Analysis of Objectives
Actors-Objectives:
The Actor-Objectives option gives matrix and bar representations of the number of indifferences, agreements or
disagreements of each actor on the studied system of objectives.
This option represents in a matrix with values -1, 0 and 1 as a result of the normalization of the agreement
values provided by the experts. Since the matrix constitutes the position of the different actors (located in
the matrix rows) towards a specific set of objectives (located in the matrix columns) the interpretation of
the results of each row reflect the particular actor's position towards the system's objectives, and the results of
each column reflect the position of all the actors towards a particular objective.
The sum of the positive ones (1) within a row (i) indicates the number of objectives that the actor (i) agrees
with. The sum of the negative ones (-1) within a row (i) indicates the number of objectives that the actor (i)
disagrees with. The sum of the zeros (0) within a row (i) indicates the number of objectives that the actor (i)
is indifferent to.
The sum of the positive ones (1) within a column (j) indicates the number of actors that agree with the objective
(j). The sum of the negative ones (-1) within a column (j) indicates the number of actors that disagree with
the objective (j). The sum of the zeros (0) within a column (j) indicates the number of actors indifferent to
the objective (j).
The Bar representation reflects in the upper side (color green) the specific objectives a particular actor
(located in the X-axes) is in favor; in the lower side (color blue) the specific objectives the same actor
is against.
Objectives-Actors:
The Objectives-Actor option gives matrix and bar representations of the number of indifferences, agreements
or disagreements of each actor on the studied system of objectives. The difference between the Actor-Objective
and the Objective-Actor option is basically the bar chart representation. In this option the objectives are
located in the X-axes of the bar chart and the actors are located in the Y-axes.
Therefore the Objective-Actors chart represent the in the upper side the specific actors in favor a particular
objective and in the lower side indicates the specific actors against the same objective.
Potential Actors-Objectives:
The Potential Actor-Objectives option gives matrix and bar representations of the indifferences and the degree
of agreements or disagreements of each actor on the studied system of objectives.
This option represents in a matrix, with values according to the criteria defined by the forecaster, the results
of the responses provided by the experts. Since the matrix constitutes the potential position of the different
actors (located in the matrix rows) towards a specific set of objectives (located in the matrix columns) the
interpretation of the results of each row reflect the particular actor's position towards the system's objectives,
and the results of each column reflect the position of all the actors towards a particular objective.
The sum of the positive values within a row (i) indicates the degree of agreement towards the objectives by the
actor (i). The sum of the negative values within a row (i) indicates the degree of disagreement towards the
objectives by the actor (i). The sum of the zeros (0) within a row (i) indicates the number of objectives that
the actor (i) is indifferent to.
The sum of the positive values within a column (j) indicates the degree of agreement of the actors towards the
objective (j). The sum of the negative values within a column (j) indicates the degree of disagreement of the
actors towards the objective (j). The sum of the zeros (0) within a column (j) indicates the number of actors
indifferent to the objective (j).
The Bar representation reflects in three (3) levels (high, medium, low) in the upper side (color green) the
specific objectives and the intensity a particular actor (located in the X-axes) is in favor; in the lower side
(color blue) the specific objectives and the intensity the same actor is against.
Potential Objectives-Actors:
The Potential Objectives-Actor option gives matrix and bar representations of the number of indifferences and
the degree of agreements or disagreements of each actor on the studied system of objectives. The difference
between the Potential Actor-Objective and the Potential Objective-Actor option is basically the bar chart
representation. In this option the objectives are located in the X-axes of the bar chart and the actors are located
in the Y-axes
Therefore the Potential Objective-Actors chart represents in the upper side the degree in which specific actors
are in favor a particular objective and in the lower side indicates the degree in which specific actors are against
the same objective.
Indifferences:
This option provides the forecaster with a bar chart indicating objectives in the X-axes and actors in the
Y-axes. Indifferences chart consist on a graphical bar representation of the specific actors presenting
indifferent position towards the particular objective located in the X-axes. The potential actor-objective
matrix is also provided in this option below the bar graph.
Alliances and Conflicts:
This option allows detection of the number of possible alliances and conflicts between actors in relation to
the system of objectives. It provides the forecaster with two (2) charts and two (2) matrixes. The charts and
the first "special" matrix of this option are the results of the last matrix (normalized MAO matrix) "specially"
multiplied by its transpose matrix.
The three different coefficient values for each variable are represented in the last three columns of the
matrix of this option. The bar chart provided in this option represents the coefficient of force of each studied
variable related to the strongest variable. In this sense, the strongest variable will be represented with the
highest bar and the value 1.
To understand the first two charts and the first "special" matrix, it is necessary to know the meaning of the
"special" multiplication mentioned before. As seen in the Actor-Objective option, the normalized MAO matrix
represents with values -1, 0 and 1 the normalization of the agreement values provided by the experts. Therefore,
while analyzing the possible alliances and conflicts, the main outcome of the matrix multiplication is to
determine the sign (positive or negative) of the interaction between the actors of the system in relation to
the set of objectives.
The MAO matrix multiplication by its transpose will not be carried out as a standard matrix multiplication
(where partial results of the multiplication of variables from row (i) of matrix A with variables of column
(j) of matrix B are added to give one unique value for cell a (i, j) of new matrix C).
Instead, the multiplication of values of row (i) of matrix A with values of column (j) of matrix B will be
classified according to their signs (positive, negative or neutral) in four different results located in a
four-quadrant cell. Each quadrant of this new cell reflects the interaction of two specific actors in relation
to the complete system of objectives.
The figure above shows a small system with three actors and two objectives. The circles indicate the interest of
the actor on the objective indicated by the small arrows. The blue circle with the minus sign (-) indicates a
negative interest, in other words, a position against the referred objective. The green circle with the plus
sign (+) indicates a positive interest (in favor of the referred objective). Finally, the gray circle with the
zero represents a neutral position or indifference towards the objective.
Theses relationships of interest of each actor on the system's objectives (reflected in the MAO matrix) are
explained in more detail in the first chart option (Actor-Objective).
The mathematical operation to obtain the matrix of alliances and conflicts (MAA) thus consists of multiplication
of the MAO matrix by its transpose. In order to visualize this operation, the following figure shows the matrix
multiplication.
As mentioned before, this operation provides the forecaster with a new matrix MAA in which each cell will present
four (4) quadrants (see figure below).
The results of this square matrix can be read by either rows or columns, since the values are symmetrically
represented on both sides of the diagonal.
For the effects of this example, the explanation here reflects the reading of the intersection of A1 with A2.
First row indicates the relationships between Actor 1 and the rest of the actors (A2 and A3) according to the set
of objectives. The intersection of A1 with A2 reflects:
- The number one (1) in the green quadrant indicates that there is one (1) objective for possible alliance between
A1 and A2 (note that both actors are against objective 1).
- The zero (0) in the blue quadrant indicates that there are no objectives for possible conflict between these two
(2) actors.
- The zero (0) in the gray quadrant indicates that there are no objectives with coincidence by indifference between
these two (2) actors.
- The number one (1) in the orange quadrant indicates that there is one (1) objective for possible conflict by
indifference between A1 and A2 (note that Actor 1 is indifferent towards objective 2 while Actor 2 is against
objective 2; this difference could probably cause a conflict by indifference since Actor 2 would try to win
Actors 1 (indifferent) to his/her side).
- Finally, this option also provides with two (2) charts or maps summarizing the results obtained in the
previous matrix. The first map represents in the upper size the number of possible alliances between the
actors (graphical representation of all the green quadrants) and in the lower side represents the number
of possible conflicts (graphical representation of all the blue quadrants). The second map represents the
coincidences and the conflicts by indifference (graphical representation of the gray and the orange quadrants).
Alliances and Conflicts Weighted:
This option allows detecting the degree of possible alliances and conflicts between actors in relation to the
system of objectives. The charts and matrixes provided in this option are basically obtained using the same
procedures already explained in the Alliances-Conflicts option. However, the matrix operations involve the
potential Actor-Objective matrix instead of the normalized MAO matrix.
The new matrix obtain in this operation is the Alliances-Conflicts Weighted matrix (MAAP) which includes the
weight of the positive or negative interest of the actors on the objectives of the system (the scale or criteria
to measure such interest is previously defined by the forecaster before starting the study).
In this sense, results will reflect the weight or degree of possible alliances and conflicts between the
actors, as well as their coincidences and conflicts by indifferences (please read explanation in Alliances-Conflicts
option, always taking into consideration that the MAO matrix in this option is not normalized).
Alliances and Conflicts Weighted With Forces:
This option allows detecting the degree of possible alliances and conflicts between actors in relation to the
system of objectives taking into consideration the coefficient of forces of the actors. The charts and matrixes
provided in this option are basically obtained using the same procedures already explained in the
Alliances-Conflicts Weighted option. However, the matrix operations involve the multiplication of the
potential Actor-Objective matrix with the actors' coefficient of forces vector.
The new matrix obtain in this operation is the Alliances-Conflicts Weighted with Force matrix (MAAVP) which
includes both the Vector of the coefficients of force and the weight of the positive or negative interest of
the actors on the objectives of the system (the scale or criteria to measure such interest is previously
defined by the forecaster before starting the study).
In this sense, results will reflect the weight with force or real degree of possible alliances and conflicts
between the actors, as well as their coincidences and conflicts by indifferences (please read explanation
in Alliances-Conflicts option, always taking into consideration that the MAO matrix in this option is not
normalized and multiplied by the force vector).
Potential Actors-Objectives Weighted With Forces:
The Potential Actor-Objectives weighted with forces option gives matrix and bar representations of the
indifferences and the degree of agreements or disagreements of each actor on the studied system of objectives
considering the actors coefficients of force.
The difference between the Potential Actor-Objective and the Potential Objective-Actor weighted with force
option is that in this option the potential MAO matrix is multiplied by the actors' Coefficients of Force
Vector.
Potential Objectives-Actors Weighted With Forces:
The Potential Objectives-Actor weighted with forces option gives matrix and bar representations of the number of
indifferences and the degree of agreements or disagreements of each actor on the studied system of objectives.
The difference between the Potential Actor-Objective weighted with Force and the Potential Objective-Actor weighted
with Force option is basically the bar chart representation. In this option the objectives are located in the
X-axes of the bar chart and the actors are located in the Y-axes.
Therefore, the Potential Objective-Actors weighted with Force chart represents in the upper side the real
degree in which specific actors are in favor a particular objective and in the lower side indicates the real
degree in which specific actors are against the same objective. (Potential Objectives-Actors)
Coefficient of Feasibility:
This option provides the forecaster with the coefficient of feasibility of the objectives of the studied system.
The coefficient of feasibility of the objectives is directly proportional to the degree of the objective approval
weighted with the actors' coefficient of forces and inversely proportional to degree of the objective disapproval
weighted with the actors' coefficient of forces. There are three (3) different representations of the
coefficients of feasibility:
Real coefficient of feasibility: r (i)
r (i) = (OA_i/sum(OA_i)) * (OA_i/sum(OA_i + OD_i) )* (1/n)
Coefficient of feasibility relative to the most feasible objective: R (max)
R (max) = r (i) / max r (i)
Coefficient of feasibility relative to the system: R (i)
R (i) = r (i) / sum r (i)
Where OA_i is the total approval of the objective (i) weighted with the actors coefficient of force, OD_i is the total
disapproval of the objective (i) weighted with the actors coefficient of force and n is the total number of objectives.
For simplicity, this coefficient is normalized using two (2) different criteria:
- dividing r (i) by the maximum real coefficient, and thus giving the relative feasibility of the objective to the most feasible objective of the system: R (max)
- dividing r (i) by the sum of the real coefficients, and thus giving the relative feasibility of the objective in the system: R (i).
The bar chart provided in this option represents the coefficient of feasibility of each studied objective related to
the most feasible objective. In this sense, the most feasible objective will be represented with the highest bar
and the value 1. The three (3) type of coefficient of feasibility are represented in a table below the bar chart.
Coefficient of Partnership:
This option provides the forecaster with the coefficient of partnership of the actors of the studied system.
The coefficient of partnership of the actors is directly proportional to the degree of the possible alliances
weighted with the actors' coefficient of forces and inversely proportional to degree of the possible conflicts
weighted with the actors' coefficient of forces (considering the system of objectives as a whole).
There are three (3) different representations of the coefficients of partnership:
Real coefficient of partnership: r (i)
r (i) = (AA_i/sum(AA_i)) * (AA_i/sum(AA_i + AC_i) )* (1/n)
Coefficient of partnership relative to the most associable actor: R (max)
R (max) = r (i) / max r (i)
Coefficient of partnership relative to the system: R (i)
R (i) = r (i) / sum r (i)
Where AA_i is the total degree of the possible alliances of actor (i) weighted with the actors' coefficient of
forces, AC_i is the total degree of the possible conflicts of actor (i) weighted with the actors' coefficient
of forces and n is the total number of actors. For simplicity, this coefficient is normalized using two (2)
different criteria:
dividing r (i) by the maximum real coefficient, and thus giving the coefficient of partnership of the actor (i)
relative to the most associable actor of the system: R (max)
dividing r (i) by the sum of the real coefficients, and thus giving the coefficient of partnership of the actor
(i) relative to the system: R (i).
The bar chart provided in this option represents the coefficient of partnership of each studied actor related
to the most associable actor. In this sense, the actor with the highest coefficient of partnership will be
represented with the largest bar and the value 1. The three (3) types of coefficients of partnership are
represented in a table below the bar chart.
|