=Paper=
{{Paper
|id=Vol-2030/HAICTA_2017_paper67
|storemode=property
|title=Multicriteria and Social Choice Methods in Assessing Water Management Plans
|pdfUrl=https://ceur-ws.org/Vol-2030/HAICTA_2017_paper67.pdf
|volume=Vol-2030
|authors=Bojan Srdjevic,Zorica Srdjevic,Yvonilde Dantas Pinto Medeiros
|dblpUrl=https://dblp.org/rec/conf/haicta/SrdjevicSM17
}}
==Multicriteria and Social Choice Methods in Assessing Water Management Plans==
https://ceur-ws.org/Vol-2030/HAICTA_2017_paper67.pdf
Multicriteria and Social Choice Methods in Assessing
Water Management Plans
Bojan Srdjevic1, Zorica Srdjevic1, Yvonilde Dantas Pinto Medeiros2
1
University of Novi Sad, Faculty of Agriculture, Department for Water Management, Trg D.
Obradovica 8, 21000 Novi Sad, Serbia
2
Escola Politécnica da Universidade Federal da Bahia
A. Novis 2, 40.210.630, Salvador, Brazil
Abstract. Selection of a good water management plan for the river basin is a
complex decision-making problem because interests of stakeholders are
usually confronted, rarely in complete agreement. If water committee has to
emulate interest and power of key parties, decision-making process can be
organized in many different ways, depending on adopted methodology for
deriving decisions and formalizing setup to implement solutions. Group
context brings individuals with different background, attitude and
(in)consistencies they will demonstrate while evaluating and/or judging
options. In this paper, we show how two methodologically distinct tools can
efficiently support group decision making at a group and sub-group level
within committee. We propose to firstly use analytic hierarchy process (AHP)
to rank management plans, and secondly, to use voting method Borda Count
(BC) for final ranking of plans selected by post analysis of the AHP results.
Illustrative example from Brazil is used to show usefulness of combined
approach.
Keywords: Decision-making; AHP; Borda Count; water management; long-
term plan.
1 Introduction
The MCDM (multi-criteria decision-making) method known as Analytic Hierarchy
Process (AHP) (Saaty 1980, 2003) and the SC (social choice) method known as
Borda Count (BC) (d’Angelo et al., 1998; Srdjevic, 2007), are employed to manage a
group decision-making process aimed at assessment of and selection of the best
among five long-term water management plans across five criteria. During one of
multiple workshops related to hierarchical decision-making processes held at the
School of Polytechnic, Federal University of Bahia, Salvador, Brazil, a special
session has been organized to analyze possibility of establishing decision-making
framework related to water management at a catchment scale and within different
group contexts. A group of 21 professionals took part in one of two sessions, which
lasted in four hours, including two half-hour breaks.
AHP is used to support individuals’ and sub-groups’ cardinal assessments and
prioritization of the decision elements and to rank management plans. Participants
541
used evaluation sheets and judged decision elements within given hierarchy by
strictly following standard AHP procedure. Once evaluation sheets are collected,
prioritization of criteria and plans is followed by the final AHP synthesis. Values of
weights for plans and decision makers are aggregated by weighted geometric mean
(WGM) method to obtain the final weights and corresponding ranking of plans. Post
analysis of the final AHP results is used to reduce set of five alternative plans to new
set of 3 best ranked plans to be used in the second part of the session.
New set of plans was included in the appropriate evaluation sheet (voting ballot)
according to requirements of the preferential method Borda Count. We selected SC
method as the second part of the decision framework due to its simplicity, easiness to
be explained to participants and as less time and effort consuming than AHP.
Sheets were distributed to individuals to set their preferences by simply ranking
alternative plans considering all criteria as implicitly condensed into unique criterion;
note that this is the case how voters usually do in real-life elections. Collected
preferential opinions of participants, as fully ordinal information (differently from
cardinal information obtained by AHP) are summarized to rank 3 alternative plans as
final group decision.
Worthy to mention is that when applying AHP and BC, awareness is required
because individuals’ background and knowledge are generally very different,
particularly if groups (and sub groups) are large. Also important is that in large river-
basin water committees, a decision-making process related to planning and overall
water management will expectedly be performed with participation of ‘oriented
committee members’ bringing particular background and mostly narrowed interest
from social, political or economic environment they are coming from. These facts
have also been a part of our recent research, but are not discussed in details in this
paper.
In strictly AHP context, reported approach recognizes importance of using equal
weights of individuals, and, at the later stage, different weights of subgroups based
on the number of members in the subgroups (larger a sub group – higher is its
weight). At a committee level, sub groups actually act as a new (virtual single)
individuals and the final preferences are determined by weighted geometric
aggregation.
For the sake of completeness and to justify our methodological choices we
consulted rich literature around group decision-making in agriculture, ecology, etc.
that allow a multiple criteria and multiple participants, multiple evaluation tables
setting, notably a lot of them applying the aggregation-disaggregation paradigm (e.g.
Morais and de Almeida, 2012; Zendehdel et al., 2010; Jonoski and Seid, 2016;
Jonoski and Seid, 2016). More methodological sources (Kadzinski et al., 2013;
Cabrerizo et al., 2014) were consulted to check our ideas related to aggregation
schemes.
Outline of the paper is as follows: after brief description of mathematical bases of
both AHP and BC, illustrative example section contains statement of the decision
problem, description of decision elements and final outcomes of AHP+BC
application. Concluding remarks are given at the end of paper.
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2 AHP and Borda Count Mathematics
2.1 Analytic Hierarchy Process (AHP) – Multicriteria Method
A philosophy of the Analytic hierarchy process (AHP) is easy to understand. Assume
that hierarchy of the decision problem consists only of a goal (G), a set of criteria Cj
(j=1, 2, M), and a set of alternatives Ai (i = 1, 2, N). This hierarchy may be called 3-
level hierarchy, with levels counting from top to bottom (Fig. 1).
G
C1 C2 CM
A1 A2 AN
Fig. 1. Hierarchy of a decision-making problem
The AHP starts by performing a sequence of Mx(M-1)/2 pairwise comparisons of
criteria with respect to a goal by using the 9-point Saaty’s scale, Table 1 (Saaty,
1980).
Table 1. Original Saaty’s scale for pairwise comparisons
Numerical values Judgment Definition
1 Equal importance
3 Weak dominance
5 Strong dominance
7 Demonstrated dominance
9 Absolute dominance
2,4,6,8 Intermediate values
This way a judgment matrix (1) of size MxM is created
⎡ a11 a12 ... a1M ⎤
⎢a a 22 ... a 2 M ⎥⎥ (1)
A = ⎢ 21
⎢ ... ... ... ... ⎥
⎢ ⎥
⎣a M 1 aM 2 ... a MM ⎦
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with entries aij (i,j=1,2,…,M) being numericals given in the first column of Table 1 as
representation of preferences elicited from the individual as judgments defined in the
righthand side of the same table. Reciprocal property of matrix A means that aij=1 for
all i=j (i, j=1, 2, M), and aij=1/aji.
If we assume that entries of the vector w=(w1,w2,,...,wM)T, commonly called
priority vector, are weights of criteria, then it is desired to determine these values so
that matrix (2) is best approximate of judgment matrix (1).
⎡ 1 w1 / w2 ... w1 / wM ⎤
⎢w /w 1 ... w2 / wM ⎥⎥
⎢ 2 1
~ ⎢ . . ... . ⎥ (2)
A=⎢ ⎥
⎢ . . ... . ⎥
⎢ . . ... . ⎥
⎢ ⎥
⎢⎣ wM / w1 wM / w2 ... 1 ⎥⎦
In standard AHP, for matrix A the maximum eigenvalue λ max is determined, and
related eigenvector is adopted as vector w. This method is generally recognized as
the eigenvector method (Saaty, 1980). There are, however, more than 20 other
methods described in scientific articles for deriving vector w, for instance: additive
normalization (Saaty, 1980), direct least squares (Chu et al., 1979), weighted least
squares (Chu et al., 1979), logarithmic least squares (Crawford and Williams, 1985),
fuzzy preference programming (Mikhailov, 2000), logarithmic goal programming
(Bryson, 1995), evolution strategy prioritization (Srdjevic and Srdjevic, 2013), and
most recently cosine maximization (Kou and Lin 2014). Useful information on these
and many other methods can be found in rich scientific literature (e.g., Golany and
Kress, 1993; Mikhailov and Singh, 1999; Srdjevic, 2005; Ishizaka and Labib, 2011;
Blagojevic et al., 2016).
Next, Nx(N-1)/2 pairwise comparisons of alternatives are performed at level 3
with respect to each criterion at level 2. This way a set of M matrices of size NxN is
created. Local eigenvectors (for each matrix one vector) are computed as before, and
a new matrix (3) of size NxM is created. Computed local vectors represent columns
of this new matrix X. Recall that elements of jth vector are partial ratings of
alternatives with respect to the jth criterion and sum to 1.
w1 w1 … wM
⎡ x11 x12 ... x1M ⎤
⎢x x 22 ... x 2 M ⎥⎥
X = ⎢ 21 . (3)
⎢ ... ... ... ... ⎥
⎢ ⎥
⎣ x N1 xN2 ... x NM ⎦
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Finally, local priority vectors are multiplied by the weights of related criterions to
obtain matrix (4), which aggregates performance ratings of all alternatives with
respect to all criteria.
⎡ w1 x11 w2 x12 ... wM x1M ⎤ ⎡ z11 z12 ... z1M ⎤
⎢w x w2 x 22 ... wM x 2 M ⎥⎥ ⎢⎢ z 21 z 22 ... z 2 M ⎥⎥ (4)
Z = ⎢ 1 21 =
⎢ ... ... ... ... ⎥ ⎢ ... ... ... ... ⎥
⎢ ⎥ ⎢ ⎥
⎣w1 x N1 w2 x N 2 ... wM x NM ⎦ ⎣ z N1 zN2 ... z NM ⎦
Summing the elements in each row of the matrix Z gives the final result (5):
weights for alternatives at fingertips of the hierarchy with respect to the goal at the
top of hierarchy.
M
wi = ∑ zij , i = 1,2,..., N (5)
j =1
The alternative with the highest weight coefficient value wi should be considered
as ‘the best alternative’, i.e. the best choice in the multicriteria sense.
2.2 Borda Count – Social Choice Method
Preferential voting methods from the SC theory exclusively use ordinal preference
information contained in the preference table (Table 2), created by collecting ballots
(in real elections). A constructed preference table usually has the following
properties. The size of the table is MxN, where M is the number of individuals and N
is the number of possible alternatives (choices). Each row represents the ranking of
alternatives performed by one individual. If j is the best alternative for individual i,
then the rank number is rij = 1; if j is the second-best alternative, then rij = 2, and so
on; if alternative j is the worst one, then rij = N.
Table 2. Preference table
Alt. 1 Alt.2 Alt. j Alt. N
Indiv. 1 r11 r12 ... r1j ... r1N
Indiv. 2 r21 r22 ... r2j ... r2N
... ... ... ... ... ... ...
Indiv. i ri1 ri2 ... rij ... riN
... ... ... ... ... ... ...
Indiv. M rM1 rM2 ... rMj ... rMN
In Borda Count, each alternative gets 1 point for each last place vote received, 2
points for each next-to-last point vote, etc., all the way up to N points for each first-
545
place vote. The alternative with the largest point total wins the election and is
declared to be the social choice.
For each rij in the preference schedule, a number
qij = N – rij + 1 (6)
is assigned by the above procedure, and the total score for alternative j is given as
M M M
(7)
Qj = ∑
i =1
q ij = ∑
i =1
( N − rij + 1) =M ( N + 1) − ∑r .
i =1
ij
The alternative j* with the highest Q value can be selected as the winner, i.e.
social choice:
Qj* = max Q j . (8)
1≤ j ≤ N
3 Example Application of the AHP+Borda Methodology
3.1 Statement of the Decision Problem
The problem is stated as to select the most desired long-term water management
plan for river basin by authorized institution such as the water committee (WC). The
WC is considered to be a decision body (global group) and what is said hereafter to
be ‘the group choice’ should be understood as ‘the WC choice’. Assuming that
individuals in sub groups will make certain decisions, the final decision should
certainly be made at the WC level in a democratic manner with respect to the
preferences derived by participating sub groups and/or their delegates.
3.2 Hierarchy
A decision problem is stated as a three-level hierarchy with: (1) a goal is at the top of
hierarchy, (2) five evaluating criteria under goal, and (3) five alternative management
plans under criteria level that is at the bottom of hierarchy Fig. 1.
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Fig. 2. Hierarchy of the problem
The hierarchy is adopted after each decision element is briefly described to all
participants at a plenary part of a session. Main decision elements (goal, criteria set
and alternatives) are as follows:
• Goal
Select the best (most desired) plan using given set of criteria
• Criteria set
Political influence criterion is considered as the gradually exposed impact of
various state and in-basin agencies and bodies, representatives of cities/villages,
stakeholders, producers and local leaders.
Economic criterion relates to real possibilities to implement the economical
process, reliability of economical parameters, estimated costs of investment,
operation and maintenance, and expected direct and indirect benefits.
Social issues criterion relates to issues such as infrastructure, demographic
changes (migration), health care and working conditions.
Environmental protection criterion relates to specific environmental and ambient
conditions such as the distribution of pleasant resorts, preservation of historical sites
and cultural values, accessing the objects and facilities, protecting water quality, and
particularly preserving acceptable sanitary conditions.
Technical criterion encapsulates interests in preserving proper spatial distribution
of projects, technical conditions for project operations, technologies involved, and
eligibility for technical improvements.
• Decision alternatives (management plans)
Plan 1 (Balance). High industrial developments are foreseen as well as intensive
irrigation. Electric power production will increase by 20% after certain
reconstructions of the existing hydroelectric objects and facilities. All users,
including big users such as irrigation and hydroelectric production, will have
547
approximately equal treatment. However, ecological and urban water requirements
will receive top priority in water allocation.
Plan 2 (Supply). Water supply (municipal and rural, human and animal) will
absolutely get an increased concern from the state agencies responsible for water
management. It will be dominantly realized by means of reservoir management.
Demographic movements from rural areas to cities and state capitals will continue
with an actual increasing trend, but will be significantly decreased by the middle of
the planning period. Irrigation will rise to only 50% of that amount estimated as
maximum by the end of the period.
Plan 3 (Irrigation). Irrigation will have a dominant role with respect to the other
water uses throughout the basin. Priority will be given to large irrigators
(development at a level higher than 80% of the estimated maximum). No water
payments are expected until 2020; only irrigation and industrial uses will be charged
afterwards.
Plan 4 (Payment). Water payments will start progressively by 2020, with revisions
of payment policy every 5 years (2025 and 2030). Pricing will be combined with an
advanced system for obtaining the water rights. Other elements of the plan are the
same as in Plan 3.
Plan 5 (Other users). This plan is a modification of Plan 1 in a way to emphasize
importance of small irrigation users, tourism, eco-tourism and other small users (such
as handmade manufacturers, ceramic industry). Intent is to enable that various users
(other than large ones) will receive a higher priority by obtaining proper water rights
and excluding payments; compensation for their uses of water will come from large
consumers in irrigation, hydroelectric production and industry by proper pricing
policy.
• Decision makers, interest groups and water committee as a global group
Participants were divided to three main interest groups:
(1) Public Authorities
(2) Civil Society
(3) Water Users.
Each participant is an individual decision-maker and fully autonomous. Note that
within the water committee as a global group, sub groups may gather individuals in
different ways for differently organized decision-making processes. In adopted
context, a group is the entire body of a water committee where ‘delegated’ decisions,
made in sub groups, have to be interpreted, justified, aggregated (by consensus or
not) and put in power.
3.3 Remarks
Several main remarks can be given to better describe the decision-making
framework:
Remark 1. WC decides by applying scientifically sound multicriteria (AHP) and
election (Borda Count) methods, followed by common aggregating techniques.
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Remark 2. WC recognizes panel meetings as principal mean of its work where
mediating rules must be adopted by consensus, and where the final decisions are to
be made. WC also recognizes ‘decentralized part’ of the decision process performed
at separate meetings of each entity. Entities are by assumption authorized to make
their own decisions and forward them to be aggregated at the WC level.
Remark 3. Each entity has ‘its own point of view’ while evaluating possible decision
alternatives and ranking them appropriately. An outcome of the decision process
conducted through each entity is forwarded to the WC level (for aggregation) as it is.
That means that no any changes, interpretations or justifications are permitted.
Remark 4. As first part of the decision-framework, the method used by each entity in
assessing criteria and management plans is AHP. Sub group consensus is assumed
where logical and/or appropriate. Although AHP produces cardinal preferences of
decision alternatives, represented by computed weights, only ordinal information is
analyzed, i.e. ranking of the alternatives.
Remark 5. Each entity (individual or specific sub group) assesses the same set of
management plans across the same criteria set.
Remark 6. By applying voting method Borda Count to the reduced set of best-ranked
plans, it is possible to come-up to the final decision: the preferable management plan.
3.4 Procedure and Results
The WC as a global group is divided into three interest groups. After individual
opinions were synthesized for each interest group, the sub-group decisions are
forwarded to an upper level: the WC level is where the final aggregation and
interpretation of result is performed. The decision procedure and obtained results
were as given below.
A total of 21 participants split into three Interest Groups (IG), namely: Public
Authorities (7 delegates); Civil Society (5 delegates); and Water Users (9 delegates).
• First part of the session - AHP evaluation
Delegates individually assessed hierarchy given in Fig. 1 by using AHP within each
IG. Each delegate had to fill-in six pairwise comparison matrices with numbers from
the Saaty’s 9-points fundamental scale. Local weights of criteria vs goal and
alternatives versus criteria are computed by the eigenvector method and standard
AHP synthesis generated the final weights of alternative plans versus global goal
(best plan) for each individual.
Based on the number of individuals in the sub-groups, participation weights of
sub groups in the WC are defined as: 40% for interest sector of water users, 34% for
public authorities and rest of 26% for civil society. By applying these weights, the
final aggregation is performed to obtain the final group decision corresponding to the
WC level, Table 3. The best plan, as the WC final choice, is Plan 1 (Balance), second
ranked is Plan 2 (Supply), and third one is Plan 5 (Other Users). Least desired plan is
Plan 3 (Irrigation). It is easy to see that Plan No. 1 (Balance) is selected as the best by
two IGs: Public Authorities and Water Users. Top ranked by Civil Society is Plan 5
(Other Users), while Plan 1 is ranked as second. Worthy to notice is also that Plans 1,
549
2 and 5 are top-3 ranked by all IGs. Notice also that final ranking mostly reflects
preferences of the third interest group (Water Users).
Table 3. Subgroups ranking and the final AHP aggregation at the WC level
IG Weights of Alternatives (Plans)
IG
weight 1 2 3 4 5
0.258 0.249 0.117 0.145 0.231
Public Authorities (7) α1=0.34
(1) (2) (5) (4) (3)
0.314 0.178 0.037 0.056 0.415
Civil Society (5) α2=0.26
(2) (3) (5) (4) (1)
0.309 0.289 0.139 0.119 0.144
Water Users (9) α3=0.40
(1) (2) (4) (5) (3)
Aggregated (WGM) 0.306 0.254 0.098 0.110 0.232
Ranking 1 2 5 4 3
• Second part of the session - Borda Count evaluation
In the second part of decision-making process, the Borda Count is employed and
within all three sub groups participants individually re-assess reduced set of
alternatives. Result of the AHP application (Table 3) showed that plans 1, 2 and 5 are
most prominent, having much higher weights then plans 3 (weight 0.098) and 4
(weight 0.110), so 21 participants re-assess only those three plans.
This time, however, they did not ranked criterions within criteria set like in AHP.
Rather, all criteria are considered as unique criterion, which describes general desire
and implicitly contains ‘a flavor’ of each criterion from the original criteria set.
Keeping this in mind, each individual ranked by importance alternatives within new
alternative set. Participants are asked to express their individual (ordinal) preferences
by filling-in appropriate boxes with integers 1-3 in distributed evaluation sheet. BC
computations were straightforward afterwards.
Individual and final ranking of alternative plans derived within each interest
group by BC is summarized in Table 4.
Table 4. Final Borda Count assessment at the WC level
IG Ranks of Alternatives (Plans)
IG
weight 1 2 5
Public Authorities α1=0.33 2 (15) 3 (12) 3 (16)
Civil Society α2=0.33 1 (6) 3 (14) 2 (10)
Water Users α3=0.33 3 (21) 1(16) 2 (17)
Final aggregate 6 7 7
Final ranking 1 2-3 2-3
Assuming that obtained three rankings in interest groups are additionally
aggregated at the WC level (by following the same Borda Count procedure and
associating equal weight to each IGs’ ranking), the best alternative is Plan 1
(Balance), while Plan 2 (Supply) and Plan 5 (Other users) share second and third
place.
550
4 Conclusions
The paper presents group decision-making framework that could be applicable as a
part of paradigm decision-making in any water committee responsible for water
management on the river basin scale. The problem is stated as to select the most
desired long-term management plan among several offered plans by assessing plans
across selected more or less conflict criteria. Presented approach illustrates how two
different methodological options in decision-making can be combined for
establishing common professional, social and political environment where people
ought to make decisions by using advanced scientifically sound techniques. First part
of session included more complex, more detailed and time and effort consuming
evaluation of management plans. Thus, we believed that it is more convenient for
participants to use simple voting method in second part of the session where final
decision is to be made.
It should be noted that the final ranking does not necessarily depend on the
number of voters, and on the size of the subgroups. So, in the SC process of voting a
large subgroup has the same power as a small subgroup. This could yield to ranking
that does not satisfy the conditions of social welfare functions, and especially the
principle of majority decision. An issue of number of members in groups or sub-
groups, importance of individuals (experts) within sub groups and across
representatives on group level, and related problems of preserving fairness,
competence and consistency - is always for discussion in practical applications. And
of course, our approach is not immune of it.
In voting part of a methodology, we imply that only representatives of different
subgroups (one person for one subgroup) within relatively large water committee
should vote. This must not be a rule. A possible new direction of research could be
how to effectively and consistently avoid any early confrontation of individuals and
sub group within WC, i.e. how to define their different weights based on
competences, i.e. expert knowledge, education, attitude, willingness, political
impacts etc.
It is important to mention that involved decision makers found proposed
methodology transparent, easy to understand and implement, and results trustful.
Acknowledgment. Authors acknowledge the financial support from the Ministry of
Education and Science of Serbia under the Fundamental scientific research program
in Mathematics, Computer Science and Mechanics; Grant No. 174003 (2011-2014):
Theory and application of the analytic hierarchy process (AHP) in multi-criteria
decision making under conditions of risk and uncertainty (individual and group
context).
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