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Ta b l e 1 . Agent distribution corresponding to x values in Figure 2
Agent Distribution in (c) to (f)
Agent Distribution in (a) and (b)
x
1
2
3
4
5
6
7
8
9
10
11
12
13
1
2
3
4
5
6
7
8
9
10
11
|
A FT
|
0
0
0
0
0
0
0
5
10
15
20
25
30
0
0
0
0
0
0
2
4
6
8
10
|
A HT
|
0
5
10
15
20
25
30
25
20
15
10
5
0
0
2
4
6
8
10
8
6
4
2
0
|
A NT
|
30
25
20
15
10
5
0
0
0
0
0
0
0
10
8
6
4
2
0
0
0
0
0
0
peak is 0.5 and A NT subset of Not Trustworthy agents where the peak is 0. We start with
A = A NT and gradually move the agents from A = A NT to A = A HT such that we reach
the state of A = A HT where all the agents belong to A HT . Later, we move agents from
A = A HT to A = A FT and we finally end up with A = A FT . Over this transformation, the
robustness of the estimated distribution of Π a S →a D ( τ ) ,
T is evaluated with respect
to the nature of trustworthiness of the agents. We carry out separate experiments by
changing: (1) The number of agents in the set A , (2) The number of interactions between
each pair of connected agents, as demonstrated in Figure 1(b), and (3) The manipulation
Algorithm. We intend to observe the influence of each one of these components on the
final estimated distribution of Π a S →a D ( τ ) ,
τ
τ
T . In all experiments, the number of
trust ratings,
|
T
|
, is equal to 5 (a commonly used value in most surveys).
Experiments with Manipulation Algorithm I. In the first set of experiments, the
manipulation algorithm I is used by agents in A . Diagrams on the left side of Figure 2
represent three different experiments where the number of agents in A and the number
of interactions among every pair of connected agents, as illustrated in Figure 1(b), have
changed. Table 1 gives the distribution of agents A into A FT
A HT over x axis
values in Figure 2. The three left side diagrams of Figure 2 demonstrate that through
migration of the agents from A NT to A HT and later to A FT ,the I increases and EE
decreases. This is a consequence of the increase in the accuracy of information provided
by the agents in A as they become more trustworthy.
Comparing the three experiments on the left side of Figure 2, increase in the number
of agents in Figures 2(c) compared to 2(a), does not improve the results over high values
of x , where the number of the agents in the A FT subset is non-zero. This indicates that
as long as the quality of the information reported by the agents in A does not improve,
increase in the number of the agents will not improve the estimated distribution of
Π a S →a D ( τ ) ,
A NT
T . However, from x =2 to the case where all agents are in A HT , EE
reduces and I increases. This indicates that if agents are not completely trustworthy, an
increase in the number of agents increments the quality of the estimated distributions.
Comparing Figures 2(c) and 2(e), increase in the number of interactions in-between
the agents has increased I and decreased EE in Figure 2(e) which is a consequence
of higher information exchanges between the agents. Thus, the possibility distributions
built by the agents are derived from more information which enhances the estimation
accuracy.
τ
Experiments with Manipulation Algorithm II. We repeat the same experiments with
manipulation algorithm II to observe the extent of influence of the chosen manipulation
algorithm by the set A on the final distribution of Π a S →a D ( τ ) ,
τ
T .TheDiagrams
 
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