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that opinion of an individual agent not only depends on its location and type
of land use but also on spatial factors like the size of an area, and the distance
to areas having strongly deviating opinions. For example, small isolated spots
in the spatial environment which have clearly a different opinion only supported
by one or few actors might less likely survive in the opinion dynamics process
than large areas of actors having similar opinions.
To represent the spatial influence on the opinion, a neighborhood representa-
tion is adopted. Based on the opinions of all agents in the simulation the spatial
influence is alculated as:
Qspa
k,g,i,j,
(
t
+1)
=
(
x
=1)
(
k
=1)
O
k,x,t
N
(8)
Where:
Qspa
k,g,i,j,
(
t
+1)
is the spatial influence factor of the opinion of agent
k
for land use
g
at location
i,j
,
O
a,k,l,t
are the opinions of agent
a
stored in cell
x
part of the set of cells
X
of the neighborhood and
N
=
.
Based on the social and spatial influence factors a weighting factor is cal-
culated which accounts for adaptation of the social distance threshold
d
.The
weighting factor is calculated according:
|
X
|∗|
K
|
Q
k,g,i,j,t
=
π ∗ Qsoc
(
k,g,i,j,t
)
+(1
− π
)
∗ Qspa
k,g,i,j,t
(9)
Where
π
is a parameter indicating the priority of the social influence versus the
spatial influence. Finally, the threshold
d
is adapted according:
d
k,g,i,j,
(
t
+1)
=
d
k,g,i,j,t
)
∗
(1
−
(
|O
k,g,i,j,t
−Q
k,g,i,j,t
|
)
τ
)
(10)
Where
d
k,g,i,j,
(
t
+1)
is the adapted
d
for agent
k
at time
t
+1.
τ
a parameter
which defines the resilience of an agent against adaptation of its opinion. Figure
1 shows the effect of various values of
τ
(1, 3 , and 9) on the adaptation factor.
An agent is only willing to update its opinion iff:
S
(
k,l
)
(
i,j
)
<d
k
i,j
(11)
To update the agent opinions the Deffuant-Weisburg approach is adapted for a
spatial context according:
O
(
t
+1)
(
a,i,j
)
=
O
(
t
)
(
a,i,j
)
+
μ
a
(
O
(
t
)
(
a,i,j
)
−
O
(
t
)
(
b,i,j
)
)
(12)
1.2
1
0.8
1
3
9
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
|O
k,g,i,j
-Q
k,g,i,j
|
Fig. 1.
Effect of different values for
τ
on the adaptation factor
