ArticlePDF Available

Abstract and Figures

We propose an individual based model of attitude dynamics which, in some conditions, reproduces primacy effec t behaviours. The primacy effect takes place when the attitude of an individual depends on the reception order of features describing an object. T ypically, when receiving a strong negative feature first, the individual keeps a negative attitude whatever the number of moderate positive features i t receives afterwards. We consider a population of individuals which recei ve the features from a media, and communicate with each other: in some cases, interactions increase the number of individuals exhibiting a pri macy effect, in other cases they decrease this number. To better understa nd this phenomenon, we developed aggregated models of the individual based model with interaction.
Content may be subject to copyright.
When do interactions increase or decrease primacy effect?
S. Huet and G. Deffuant
Cemagref, LISC, BP 50085, F-63172 Aubière Cedex
sylvie.huet@cemagref.fr - guillaume.deffuant@cemagref.fr
Abstract: We propose an individual based model of attitude dynamics
which, in some conditions, reproduces primacy effect behaviours. The
primacy effect takes place when the attitude of an individual depends on the
reception order of features describing an object. Typically, when receiving a
strong negative feature first, the individual keeps a negative attitude
whatever the number of moderate positive features it receives afterwards.
We consider a population of individuals which receive the features from a
media, and communicate with each other: in some cases, interactions
increase the number of individuals exhibiting a primacy effect, in other
cases they decrease this number. To better understand this phenomenon, we
developed aggregated models of the individual based model with
interaction.
Keywords
: Primacy effect, Information filtering, Agent-based model, aggregated model, collective effects
of interactions
1 Introduction
“Attitude is a psychological tendency that is expressed by evaluating a particular entity with some
degree of favour or disfavour” Eagly and Chaiken (1998). Attitudes have been postulated to
motivate behaviour and to exert selective effects at various stages of information processing (Eagly
and Chaiken 1998): information may be filtered by the individuals, i.e. they ignore it. Festinger in
his theory of cognitive dissonance (1957) proposes some mechanisms for this selection: people seek
out information that supports their attitudes and avoid information that challenges them, in order to
minimise their cognitive dissonance. Following this theory, even if they assimilate information
which contradicts their global attitude, people are reluctant to talk about it, because they avoid
expressing their dissonance. Such selection mechanisms can imply sensitivity to the order of
information delivery. Without making assumptions about selection mechanisms, Asch (1946),
Miller and Campbell (1959) have shown one of the main known order effects: the primacy effect.
The primacy effect occurs when somebody who encounters two opposing messages forms
judgments more consistent with the first message. Our main purpose is to model this individual bias
in order to study what it implies at an aggregated level. In other words, we ask what such an
individual bias can change in a population dynamics.
Several researches in social modelling include some effect of attitude on information transmission
and vice-versa (Allport and Postman 1947; Lawson and Butts 2004; Galam 2003, Huet and
Deffuant 2006; Tsimring and Huerta 2003). The bounded confidence models (Urbig 2003, Urbig
and Malitz 2005) implement reception and emissions filters on attitudes or opinions. In the model
of innovation diffusion of Deffuant et al. (2005), this opinion dynamics is coupled with an
information propagation. However, none of these models focuses specifically on the primacy effect.
We propose a simple agent based model (ABM) of individual primacy effect, which abstracts from
the cited researches in social psychology. We particularly focus on the following question: do the
interactions between agents modify the likelihood of individual primacy effect in the population?
With the simple model we consider, the answer is clearly positive. In some cases, the number of
agents which show primacy effect is significantly higher, and in other cases significantly lower
when agents interact than when they are isolated. To better understand the interaction effect, we
follow a general approach of “double-modelling” (Deffuant 2004) which aims at providing
explanations of the collective effects observed in ABM simulations, using aggregated models of the
ABM behaviour. Thus, we build two analytical aggregated models of the agent-based model global
behaviour, following the method presented in (Deffuant and Huet 2006b). Our previous papers are
limited to some cases where interactions increase primacy effect (Huet and Deffuant 2006, Deffuant
and Huet 2006a). This paper provides also cases where interactions decrease the number of primacy
effect in the population.
First, we describe the individual-based model we study. In section 3, we focus on the analysis of the
dynamics without interactions. Section 4 is devoted to dynamics with interactions. Then, we use
aggregated models in order to explain the interaction effects. Finally, we conclude and outline next
steps of this research.
2 Sensitivity to event order and primacy effect: an individual model
2.1 A model of dynamics of attitudes
A central concept of our model is attitude, understood as a psychological tendency that is expressed
by evaluating a particular entity with some degree of favour or disfavour (Eagly and Chaiken 1993).
We model the dynamics of attitude considering its links with information. Attitude formation and
attitude change are linked to accumulation and organization of information about people, objects,
situations and ideas. Moreover, attitudes motivate behaviour and exert selective effects on
information processing.
The basis of our modelling consists of the dissonance theory (Festinger 1957) on the one hand, and
on Allport’s work on rumor diffusion (1947) on the other hand. We notice that individuals avoid
incongruent information, and, keep only important information.
We consider a population of N individuals who discuss about an object. As shown on figure 1, we
define this object by a set of features
(
)
dF ...,2,1=
, which are associated with positive or negative
real values
(
)
dj
uuu ,...,,...,
1
with
j
u
. An individual can have a partial view of the object, in
which case it has a real value for some features and nil for others. To simplify we use feature
instead of feature value.
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
value
or nil
OBJECT’S DESCRIPTION
Features
Figure 1. The description of an attitude object
An individual i is characterised by:
g: an initial attitude (In the following, we suppose that all individuals of the population have
the same initial attitude).
L
i
: a subset of F containing the features currently retained by the individual; This list is
supposed empty at the beginning.
+=
i
Lj
ji
ugG : the global attitude about the object. This choice can be related to
information integration theory of Anderson (1971),
a neighbourhood corresponding to the subset of individuals with whom i can communicate.
The dynamics of the model have four main aspects:
1. Exposure to feature values: individuals are exposed to features, which are made available
by the medium, or, interaction between individuals.
2. Selective retaining: individuals retain a feature if it is important enough. Incongruent
features are more difficult to retain than congruent ones. A feature is congruent when it has
the same sign as the individual’s global attitude to the object, incongruent otherwise. In
other words, when
0.
ji
uG , feature j is said congruent for individual i, and incongruent
otherwise. The dynamics of filtering are determined by a positive number,
Θ
the
incongruence threshold. Being told about feature j, an individual will react as follows (see
figure 2) :
If j is congruent “retain the feature.
If j is incongruent: if
Θ>
j
u
“retain the feature”; otherwise “ignore the feature” .
Here, “retain the feature” means that j is added to L
i
(if L
i
does not include j yet), “ignore the
feature” means that the feature is filtered (not added to L
i
).
3. Selective emission: individuals only talk about congruent features
4. Computation of attitude: an individual computes its global attitude each time it retains a
new feature. As presented in the characteristics of the individual, the global attitude to the
object is the sum of the feature values the individual retained and its initial attitude, g.
0
Feature
Θ
retainedretained filtered
0
Feature
Θ
retainedretained filtered
Figure 2. For g > 0, the negative features are filtered if they have an absolute value lower than
Θ
.
2.2 Individual trajectories
From the definition of the dynamics presented above and if we assume that each feature is equally
diffused to all individuals, it is easy in most cases to define the final sign of each initial group of the
population. We consider that a feature is randomly delivered to the population. The delivery
frequency is, on average, the number of individuals who are exposed to a feature per iteration.
2.2.1 Most cases are simple
We first consider very simple cases, in which the model behaviour is easy to predict:
-
If all the features are of the sign of g, then the final global attitude is the sum of g and all the
features.
-
If all the features are higher, in absolute value, than
Θ
the "incongruence" threshold, then the
final global attitude is the sum of g and all the features.
-
If all the features are, in absolute value, below
Θ,
then final global attitude is the sum of g
and all the features of same sign as g.
In these cases, the individual is not sensitive to the order of feature reception. Thus, we have only
one possible trajectory for each individual.
However, in other cases, individuals are sensitive to order of feature reception and exhibit the
primacy effect. In these cases, an individual has several possible trajectories depending on the order
feature reception.
2.2.2 Some cases are sensitive to feature order
We now consider an individual with an initial attitude g > 0, and an object with at least one negative
feature of absolute value higher than
Θ
, and positive features lower than
Θ
(the same reasoning can
be done with inverted signs). In this case, the final attitude can depend on the reception order:
-
If the individual receives the negative feature first, if g is low enough, it can change its
global attitude, and the positive features become incongruent. As they are lower than
Θ
, they
are not retained.
-
If the individual receives the positive features first, these features are necessarily retained.
When the individual attitude is sensitive to the feature reception order, we can observe primacy
effect: the individual’s attitude sign is defined by the first few features it receives.
This leads us to our more concrete example to help understand how effect appears. We suppose that
the initial attitude g is positive. Then we consider an object described by 5 features: two major
negative ones, called of value - U, such that U >
Θ
, and three positive ones, called u, such that u <
Θ.
We suppose that the object is globally neutral, that is: 3u 2U = 0. For instance, we choose U =
6 and u = 4, with
Θ
= 5.
Figures 3 shows the evolution of a global attitude, for a given reception order. Initially, our
individual has an attitude g = 6.5. First, it receives a positive feature, which is retained because it is
congruent, and its attitude increases to 10.5. Second, it then receives a negative feature, which is
incongruent, but is retained because its absolute value is higher than the threshold, and its attitude
decreases to 4.5. Next, it receives the second negative feature, which is incongruent and also
retained and its attitude decreases to –1.5. It is now going to be exposed to the fourth and the fifth
positive features, which are incongruent with an absolute value below the threshold, and therefore
they are not retained. Its attitude thus does not change anymore. It has finally a negative attitude
although the object is globally neutral.
0
-2
0
2
4
6
8
10
12
rank of publication
attitude
1st: u
-2
0
2
4
6
8
10
12
rank of publication
attitude
2nd: U
-2
0
2
4
6
8
10
12
rank of publication
attitude
3rd: U
-2
0
2
4
6
8
10
12
rank of publication
attitude
4th: u
-2
0
2
4
6
8
10
12
rank of publication
attitude
5th: u
-2
0
2
4
6
8
10
12
rank of publication
attitude
Figures 3. Example of temporal evolution of the attitude of an individual which receives features in order u, U, U, u, u
The figure 4 shows another order of feature exposure which begins with the three consecutive
positive features received first. All features are retained in this case and our individual’s attitude
follows another trajectory, leading to a final positive attitude.
Individual trajectories for
g
= 6.5, U = -6 and u = 6
-4
0
4
8
12
16
20
time 0 1st 2nd 3rd 4th 5th
rank of publication
attitude
UUuuu
uuuUU
Figure 4. Two possible individual trajectories
A last diagram on figure 5 shows the ten possible trajectories of attitude. As all positive features are
equal and all negative features are also equal, we just have to consider 10 different feature orders to
describe all possible individual trajectories. Depending on the cases, the first, the two first, or at the
most, the three first features received determine the final sign of attitude: this is the primacy effect.
Individual trajectories for
g
= 6,5; U = -6 and u = +4
-8
-4
0
4
8
12
16
20
time 0 1st 2nd 3rd 4th 5th
rank of publication
attitude
UUuuu
UuUuu
UuuUu
UuuuU
uUUuu
uUuUu
uUuuU
uuUUu
uuUuU
uuuUU
Figure 5. All possible individual trajectories in case g = 6.5, 5 features composed of 2 U and 3 u with U = -6 and u = +4
3 Isolated individuals
3.1 A directly readable global state
We consider now a population of isolated individuals, with the same initial attitude g. Each
trajectory shown on figure 5 has the same probability of occurring. Figure 6, shows the final state,
of the population, which includes, 70 % of individual with a final positive attitude, because we
observe 7 final positive trajectories out of 10 total trajectories, and, 30 % of individual with a final
negative attitude, because we observe 3 final negative trajectories out of 10 total trajectories.
Individual trajectories for g = 6,5; U = -6 and u = 4
-8
-4
0
4
8
12
16
time 0 1st 2nd 3rd 4th 5th
rank of publication
attitude
UUuuu
UuUuu
UuuUu
UuuuU
uUUuu
uUuUu
uUuuU
uuUUu
uuUuU
uuuUU
10 different
trajectories
3 are negative after being
exposed to all features
7 are positive after
being exposed to all
features
Figure 6. Deducing final population state from individual possible trajectories, in case g = 6.5, 5 features composed of 2
U and 3 u with U = -6 and u = +4
3.2 The major role of g, the initial attitude
We can observe on figure 7 the final percentage of negative individuals for various values of the
initial attitude, g. Horizontal axis represents the attitude intervals corresponding to one possible
value of the effect defined as the percentage of final negative attitudes. Since we are on the zone of
"primacy effect", from g>0 to g<|2U|, we observe its effect: from 80% to about 10% of individuals
are finally negative. This takes place even though we have no negative individuals initially and a
neutral global value for the object. This strong influence of the initial attitude g can be seen as the
first primacy effect.
We can read again that, for an initial attitude of 6.5, 30% of final attitudes are negative.
0
20
40
60
80
100
0 < g <
0,5u
0,5u < g <
u
u < g <
1,5u (or
<U)
1,5u < g <
2u
2u < g < 3u
(or <2U)
g > 3 u (or
>2U)
initial atttitude g
% of negative individuals
no interaction
Figure 7. Final percentage of negative individuals for various value of g
4 Population state from simulated individuals in interaction
We add interaction between individuals by a simple algorithm. We consider two cases:
an individual with a reception and an emission filter;
an individual with only a reception filter; this last case will help us to better qualify the result.
To simulate the interactions, we choose at random a couple (i,j) in the population. In the case of an
emission and reception filter, i tells j about one of its randomly chosen congruent features. In the
case of only a reception filter, i tells j about one of its features, chosen at random, whether it is
congruent or not. The complete algorithm, containing exposure to the diffusion by media and
exposure from interaction is:
For a population of N individuals, at each time step:
N times repeat:
Media diffusion. choose individual i at random with probability f, choose feature j at random in the
object, send feature j to individual i.
Interactions: choose couple of individuals (i,j) at random:
Emission and reception filter case: i tells j about one of its randomly chosen congruent features
Reception filter case: i tells j about one of its randomly chosen features.
Now, we examine how primacy effect can be amplified or decreased by the interactions. We
illustrate these phenomena using the same example as previously.
4.1 Interactions can increase the number of primacy effects
Figure 8 shows a comparison of the number of final negative attitudes (and therefore of primacy
effect) between the isolated and the interaction (with reception and emission filters) cases. The
isolated case is represented by brown bars, and the interaction case is represented in green bars
(average results on 100 replications).
for g=6.5: 30%
We observe that, for an initial attitude ranging from 0 to the absolute value of the most important
incongruent feature (in this case 6), interactions induce more negative final attitudes than the
isolated case. For example, for an initial attitude g = 2.5, we obtain 83% of negative individuals
with “interaction”, but only 70% in the for isolated individuals.
0
20
40
60
80
100
0 < g <
0,5u
0,5u < g <
u
u < g <
1,5u (or
<U)
1,5u < g <
2u
2u < g < 3u
(or <2U)
g > 3 u (or
>2U)
initial atttitude g
no interaction both filters
Figure 8. Final percentage of negative individuals for various values of g for both approaches: deduce from analysis of
isolated individual and simulated with interaction between individuals
We might think that the emission filter explains this result, but this is not the case. On figure 9, we
add to our previous results the case of interactions without emission filter (in purple). We also
observe an increase of primacy effect, in some cases higher, in some cases lower than the increase
observed with the emission filter, but for these values of g, we observe an increase of primacy effect
due to the interactions, for interactions with or without emission filter. We shall refer to this as the
“decrease primacy effect (EB)” effect of interactions.
0
20
40
60
80
100
0 < g <
0,5u
0,5u < g <
u
u < g <
1,5u (or
<U)
1,5u < g <
2u
2u < g < 3u
(or <2U)
g > 3 u (or
>2U)
initial atttitude g
no interaction only reception filter both filters
Figure 9. Zone of primacy effect increasing. Final percentage of negative individuals for various value of g for three
dynamics: isolated individual; interactions with both filters (reception and emission) and interactions with reception
filter only.
83%
70%
4.2 The interaction can decrease the effect of individual primacy effect
On the right of the figure 10, we note that an initial attitude g = 8.5, the isolated case yields 10% of
negative individuals whereas the “interaction with both filters” yields only 0.4% of them (green
bars). This is the “decrease primacy effect (EB)” effect of interaction. This effect takes place for
initial attitudes between U and 2U, which correspond to the values between the absolute value of
the most negative feature U and the sum of the absolute values of positive features. This implies
that this “decrease EB” effect cannot be observed with object having only one negative feature (as
in our first investigations).
0
20
40
60
80
100
0 < g <
0,5u
0,5u < g <
u
u < g <
1,5u (or
<U)
1,5u < g <
2u
2u < g < 3u
(or <2U)
g > 3 u (or
>2U)
initial atttitude g
no interaction only reception filter both filters
Figure 10. Zone of decreasing primacy effect. Final percentage of negative individuals for various value of g for three
dynamics: isolated individuals; interactions with both filters (reception and emission) and interactions reception filter
only
Note that with only a reception filter (in purple), we do not observe the decrease EB effect. In fact,
an individual which has an initial attitude comprised between U and 2U and which receives first a
negative feature, has still a positive attitude. Due to the emission filter, it does not communicate
about the negative feature it retained while others communicate the positive feature. If it receives a
positive feature right after the negative one, it will never be negative. The only possibility to be
negative is to receive the two negative features first. The probability of this case is decreased by the
interactions because these interactions are only about the positive features.
4.3 These interaction effects persist even the object is not neutral
We observed that the primacy effect can be increased or decreased by interactions. Until now we
considered a neutral object (i.e. the sum of features is 0). We can check that this effect remains
when the object is slightly positive or negative. Here, we increase or decrease the global value of
the object. We have changed values of U or u with respect of conditions to observe the primacy
effect.
In the case of an "increasing EB" interaction effect, table 1 presented values of U and u we have
tested with g = 2.5. For the case of an "increasing primacy effect" interaction effect, the tested value
with g = 6.5 are presented in table 2.
0.4% for g=8.5
10% for g=8.5
U u
Global value of the
object (sum of
features)
-6 4
0
-5,5 4
1
-6 4,5
1,5
-5 4
2
-6 5
3
-6 5,5
4,5
Table 1. Values of U and u implying different global
values of the object tested with g = 2.5
U u
Global value of the
object (sum of
features)
-6 4
0
-6 3,5
-1,5
-6 3
-3
-6 2,5
-4,5
-6 2
-6
-6 1,5
-7,5
-6 1
-9
-6 0,5
-10,5
Table 2. Values of U and u implying different global
values of the object tested with g = 6.5
Figures 11 show that the interaction effect remains in average for several positive or negative
objects. On the left, we can see the "increasing" negatives effect persists for a positive global value
of 1.5. On the right, the "decreasing effect" effect persists for a negative global value of -6.
5 features, g = 2.5
0
1000
2000
3000
4000
5000
0 1 1,5 2 3 4,5
object's global value
number of negatives
average without interaction average with interaction
5 features, g = 6.5
0
1000
2000
3000
4000
5000
0 -1,5 -3 -4,5 -6 -7,5 -9 -10,5
object's global value
number of negatives
average without interaction average with interaction
Figures 11. Increase EB (on the left) and decrease EB (on the right) effects of interaction for different global values of
the object.
To better understand the interaction effect, we build aggregated models using the individual
trajectories identified in section 2 taking into account interactions.
5 Analysis of the result using aggregated models
5.1 How to build aggregated models?
The building method has been elaborated to study the "increase primacy effect" interaction effect
for a three feature object (Deffuant and Huet 2006b). Now, we built two aggregated models for a 5
feature object: one to study the "increase EB" interaction effect; the other to study the "decrease
EB" interaction effect.
The general idea to build the aggregated model is to consider groups of agents and to define the
transfer equations which rule the flows of probability densities between the groups. First, we need
to determine the groups, and the possible flows between them. A group is defined by a list of
retained features. These groups depend on the value of the initial attitude g. Table 3 lists the final
sign of the ten possible individual trajectories: we see that the primacy effect can be observed for 0
< g < 3u because some trajectories are finally positive while others are negative. We know from the
study presented above that the "increase EB" interaction effect appears for 0 < g < 1.5u and the
"decrease EB" interaction effect appears for 1.5u < g < 3u.
Exposure
order
g < 0 0 < g <
0.5u
0.5u <
g < u
u < g <
1.5u
1.5u < g
< 2u
2u < g < 3u
g > 3 u
UUuuu - - - - - - +
UuUuu - - - - - + +
UuuUu - - - - + + +
UuuuU - - - - + + +
uUUuu - - - - - + +
uUuUu - - - + + + +
uUuuU - - + + + + +
uuUUu - - - + + + +
uuUuU - + + + + + +
uuuUU - + + + + + +
Table 3. Final sign of attitude for the ten different trajectories and all different values of g
We select two possible sets of values of g to construct two aggregated models: one corresponding to
an "increase EB" interaction effect, u < g < 1.5u ; the other corresponding to a "decrease EB"
interaction effect, 2u < g < 3u. Following the method presented in Deffuant and Huet (2006), we
simplified the problem by aggregating the groups from which have the same sign of attitude.
Figures 12 and 13 show the graph of the different groups to model the "increase EB" (figure 12) and
the "decrease EB" interaction effects (figure 13).
{}
{U*}
{u}
{uU}
{uu*}
{uUU}
{uUu*}
Figure 12. The graph of transitions between the groups for u < g < 1.5u, defined by the set of retained features (increase
EB interaction effect). The groups with a negative attitude are in grey.
{}
{U}
{u*}
{UU}
{Uu*}
Figure 13. The graph of transitions between the groups for 2u < g < 3u, defined by the set of retained features. (decrease
EB interaction effect) The groups in grey have a negative attitude.
The second stage of the modelling approach is to determine the flow through each transition. This
requires to evaluate the probability that the agents in each group retain a feature which makes them
change their group. This probability is directly related to the features which are sent by each group.
This is broken down in tables 3 and 4. For example, you can read in the third column of the table 3
that all individuals who has received a U at first only talk to others about the feature U.
Group Media {U*} {u} {Uu} {uu*} {uUU}
{uUu*}
Communicated
features
U, u U u U u U u
Table 3: communicated features for each group in the case u < g < 1.5u or U.(increase EB effect)
Group Media {U} {u*} {UU} {Uu*}
Communicated features U, u none u U u
Table 4: communicated features for each group in the case 2u < g < 3u or 2U.(decrease EB effect)
This work done, it is possible to write down evolution equations of each group, summing up the
flows in and subtracting flow out the group. For u < g < 1.5u, we get:
)(
***0
0
uUuuUUuuuUUu
SSSSSSfS
dt
dS
++++++=
++=
uUUU
U
SS
f
S
dt
dS
*0
*
5
2
( )
++++++
++++=
*****0
3
2
5
4
5
3
uuuUuuUuuUUUuuUuUuuuu
u
SSSSSS
f
SSSSS
f
S
dt
dS
( ) ( )
++++++
++=
uUuuuUuuuUUUuUuUUUu
uU
SSSSSS
f
SSS
f
S
dt
dS
****
3
2
2
1
5
3
5
2
( )
++++=
uUuuuUuuu
uu
SSSS
f
S
dt
dS
**
*
3
2
5
2
( )
++=
uUUUuU
uUU
SS
f
S
dt
dS
*
2
1
5
( )
++++=
**
*
3
2
5
2
uUuuuuUuuU
uUu
SSSS
f
S
dt
dS
with:
S
0
: proportion of individuals with a void list of retained features,
S
u
: proportion of individuals with a list of retained features containing only u,
S
U*
: proportion of individuals following all trajectories beginning with U,
S
uU
: proportion of individuals with a list of retained features containing only u at first and U at
second
S
uu*
: proportion of individuals following all trajectories beginning with uu .
S
uUU
: proportion of individuals following all trajectories beginning with uUU .
S
uUu*
: proportion of individuals following all trajectories beginning with uUu .
f : frequency of media feature communication.
For 2u < g < 3u or 2U, we have:
)(
***0
0
UuUUu
SSSfS
dt
dS
+++=
)
5
3
(
**0
*
Uuu
u
SS
f
S
dt
dS
++=
)
2
5
4
()
5
2
(
**
*
*0 Uuu
UU
UUU
U
SS
S
f
SS
f
S
dt
dS
++++=
)
2
5
(
** UU
U
UU
S
f
S
dt
dS
+=
)
5
3
(
**
*
UuuU
Uu
SS
f
S
dt
dS
++=
with :
S
0
: proportion of individuals with a void list of retained features,
S
U
: proportion of individuals with a list of retained features containing only U,
S
u*
: proportion of individuals following all trajectories beginning with u,
S
UU*
: proportion of individuals following all trajectories beginning with UU,
S
Uu*
: proportion of individuals following all trajectories beginning with Uu .
f : frequency of feature diffusion by the media.
The systems can be simulated considering different values for dt. After several tests, we chose dt =
0.1. We compute the evolution of groups at the end by calculating, for each group S:
dt
dt
dS
SS +=
The final number of negative attitudes in the population is obtained by summing values of finally
negative trajectories.
5.2
Comparing aggregated models with the agent-based model
For the ABM, we consider a population of 5041 individuals. From runs of the ABM and aggregated
models, it results that the part of final negatives in the population for:
u
<
g
< 1.5
u
is
53.3% on average for the ABM (with a minimum of 45% and a maximum of
64% on 100 replications) and 53.2% for the aggregated model with
dt
= 0.1 ;
2
u
<
g
< 3
u
is 0.4% on average for the ABM (with a minimum of 0.2% and a maximum of
0.8% on 100 replications) and 0.4% for the aggregated model with
dt
= 0.1 ;
It appears that the aggregated model gives an accurate approximation of the average number of
negative individuals in the population.
Figures 14 show the evolution of the part of agents in each group during the simulation for the
ABM on the one hand, and for the aggregated model on the other hand. One more time, we observe
that both models, ABM and aggregated, give very close results.
2u < g < 3u
0
0,2
0,4
0,6
0,8
1
time
proportion of negatives
U aggregated u* aggregated UU* aggregated Uu* aggregated
U IBM u* IBM UU* IBM Uu* IBM
u < g < U
0
0,1
0,2
0,3
0,4
0,5
time
proportion of negatives
U aggregated u* aggregated uU aggregated
uu* aggregated uUU* aggregated uUu* aggregated
U* IBM u IBM uU IBM
uu* IBM uUU IBM uUu* IBM
Figures 14. Comparison of trajectories of each groups of aggregated and IBM model. Top: "decrease" interaction effect
case; bottom: "increase" interaction effect case. One measure of the IBM's replicas is put all the ten measures of the
aggregated model
5.3 Better understand the interaction effect with the analysis of the aggregated
models results
From the results of the aggregated model, we obtain the proportion at each time step of the negative
feature
U
communicated during interactions. This proportion of
U
emission by interaction can be
compared with the proportion of
U
emission from the media. Figures 15 and 16 show this
comparison for both "increase EB" and "decrease EB" cases.
0
0,1
0,2
0,3
0,4
0,5
0,6
Time
proportion of U emission
from uUU and U* from media from uUU from U*
Figure 15. Comparison of probability of U emission due to interaction with the probability of U emission due to
medium for the "increase EB" interaction effect case
We see on figure 15 that the global probability of
U
emission by interaction begins at a value equal
to probability of
U
emission by medium. It increases with the
U
emission from the negative group
uUU
.
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
Time
proportion of U emissions
U emission from UU* from media
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
0,004
0,0045
0,005
Time
probability to emit U
Figure 16. Comparison of probability of U emission due to interaction with the probability of U emission due to
medium for the "decrease" interaction" effect case
Contrary to the "increase EB" case, we see on figure 16, for the "decrease EB" case that the global
probability of
U
emission by interaction is always lower than the probability of
U
emission by the
media. Due to the emission filter, we can see on figure 15 that no group of the two initial branches
of the "trajectories" emits
U
.
ZOOM
We can think that the frequency of diffusion, which defines how many agents on average during an
iteration are exposed to a feature delivered by the media (parameter
f)
can change the result and
suppress the interaction effect. From previous work on the ABM (Deffuant and Huet 2006), we
know that for weak frequency of diffusion (0.001 and less), the model tends to yield replicas in
which either all final attitudes are positive, or all are negative. Thus, for a weak frequency of
diffusion, the aggregated model can not be equivalent to the individual based model. However, for
higher frequency of diffusion, we can study the persistence of the interaction effect with the
aggregated model varying the media diffusion frequency.
0,480
0,490
0,500
0,510
0,520
0,530
0,540
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
f
probability of negatives
without interaction case aggregated models
0,000
0,020
0,040
0,060
0,080
0,100
0,120
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
f
probability of negatives
without interaction case aggregated models
Figures 17. Comparison of final negatives part for different value of the frequency parameter f in case "without
interaction" and case "with interaction" with the aggregated models: "increase" interaction effect case on top;
"decrease" interaction" effect case at bottom.
Figures 17 show the sensitivity of the results to variations of
f.
We notice that, even when the
frequency is at its maximum value 1, the "increase" or "decrease" EB interaction effects are
maintained, even if they are lower. Frequency does not change so much the part of final negatives
in the population.
Figure 18 shows that, when the initial attitude
g
is less than the absolute value of the negative
feature, we observe the “increase EB” effect; and we observe that the proportion of final negative
trajectories (shown in blue in the graph) is higher than the proportion of negative feature diffused by
the medium (shown in red in the graph). Thus, the interactions diffuse more negative features than
the medium does. Notice also that only one negative feature is sufficient to observe this “amplified”
effect.
Of course, as we have previously observed, no particular interaction effect takes place when the
proportions of negative features emitted by interactions and by the medium are equal (see Deffuant
and Huet, 2006b).
For several negative features, we have the “decreasing EB” effect each time the proportion of
negative trajectories, in blue, is lower than the proportion of negative feature diffusion, in red. In
this case, more positive features are diffused by the interactions than by the medium.
This simple analysis provides a means to quickly estimate the effect of the interactions on the
primacy effect.
Primacy bias zone for a message {UUuuu}
0
0,2
0,4
0,6
0,8
1
g< 0 0 < g < 0.5u 0.5u < g < u u < g < 1.5u 1.5u < g < 2u 2u < g < 3u
probability
Probability of final negative trajectories Probability of the negative feature diffusion
Figure 18. The asymmetrical individual reception filter
6 Conclusion and future research
We propose an individual based model of "information" filtering, which refers to the theory of
cognitive dissonance of Festinger and work on rumor from Allport. In this model, an individual
attitude can be sensitive to the order of feature publication, and in this case, we observe a primacy
effect at the individual level. This order sensitivity is due to an asymmetrical reception filter, which
filters the incongruent features which have an absolute value below a threshold.
This sensitivity to the order takes place in the case of neutral objects where the sum of some major
negative features equal to the sum of some minor positive features. The signs can of course be
inverted without modifying the conclusions. The major features have an absolute value higher than
the threshold, while the minor ones have an absolute value which is below the threshold.
Interactions between individuals modify the proportion of individuals subject to the primacy effect:
1.
they increase the primacy effect when initial attitude
g
is below
U
; the reception filter is
responsible for this effect. This occurs each time the object of discussion is described by
more than two features;
2.
they decrease the primacy effect when the initial attitude is above
U
; this effect is due to the
emission filter. This effect occurs only if the object of discussion is described by 5 or more
features.
Moreover, in other experiments, we observe that primacy effect still takes place on objects which
are moderately negative or positive (i.e. not neutral).
We analysed the increase and decrease primacy effect interaction effects, using an aggregated
model. These analyses helped us to understand these phenomena, and led us to propose a simple
indicator to predict the nature, and to some extent the amplitude of this interaction effect.
In the future, we plan to study in more details the effect of the structure of interaction and the spatial
distribution of initial attitudes on the "interaction" effect, following the work initiated in (Deffuant
and Huet 2006b). Moreover, we have found no social psychological reference about of the effects
of interactions on the “primacy effect”. This work suggests to perform experimental studies,
particularly in laboratory, in order to check if the existence of these interaction effects on real
subjects. We have not competences to run such experiments. Thus this conclusion is also a call to
whom is interested in.
7 References
ALLPORT, G.W.; POSTMAN; L. (1947) The psychology of rumor. Russel & Russell, Inc., 1947,
1965.
ASCH, E.S. (1946) Forming Impressions of Personality.
Journal of Abnormal and Social
Psychology,
41:258-290.
ANDERSON, N. H. (1971). Integration theory and attitude change.
Psychological Review, 78,
171–
206.
DEFFUANT, G.; HUET, S. and AMBLARD, F. (2005) An individual-based model of innovation
diffusion mixing social value and individual payoff dynamics.
American Journal of
Sociology,
110-4, January, pp.1041-1069.
DEFFUANT, G. (2004) Modéliser les Systèmes Complexes. Quelques pistes pour relever le défi.
Habilitation dissertation
.
DEFFUANT, G. and HUET, S. (2006a) Propagation effect of filtering incongruent information.
Journal of Business Research,
9 p., forthcoming.
DEFFUANT, G. and HUET, S., 2006b Collective Reinforcement of First Impression Bias. First
World Congress on Social Simulation, Kyoto (Japan), August.
DEFFUANT, G.; WEISBUCH, G.; AMBLARD, F.; FAURE, T. (2003) Simple is beautiful... and
necessary.
Journal of Artificial Societies and Social Simulation
, 6(1).
EAGLY, A.H.; CHAIKEN, S. (1998)
The psychology of attitudes
. Thomson/Wadsworth; 1993,
1998, 800 pages
FESTINGER, L. (1957)
A Theory of Cognitive Dissonance
. Stanford, CA: Stanford University
Press.
GALAM, S. (2003) Modelling rumors: the no plane Pentagon French hoax case
. Physica A
. Vol.
320., pp 571-580.
HUET, S. and DEFFUANT, G. (2006) Effets d’un filtre cognitif sur la diffusion d’information.
MOSIM 2006
, Rabat.
LAWSON, G.; and BUTTS, C.T. (2004) “Information Transmission Through Human Informants:
Simulation”,
CASOS’04.
MILLER, N. and CAMPBELL, D. T. (1959) Recency and primacy in persuasion as a function of
the timing of speeches and measurements.
Journal of Abnormal and Social Psychology
, 59, 1-
9
TSIMRING, L.S.; and HUERTA, R
.
(2003)
Modeling of Contact Tracing in Social Networks.
Physica A
, 325, pp. 33-
39.
URBIG, D.
(2003)
Attitude Dynamics With Limited Verbalisation Capabilities.
Journal of Artificial
Societies and Social Simulation (JASSS)
. vol. 6 no. 1.
URBIG, D. and MALITZ R. (2005)
Dynamics of Structured Attitude and Opinions
. Third
Conference of the European Social Simulation Association Proceedings, September 5-8,
Koblenz, Germany, 206-212.
... The attitude dynamic model we propose postulates multidimensional attitudes, like in [27] [29] [30] [31] [32] [33] [34] [36] [43] [44]. ...
Article
Full-text available
This paper explores the dynamics of attitude change in 2 dimensions (2D) as a result of social interaction. We add a rejection mechanism into the 2D bounded confidence (BC) model proposed by Deffuant et al (2001). Individuals are characterised by twodimensional continuous attitudes, each associated with an uncertainty u, supposed constant in this first study. Individuals interact by random pairs. If their attitudes are closer than u on both dimensions, or further than u on both dimensions, or closer than u on one dimension and not further than u + delta u on the other dimension, then the rules of the BC model apply. But if their attitudes are closer than u on one dimension and further than u + delta u on the other dimension, then the individuals are in a dissonant state. They tend to solve it by shifting away their close attitudes. The model shows metastable clusters, which maintain themselves through opposite influences of competitor clusters. Our analysis and first experiments support the hypothesis that, for a large range of uncertainty values, the number of clusters grows linearly with the inverse of the uncertainty, whereas this growth is quadratic in the BC model.
... In this perspective, the effect of the opinion or attitude[9]attraction has been widely studied[5,7,8,12,13,21]. Fewer works are dedicated to both attraction and rejection mechanisms[18][19][20],[27],[31,32]. We have recently proposed a model inspired from the socio-psychological theories[17](dissonance[10], the social judgement[28]and the self-categorization[30]), which couples attraction and rejection in a multidimensional approach as in[1],[22],[6,11,16,19,20,31,32]. We observe that this model generally leads to more consensus than when attraction is the only mechanism. ...
Article
Full-text available
We propose a new opinion dynamic model based on the experiments and results of Wood et al. (1996). We consider pairs of individuals discussing on two attitudinal dimensions, and we suppose that one dimension is important, the other secondary. The dynamics are mainly ruled by the level of agreement on the main dimension. If two individuals are close on the main dimension, then they attract each other on the main and on the secondary dimensions, whatever their disagreement on the secondary dimension. If they are far from each other on the main dimension, then too much proximity on the secondary dimension is uncomfortable, and generates rejection on this dimension. The proximity is defined by comparing the opinion distance with a threshold called attraction threshold on the main dimension and rejection threshold on the secondary dimension. With such dynamics, a population with opinions initially uniformly drawn evolves to a set of clusters, inside which secondary opinions fluctuate more or less depending on threshold values. We observe that a low attraction threshold favors fluctuations on the secondary dimension, especially when the rejection threshold is high. The opinion evolutions of the model can be related to some stylized facts.
Thesis
Full-text available
This thesis is composed in two parts, both dedicated to individual-based modeling of social systems. While the first part is very practical, decision-support oriented, presenting a model which studies the evolution of a rural population, the second part is more theoretical, interested in various mechanisms allowing individual to accept or resist to social influence. In the first part, we propose an individual-based model of the European rural municipalities and describe its implementation for a French region: the Cantal département. We use a new sample-free algorithm for generating the initial population, while classical methods require an initial sample. We design and parameterize the individual activity dynamics with data from the European Labour Force Survey database. The individual dynamics includes an original heuristic for labour statuses and employments changes, based on individual age, profession and activity sector when she is occupied. The last part of the model deals with dynamics that we have not been able to derive from data, mainly the demographic dynamics. Based on the Occam razor principle, we test very simple dynamics and choose them on their capacity to lead to model results close to reference data from the French National Statistical Office. In particular, we propose a simple residential mobility model, partly ruling the emigration, which integrates decision to move and location choice. In the second part, with a more theoretical approach, we study the collective effects of various mechanisms leading individuals to resist or accept social influence. A first mechanism leads individuals to neglect some features of an object if they are not important enough or incongruent. These individuals exhibit the primacy bias because their attitudes are determined by the first accepted feature. We show that this bias increases when individuals directly exchange about features compared to when they only get the features from the media, in a random order. The second mechanism is a rejection reaction that we suppose occurring because of the discomfort taking place when individuals are close on one dimension of attitude and far on another dimension. The main effect of this rejection mechanism is to lead to a lower number of clusters than with the attraction mechanism alone. A discussion of these models with respect to the social psychology literature ends this part. Finally, I discuss the complementarity between the approaches presented in the two parts of this document and try to identify some perspectives based on this complementarity.
Article
Full-text available
This thesis is dedicated to individual-based modeling of social systems. While the first part is very practical, decision-support oriented, presenting a model which studies the evolution of a rural population, the second part is more theoretical, interested in various mechanisms allowing individual to accept or resist to social influence. Firstly, we propose an individual-based model of the European rural municipalities implemented for the French Cantal département. We use a new sample-free algorithm for generating the initial population, while classical methods require an initial sample. We design and parameterize the individual activity dynamics with data from the European Labour Force Survey database. The individual dynamics includes an original heuristic for labour statuses and employments changes, based on individual age, profession and activity sector when she is occupied. The last part of the model deals with dynamics that we have not been able to derive from data, mainly the demographic dynamics. Based on the Occam razor principle, we test very simple dynamics and choose them on their capacity to lead to model results close to reference data. In particular, we propose a simple residential mobility model, partly ruling the emigration, which integrates decision to move and location choice. Secondly, we study the collective effects of various mechanisms leading individuals to resist or accept social influence. A first mechanism leads individuals to neglect some features of an object if they are not important enough or incongruent. These individuals exhibit the primacy bias because their attitudes are determined by the first accepted feature. We show that this bias increases when individuals directly exchange about features compared to when they only get the features from the media, in a random order. The second mechanism is a rejection reaction that we suppose occurring because of the discomfort taking place when individuals are close on one dimension of attitude and far on another dimension. The main effect of this rejection mechanism is to lead to a lower number of clusters than with the attraction mechanism alone.
Article
Full-text available
This paper explores the dynamics of attitude change in two dimensions resulting from social interaction. We add a rejection mechanism into the 2D bounded confidence (BC) model proposed by Deffuant et al. (2001). Individuals are characterized by two-dimensional continuous attitudes, each associated with an uncertainty u, supposed constant in this first study. Individuals interact through random pairs. If their attitudes are closer than u on both dimensions, or further than u on both dimensions, or closer than u on one dimension and not further than u + δ u on the other dimension, then the rules of the BC model apply. But if their attitudes are closer than u on one dimension and further than u + δ u on the other dimension, then the individuals are in a dissonant state. They tend to solve this problem by shifting away their close attitudes. The model shows metastable clusters, which maintain themselves through opposite influences of competitor clusters. Our analysis and first experiments support the hypothesis that, for a large range of uncertainty values, the number of clusters grows linearly with the inverse of the uncertainty, whereas this growth is quadratic in the BC model.
Article
Full-text available
Dans le modèle de dynamiques d'attitudes (ou opinions) à "confiance limitée" (CL), deux individus se rapprochent lors d'une rencontre si leur différence est inférieure à un seuil. Nous considérons des individus avec deux attitudes, et nous ajoutons au modèle CL un mécanisme de rejet. Si deux individus sont très éloignés sur la première attitude et très proches sur la seconde, alors ils résolvent la contradiction en s'éloignant l'un de l'autre sur la seconde attitude. En considérant une population d'individus initialement aléatoirement distribués, le modèle exhibe des attracteurs composés de groupes métastables dans l'espace 2D, qui se maintiennent dans une compétition entre attraction et rejet. L'analyse du modèle et les simulations montrent que le nombre final de groupes croît linéairement avec l'inverse de l'incertitude des individus, alors qu'il croît quadratiquement dans le modèle CL en 2D
Article
Full-text available
The authors propose an individual-based model of innovation diffusion and explore its main dynamical properties. In the model, individuals assign an a priori social value to an innovation which evolves during their interactions with the "relative agreement" influence model. This model offers the possibility of including a minority of "extremists" with extreme and very definite opinions. Individuals who give a high social value to the innovation tend to look for information that allows them to evaluate more precisely the individual benefit of adoption. If the social value they assign is low, they neither consider the information nor transmit it. The main finding is that innovations with high social value and low individual benefit have a greater chance of succeeding than innovations with low social value and high individual benefit. Moreover, in some cases, a minority of extremists can have a very important impact on the propagation by polarizing the social value.
Article
Full-text available
We propose a simple model of attitude dynamics in which an agent tends to ignore the features which contradict its views. For instance, having received a first very negative feature, the agent may stop to consider any moderately positive feature. We call this phenomenon "first impression bias" (FIB). We consider a population of agents which are all in contact with a media, communicating randomly chosen features of an object. In some cases, we observe on simulations that FIB is significantly more frequent when the agents interact with each other than when they are only in contact with the media. We design an analytical aggregated model of the global agent-based model behaviour which helps to explain the higher number of FIB due to the interactions.
Article
Full-text available
This article offers a new perspective for research on opinion dynamics. It demonstrates the importance of the distinction of opinion and attitude, which originally has been discussed in literature on consumer behaviour. As opinions are verbalised attitudes not only biases in interpretation and adoption processes have to be considered but also verbalisation biases should be addressed. Such biases can be caused by language deficits or social norms. The model presented in this article captures the basic features of common opinion dynamic models and additionally biases in the verbalisation process. Further, it gives a first analysis of this model and shows that precision as bias in the verbalisation process can influence the dynamics significantly. Presenting and applying the concept of area of influential attitudes the impact of each parameter (selective attitude, selective interpretation, and precision) is analysed independently. Some preliminary results for combined effects are presented.
Article
A contribution to the JASSS forum, in reaction to the paper in FASZ about our model of extremism.
Article
Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks which incorporates an additional (traced) state. We describe a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also discuss the role of contact tracing in epidemics control in small-world and scale-free networks. Effectiveness of contact tracing grows as the rewiring probability is reduced.
Article
Applies a theory of information integration to attitudes and social judgments, based on a principle of information integration. Exact tests based on analysis of variance are given for 4 applications of a simple but general algebraic model of judgment, and these applications are reconsidered under the further restriction imposed by the averaging hypothesis. Qualitative comparisons are made to several other theories of attitude change. Molar and molecular analyses of communication structure are considered briefly and the analysis of inconsistency resolution within integration theory is discussed. It is concluded that integration theory has had reasonable success in the areas of learning, perception, judgment, decision making, and personality impressions, as well as attitude change. It may thus provide a beginning to a unified general theory. (6 p. ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
Although there is a large body of work concerned with information moving from person to person via "word of mouth" mechanisms, mathematical modeling of message content per se continues to be underdeveloped. Such models are of particular concern in the area of crisis response, wherein the need for accurate situation assessment based on informant reports motivates detailed modeling of information transmission among persons at an incident site. As a first step towards the modeling of information transmission in crisis contexts, we introduce a simple model based on prior findings from the literature on rumor propagation and informant accuracy. This model is calibrated using data from Allport and Postman's (1947) famous information transmission study, and various implications of the model for the fidelity of information transmission are explored.
Article
The order in which opposing arguments were presented the time interval between them and the time of testing were varied for eight groups a significant recency effect was found under the conditions most favorable to recency as predicted from the application of Ebbinghaus decay curves.