w„E\E(i, g, t, x)-A(i, g, t)\
Gl
(=i«=iL
(4)
Sam Matheson et al.
540
1
T G
w,,ÉÉ £(i, g, t, x)-E(j,
1
—
(5)
2rE..
Cri /=lg=l
tiy\X)
g, t, x)\
T G
2. ZJ w ʣ(i,g,f,x)-Z(z',g,0
GT i=i g=lL * '=i
1 £
5,'(x) = — I
/
r ,
(6)
i'
(7)
Cri g=l
7'
'/• I
HT,\E(i,g,s,x)-E(i,g,t,x)\
i^(jc) = — ££
G7
;=1
2TZE„
(8)
G-/ g=i
B'(x)
GI g=i
w E S £(/, g, ?, x) -Z(z, g, 0
(9)
where Bx{x) = average intratemporal fairness measure which is the weighted sum
of deviations from a proportional impact allocation for all groups; B2(x) = average
intratemporal fairness measure which is the weighted sum of deviations from an
equal impact allocation for all groups; B3(x) = average intratemporal fairness
measure which is the weighted sum of deviations from an allocation that meets the
needs of all groups; B'x{x) = average intertemporal fairness measure which is the
weighted sum of deviations from a proportional impact allocation for all groups;
B'2{x) = average intertemporal fairness measure which is the weighted sum of
deviations from an equal impact allocation for all groups; B'3{x) = average intertemporal fairness measure which is the weighted sum of deviations from an
allocation that meets the needs of all groups; G, I, T, X = number of different
impact types, number of groups, number of time steps and number of project
alternatives, respectively; i, g, t,x = indices for group, impact type, time step and
alternative, respectively, such that l < g < G , 1 <I <I, \<t<T and 1 < x < X; j
and s = group and time indexes, respectively, that are required for pairwise comparisons such that 0 <j < I and 1 < s < T; wg = weights on impact type g, such that:
G
E w = 1 ; E(i, g, t, x) = magnitude of impact type g acting on group i during time
«=i
g
step t that results from project alternative x; Egu = average impact defined over all
-:
•
combination of impact type, time step and alternative such that
r
JV
r
groups for a given a
Em = — YjE(i,g,t,x) ; Eigx = average impact defined over all time steps for a given
/«=.
combination of group, impact type and alternative such that E-
1 i
=^zHE{i,g,t,x);
A(i, g, t) = magnitude of group i's contribution towards receiving impact type
Distributive fairness considerations in sustainable project selection
541
during time t; and Z(i, g, t) = magnitude of impact type g that meets group f's needs
during time step t.
Equations (4)-(6) are based on the three fair allocation objectives applied to the
impacts distributed among groups during a given time step which are then averaged
over all time steps. Equations (7)-(9) are based on the three fair allocation objectives
applied to the impacts distributed over all time steps for a given group which are then
averaged over all groups. These distance-based measures may be further combined
into overall measures of intratemporal and intertemporal fairness by a weighted
average approach. This may be accomplished by using a normalized Cartesian-based
distance metric shown below:
2
tql
a(x) =
v=l
B,{x)
Bl(x)
tql BU-B:
\\i(x) =
(10)
B.,-B,
(ii)
V=I
where a(x) = magnitude of average intratemporal fairness for a given project
alternative x, such that 0 < a(x) < 1 ; y/(x) = magnitude of average intertemporal
fairness for a given project alternative x, such that 0 < y/{x) < 1 ; v = index for
different fair allocation objectives; qr = weight attached to fair allocation objective
3
v such that: Y,qv = 1 ; Bv(x) m\âB'v{x) = magnitudes of the three intratemporal and
v=1
three intertemporal fair allocation approaches; B.(x) andi?»(x) = minimum values
of Br(x) and B',(x) across all v given a project alternative x; and Btt(x) mdBL(x)
= maximum values of Br(x) &nàB'v{x) across all v given a project alternative x.
Thus, distance-based measures that reflect proportionality, equality and need fair
allocation objectives are expanded to account for comparisons both within and between
time steps for more than one type of impact. The expanded fairness measures are
formulated in this work as averages of fairness comparisons across time steps, groups
and different impact types. In equations (4)-(ll) weights wg and qv are used to
represent the relative importance of fairness considerations among different projectrelated impacts and the relative importance placed on the three different fair allocation
objectives, respectively. These weights represent the affected group's preferences and
may be obtained, for example, by a social survey. According to Cohen (1978), the use
of predetermined weights is a simple way of incorporating preferences into the decision
making process but assumes that weights remain constant regardless of the objective
functions' magnitudes and the willingness to trade-off one objective for another is
independent of the magnitudes of the objective function values. This issue requires
further investigation, however, it should be noted that the overall fairness measures
presented in equations (10) and (11) may represent the social objective function of the
groups and their views of intratemporal and intertemporal fairness, respectively.
542
Sam Matheson et al.
Uncertainty in fairness measurement may arise from employing an inappropriate
fairness measure. For example, a fairness measure that does not accurately describe
the perceived fairness of the groups managed may introduce uncertainty into the
analysis. Uncertainty may also arise from unknown values for the weights that reflect
the relative importance of each type of impact or fair allocation objective. Another
type of uncertainty may arise due to prediction errors, e.g. errors in the predictions
of the impact estimates over time. Impacts may increase, decrease, remain constant,
or be some combination of these trajectories over time and the number of impacts
that affect each group may also change over time. The uncertainty introduced by
considering an increased temporal horizon may be so great that a fairness analysis
may be untenable. Clearly, additional investigation of uncertainty reduction for the
distributive fairness measures is needed.
AN APPLICATION OF THE DISTRIBUTIVE FAIRNESS MEASURES FOR
SELECTING A POWER SUPPLY ALTERNATIVE IN NORTHERN
MANITOBA, CANADA
The generalized fairness measures presented in equations (10) and (11) are applied in
this section for a preliminary analysis of a case study that involves selecting among
two different power supply technologies for seven remote communities located in
northern Canada's Boreal forest approximately 560 km northeast of Winnipeg,
Manitoba. The power supply alternatives being considered to satisfy the 40-year load
forecast are dispersed diesel generation and land line connection to Manitoba
Hydro's central power grid. The remote seven communities of Oxford House, Gods
Lake, Gods River, Red Sucker Lake, Garden Hill, Wasagamack and St Theresa
Point currently have electricity supplied by diesel generators in each community.
Three additional nearby communities, Nelson House, Cross Lake and Split Lake, are
supplied by a land line connection to Manitoba Hydro's central system. These three
latter nonremote communities are used as reference communities for the fairness
comparisons in this case study, because they are in the vicinity of, and have similar
demographic characteristics to, the seven remote communities listed above. The
dispersed diesel generation alternative for this region would require the addition of
diesel generating units to each community over time in order to meet the forecasted
peak loads. The other alternative, a transmission line originating at the Kelsey
Generating Station as shown in Fig. 1, would connect Oxford House, Gods Lake,
Gods River, Red Sucker Lake, Wasagamack, Garden Hill and St Theresa Point to the
provincial power grid. While Manitoba Hydro (1993) considered other power
generation methods such as small-scale hydro, central biomass and dispersed
biomass, these alternatives were found to be uneconomical compared to the
construction of a transmission line connection to the central power grid.
Within each community there are residential consumers and nonresidential
consumers who pay for the energy consumed. Nonresidential consumers are
composed of commercial and government facilities. As the diesel alternative creates
higher energy costs than the land line alternative, each alternative may be seen to
Distributive fairness considerations in sustainable project selection
543
Fig. 1 Vicinity map of the seven remote communities (Manitoba Hydro, 1993).
result in different economic impacts among consumers. Other impacts are likely,
such as particulate emissions associated with the diesel alternative, but are not
considered here due to a lack of monitoring information for these facilities. Matheson
(1997) estimates annual average energy costs from 1997 to 2037 (in 1993 Canadian
dollars) for both residential and nonresidential customers in the seven communities
that may result from the implementation of a project alternative and the three
communities that are included for the sake of comparison. These estimates are based
on historical demand data, population projections and historical rate records over a
25 year period.
Due to space limitations, the estimates of annual average energy costs are listed
in Tables 1 and 2 for residential consumers and nonresidential consumers,
respectively, for the years 1997, 2017 and 2037 only (in 1993 Canadian dollars). As
Table 1 shows, both residential and nonresidential consumers in the nonremote
communities of Cross Lake, Nelson House and Split Lake are not affected by the
project alternatives since these communities are only included for comparison with
the seven potentially impacted communities. Therefore, the annual average energy
cost per megawatt-hour for these communities in any year remains constant over all
alternatives. Also shown in Table 1, for a given community in a given year, is a
slight decrease in annual average energy costs for residential consumers in the seven
remote communities when the land line alternative is implemented in 1997. This may
be a result of an annual average increase in demand per residential meter after a
community switches to a land line power supply since Manitoba Hydro's land line
544
Sam Matheson et al.
Table 1 Average energy costs (1993 Can$ per megawatt-hour) for a residential consumer.
Community
Cross Lake
Nelson House
Split Lake
Oxford House
Gods Lake
Gods River
Red Sucker Lake
Garden Hill
St Theresa Point
Wasagamack
Dispersed diesel:
2017
1997
51.42
52.21
52.55
51.43
51.97
50.98
84.22
73.43
83.92
73.83
73.39
61.95
74.64
63.21
83.08
74.52
71.50
81.31
82.50
72.58
2037
50.86
50.87
50.48
67.62
68.18
57.65
58.68
69.33
66.17
67.11
Land line:
1997
52.52
52.55
51.97
59.19
59.13
57.23
57.49
58.97
58.69
58.90
2017
51.42
51.43
50.98
52.07
52.06
51.77
51.81
52.04
52.00
52.03
2037
50.86
50.87
50.48
51.06
51.05
50.88
50.91
51.04
51.02
51.03
Table 2 Average energy costs (1993 Can$ per megawatt-hour) for a nonresidential consumer.
Community
Cross Lake
Nelson House
Split Lake
Oxford House
Gods Lake
Gods River
Red Sucker Lake
Garden Hill
St Theresa Point
Wasagamack
Dispersed diesel:
1997
2017
45.69
43.82
45.29
43.49
42.97
45.42
430.49
431.73
433.36
434.13
433.34
436.13
432.32
434.35
432.48
433.99
431.19
432.68
428.61
427.86
2037
43.04
42.78
42.20
429.81
432.84
431.99
431.28
431.43
430.39
427.48
Land line:
1997
45.69
45.29
45.42
55.39
61.13
66.32
61.93
60.88
57.58
48.81
2017
43.82
43.49
42.96
45.31
45.63
45.81
41.58
45.61
45.46
44.48
2037
43.04
42.78
42.20
43.59
43.69
43.75
38.89
43.69
43.64
43.28
residential rate structure reflects decreasing marginal costs to the consumer. A
decrease in annual average energy costs for nonresidential consumers under the land
line alternative is shown in Table 2 for a given remote community in a given year.
This occurs due to the decrease in remote nonresidential energy rates to the current
level of nonremote nonresidential energy rates.
The overall fairness measures presented in equations (10) and (11) are
applied to this case study for an annual time step in order to examine the
temporal variability of the average energy cost per megawatt-hour accruing to
different energy consumers in different communities. When considering intratemporal fairness as defined in equations (4)-(6), a given energy consumer type
evaluates fairness based on the amount that customers of the same type pay in the
other nine communities during a given year. When considering intertemporal
fairness as defined in equations (7)-(9), an energy consumer in a community
evaluates fairness based on comparing average annual energy costs that act on
that consumer, in a given community during a given year, with the average
annual energy costs for the same type of consumer in the same community over
the remaining 39 years.
Distributive fairness considerations in sustainable project selection
545
Of the proportionality, equality and need based fair allocation objectives
considered in this work, the equality approach is judged to be the most applicable
for both intratemporal fairness and intertemporal fairness comparisons of user unit
costs in this case study because the quantification of each group's contribution to
the project and need for electricity require further examination. Allocation
objectives of perfect proportionality and satisfaction of need may be important,
however, when considering other impact distributions for this case study. The
approach taken here is to apply the generalized distributive fairness measures in
equations (10) and (11) to the residential consumers and the nonresidential
consumers. Equations (5) and (8) are calculated by setting the number of groups, /,
equal to 10; the number of time steps, T, equal to 40; and the number of different
impact types, G, equal to 1. Here, the E(i, g, t, x) are the annual average energy
cost per megawatt-hour data contained in Tables 1 and 2. Equations (10) and (11)
are then applied by using the weight of unity for q2, since this work only focuses
on equality and the residential and nonresidential data shown in Tables 1 and 2.
The results of this application are shown in Table 3. The intratemporal
fairness measure, a(x), indicates that fairness, in terms of average annual energy
costs per megawatt-hour, may increase for both the residential and nonresidential
consumers if the land line alternative is selected because the average annual cost
per megawatt-hour will be more equal to that experienced by the nonremote
communities if the land line alternative is selected. The intertemporal fairness
measure, yAx), does not indicate a difference among project alternatives as the
average annual energy cost per megawatt-hour, for a given consumer group,
remains fairly constant over time. The greatest intratemporal fairness increase
associated with switching from dispersed diesel supply to a land line supply
would be experienced by nonresidential consumers who are worse off under the
existing dispersed diesel energy supply. This can be seen in Table 3 by
comparing the fairness measure magnitudes of 0.26 and 0.02 for the dispersed
diesel and land line alternatives, respectively. Of course, other types of impacts,
such as impacts to health and safety may show a greater difference between
alternatives for fairness considerations. The analysis of average annual energy
costs per megawatt-hour is only one of a number of different impacts associated
with each project alternative and thus represents a partial perspective of the
perceived fairness present in this system. As data on these and other impacts
such as environmental changes and reliability of power supply become available,
for each alternative, further comparisons should be made before the analyst could
advise the decision maker.
Table 3 Intratemporal and intertemporal measure magnitudes for each alternative.
Alternative
Dispersed diesel
Land line
a(x)
Intratemporal Fairness Measure
Residential
Nonresidential
0.08
0.26
0.01
0.02
if(x)
Intertemporal Fairness Measure
Residential
Nonresidential
0.01
0.01
0.01
0.01
546
Sam Matheson et al.
SUMMARY AND CONCLUSIONS
While intragenerational and intergenerational equity, or intratemporal and
intertemporal fairness, respectively, are often advocated as being fundamental to the
concept of sustainable development, these issues are rarely discussed in detail or
applied to real engineering case studies. Sustainable development, fair allocation
objectives, empirical distance-based fairness measures and their evaluation and the
application of these measures to real problems, have been discussed here. This work
develops generalized intratemporal and intertemporal distributive fairness measures
that may be used as criteria for sustainable project selection and are based on the fair
allocation objectives of perfect proportionality, perfect equality and satisfaction of
needs. These generalized fairness measures incorporate the three common perceptions of fair allocation by employing a weighted average of the extended
proportionality, equality and need based fairness measures.
The generalized fairness measures are a first attempt at an approach for
measuring distributive fairness in different cases and over long time horizons. It
should be mentioned that the generalized fairness measures are mathematical abstractions of a social objective function and should be considered empirical measures of
fairness. They may serve as a starting point from which more refined fairness
measures for sustainable project selection may be developed. Additionally, the
formulation of these measures may serve to guide data collection efforts for the
purposes of fairness evaluation for sustainable project selection.
The generalized fairness measures presented in this work may be used as criteria
for sustainable project selection and may also be useful for other applications in civil
engineering. For example, the generalized fairness measures might be modified and
used to develop reservoir operating strategies that distribute reservoir related impacts
in some fair manner. Efforts to explore this application are currently underway. At
this time, the main limitations in applying this approach are seen to be the estimation
of the weights required by the fairness measures and impact distributions that result
from each project alternative. Impact assessment and impact valuation, particularly
for impacts over long time horizons are daunting tasks and remain to be addressed.
The measures developed here are applied to a preliminary case study of the
selection of either a dispersed diesel generation or land line based connection to a
central power grid in order to meet energy demands in a region over a 40-year
horizon. The fairness measures are applied to annual average energy costs per
megawatt-hour accruing to residential and nonresidential energy consumers in seven
communities as a result of implementing either project alternative. The distributive
fairness measures formulated for this case study are based on a perfect equality fair
allocation objective. The measures indicate that intratemporal fairness, regarding the
distribution of average annual energy costs per megawatt-hour, particularly for the
nonresidential energy consumers, may be increased by choosing the land line alternative. However, this case study only illustrates the application of the generalized
fairness measures to one project related impact distribution and should not be considered a comprehensive fairness evaluation for this system. Clearly, additional
project related impacts are possible and as data become available, a further évalua-
Distributive fairness considerations in sustainable project selection
547
tion must be conducted before one could present the complete analysis to a decision
maker.
While fairness considerations have been discussed for at least two millennia by
philosophers (see Aristotle in Thomson, 1985), fairness considerations in the context
of civil engineering projects are seldom formally incorporated in actual project
selection, and much work remains to be conducted in order to rethink an old concept
in the context of real engineering problems. Research efforts should be directed at
investigating the relevance of perfect proportionality and satisfaction of need
allocation objectives in project selection and at identifying the factors that influence
the relative importance placed on different fair allocation objectives. Additionally,
much work remains in defining and measuring needs. Moreover, efforts toward
reducing associated measurement, weighting and impact prediction uncertainties need
to be undertaken and ultimately the various approaches for measuring fairness need
to be validated. Civil engineering projects, particularly the provision of public
services, may affect a large number of people, thus fairness considerations may be
important for effective selection and implementation of such projects.
Acknowledgements The authors thank D. Burn, S. Simonovic and E. Onyebuchi for
their insightful comments during many discussions of this work. Additionally, the
authors greatly appreciate the excellent comments made by the independent reviewers
of this article. The authors are grateful for the support provided by Manitoba Hydro
under award no. G105; the University of Manitoba Research Development Fund; the
Natural Science and Engineering Research Council of Canada under award no.
0GP041643; and the International Institute for Applied Systems Analysis,
Laxenburg, Austria, under the Institute Scholars Program. The views expressed in
this work are solely of the authors and Manitoba Hydro does not endorse this work
in any way.
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