=Paper=
{{Paper
|id=Vol-1569/paper3
|storemode=property
|title=Valorizing Prejudice in MAS:
A Computational Model
|pdfUrl=https://ceur-ws.org/Vol-1569/paper3.pdf
|volume=Vol-1569
|authors=Rino Falcone,Alessandro Sapienza,Cristiano Castelfranchi
|dblpUrl=https://dblp.org/rec/conf/atal/FalconeSC15
}}
==Valorizing Prejudice in MAS:
A Computational Model==
https://ceur-ws.org/Vol-1569/paper3.pdf
Valorizing Prejudice in MAS:
A Computational Model
Rino Falcone Alessandro Sapienza Cristiano Castelfranchi
ISTC-CNR ISTC-CNR ISTC-CNR
Rome, Italy Rome, Italy Rome, Italy
rino.falcone@istc.cnr.it alessandro.sapienza@istc.cnr.it cristiano.castelfranchi@istc.cnr.it
ABSTRACT 1. INTRODUCTION
In MAS studies on Trust building and dynamics the role of In MultiAgent Systems (MAS) and Online Social Networks
direct/personal experience and of recommendations and reputation (OSN) studies on Trust building and dynamics the role of
is proportionally overrated; while the importance of inferential direct/personal experience and of recommendations and reputation
processes in deriving the evaluation of trustees’ trustworthiness is (although important) is proportionally overrated; while the
underestimated and not exploited. importance of inferential processes in deriving the evaluation of
trustee's trustworthiness is underestimated and not sufficiently
In this paper we focus on the importance of generalized
exploited (a part from the so called “transitivity”, which is also,
knowledge: agents' categories. The cognitive advantage of very often, wrongly founded).
generalized knowledge can be synthesized in this claim: "It allows
us to know a lot about something/somebody we do not directly In particular, generalization and instantiation from classes and
know". At a social level this means that I can know a lot of things categories [8], and analogical reasoning (from task to task and
on people that I never met; it is social "prejudice" with its good from agent to agent) really should receive much more attention. In
side and fundamental contribution to social exchange. In this this paper we focus on the importance of generalized knowledge:
study we experimentally inquire the role played by categories' agents' categories. The cognitive advantage of generalized
reputation with respect to the reputation and opinion on single knowledge (building classes, prototypes, categories, etc.), can be
agents: when it is better to rely on the first ones and when are synthesized in this obvious claim: "It allows us to know a lot
more reliable the second ones. Our claim is that: the larger the about something/somebody we do not directly know" (for
population and the ignorance about the trustworthiness of each example, I never saw Mary's dog, but - since it is a dog - I know
individual (as it happens in an open world) the more precious the hundreds of things about it).
role of trust in categories.
At a social level this means that I can know a lot of things on
This powerful inferential device has to be strongly present in people that I never met; it is social "prejudice" with its good side
WEB societies supported by MAS. and fundamental contribution to social exchange. How can I trust
(for drugs prescription) a medical doctor that I never met before
Categories and Subject Descriptors and nobody of my friends knows? Because he is a doctor!
I.2.11 [Artificial Intelligence] : Distributed Artificial Of course we are underlining the positive aspects of generalized
Intelligence - multiagent systems knowledge, its essential role for having information on people
never met before and about whom no one gave testimony. The
General Terms more rich and accurate this knowledge is, the more it is useful. It
offers huge opportunity both for realizing productive cooperation
Experimentation, Human Factors, Reliability, Theory and for avoiding risky interactions. The problem is when the
uncertainty about the features of the categories is too large or it is
Keywords too wide the variability of the performers within them. In our
Trust and reputation, Cognitive models, Social simulation culture we attribute a negative sense to the concept of prejudice,
and this because we want underline how generalized knowledge
can produce unjust judgments against individuals (or groups)
when superficially applied (or worst, on the basis of precise
discriminatory intents). Here we want rather point out the positive
aspects of the prejudice concept.
In this study we intend to explain and experimentally show the
advantage of trust evaluation based on classes' reputation with
respect to the reputation and opinion on single potential trustees
(partners). In an open world or in a broad population how can we
have sufficient direct or reported experience on everybody? The
quantity of potential trustees in that population or net that might
be excellent partners but that nobody knows enough can be high.
Our claim is that: the larger the population and the ignorance which contributes are more important in the aggregation phase
about the trustworthiness of each individual the more precious the [15][19]. For instance, in [7] authors provide a system able to
role of trust in categories. If I know (through signals, marks, recommend to users group that they could join in Online Social
declaration, ...) the class of a given guy/agent I can have a reliable Network. Here it is introduced the concepts of compactness of a
opinion of its trustworthiness derived from its class-membership. social group, defined as the weighted mean of the two dimensions
It is clear that the advantages of such cognitive power provided by of similarity and trust.
categories and prejudices does not only depend on Even in [12] authors present a clustering-based recommender
recommendation and reputation about categories. We can system that exploits both similarity and trust, generating two
personally build - by generalization - our evaluation of a given different cluster views and combining them to obtain better
category from our direct experience with its members (this is fact results.
happens in our experiments for the agents that later have to
propagate their recommendation about). However, in this Another example is [6] where authors use information regarding
simulation we have in the trustor (which has to decide whom rely social friendships in order to provide users with more accurate
on) only a prejudice based on recommendations about that suggestions and rankings on items of their interest.
category and not its personal experience. A classical decentralized approach is referral systems [21], where
agents adaptively give referrals to one another.
After a certain degree on direct experiences and circulation of
recommendations, the performance of the evaluation based on Information sources come into play in FIRE [13], a trust and
classes will perform better; and in certain cases there will be no reputation model that use them to produce a comprehensive
alternative at all: we do not have any evaluation on that assessment of an agent’s likely performance. Here authors take
individual, a part from its category; either we work on inferential into account open MAS, where agents continuously enter and
instantiation of trustworthiness or we loose a lot of potential leave the system. Specifically, FIRE exploits interaction trust,
partners. This powerful inferential device has to be strongly role-based trust, witness reputation, and certified reputation to
present in WEB societies supported by MAS. We simplify here provide trust metrics.
the problem of the generalization process, of how to form The described solutions are quite similar to our work, although we
judgement about groups, classes, etc. by putting aside for example contextualized this problem to information sources. However we
inference from other classes (higher or sub); we build opinion do not investigate recommendations with just the aim of
(and then its transmission) about classes on the bases of suggesting a particular trustee, but also for inquiring categories’
experience with a number of subjects of a given class. recommendations.
First of all, we want to clarify that here we are not interested in
steretypes, but in categories. We define steretypes as the set of
features that, in a given culture/opinion, characterize and
2. RECOMMENDATION AND
distinguish that specific group of people. REPUTATION: DEFINITIONS
Knowing the stereotype of an agent could be expensive and time Let us consider a set of agents Ag1, ..., Agn in a given world (for
consuming. Here we are just interested in the fact that an agent example a social network). We consider that each agent in this
belongs to a category: it has not to be a costly process and the world could have trust relationships with anyone else. On the
recognition must be well discriminative and not-cheating. There basis of these interactions the agents can evaluate the trust degree
should be visible and reliable "signals" of that membership. In of their partners, so building their judgments about the
fact, the usefulness of categories, groups, roles, etc. makes trustworthiness of the agents with whom they interacted in the
fundamental the role of the signs for recognizing or inferring the past.
category of a given agent. That's why in social life are so The possibility to access to these judgements, through
important coats, uniforms, titles, badges, diplomas, etc. and it is recommendations, is one of the main sources for trusting agents
crucial their exhibition and the assurance of their authenticity outside the circle of closer friends. Exactly for this reason
(and, on the other side, the ability to falsify and deceive). In this recommendation and reputation are the more studied and diffused
preliminary model and simulation let us put aside this crucial tools in the trust domain [16].
issue of indirect competence and reliability signaling; let us We define
assume that the membership to a given class or category is true
and transparent: the category of a given agent is public, common Re cx, y,z (τ ) (1)
knowledge.
Differently from [2][11][18], in this work we do not address the where x, y, z ∈ { Ag1 , Ag2 ,...., Agn } , we call D the
problem of learning categorical knowledge and we assum that the
specific domain: D ≡ { Ag1 , Ag2 ,...., Agn }
categorizzation process is objective.
Similarly to [3], we give agents the possibility to recommend and
0 ≤ Re c x, y,z (τ ) ≤ 1
categories and this is the key point of this paper.
τ, as established in the trust model of [4], is the task on which the
In the majority of the cases available in the literature, the concept recommender expresses the evaluation about y.
of recommendation is used concerning recommender systems [1].
These ones can be realized using both past experience (content- In words: Re c x, y,z (τ ) is the value of x’s recommendation
based RS) [14] or collaborative filtering, in which the contribute about y performing the task τ, where z is the agent receiving this
of single agents/users is used to provide group recommendations recommendation. In this paper, for sake of simplicity, we do not
to other agents/users. introduce any correlation/influence between the value of the
Focusing on collaborative filtering, the concepts of similarity and recommendations and the kind of the agent receiving it: the value
trust are often exploited (together or separately) to determine
of the recommendation does not depend from the agent to whom
where x ∈ { Ag1 , Ag2 ,...., Agn } and
it is communicated.
So (1) represents the basic expression for recommendation. Cy ⊆ { Ag1 , Ag2 ,...., Agn } ,
We can also define a more complex expression of 0 ≤ Re cx,Cy,z (τ ) ≤ 1
recommendation, a sort of average recommendation:
Agn In words:
Re c x,Cy,z (τ )
is the value of x’s recommendation
∑ Re c x,y,z (τ ) / n (2) about the agents included in category Cy when they perform the
task τ, (as usual z is the agent receiving this recommendation).
x=Ag1
We again define a more complex expression of recommendation,
in which all the agents in the domain express their individual a sort of average recommendation:
recommendation on the agent y with respect the task
τ
and the
total value is divided by the number of agents. Agn
We consider the expression (2) as the reputation of the agent y ∑ Re c x,Cy,z (τ ) / n (6)
with respect to the task
τ
in the domain D. x=Ag1
Of course the reputation concept is more complex than the in which all the agents in the domain express their individual
simplified version here introduced [5][17]. recommendation on the category Cy with respect the task
τ
and the
It is in fact the value that would emerge in the case in which we total value is divided by the number of agents.
receive from each agent in the world its recommendation about y We consider the expression (6) as the reputation of the category
(considering each agent as equally reliable). Cy with respect the task τ
in the domain D.
In the case in which an agent has to be recommended not only on Now we extend to the categories, in particular to Cy, the
one task but on a set of tasks
(τ1
,
...,
τk),
we could define instead of recommendations on a set of tasks
(τ1, ...,τk):
(1) and (2) the following expressions:
k
k
∑ Re c (τ i ) / k (3)
∑ Re c x,Cy,z (τ i ) / k
x, y,z i=1
i=1 (7)
that represents the x’s recommendation about y performing the set that represents the value of x’s recommendation about the agents
of tasks (τ1,...,τk), where z is the agent receiving this included in category Cy when they perform the set of tasks
recommendation. (τ1,...,τk).
Imagine having to assign a meta-task (composed of a set of task) Finally, we define:
to one of several agents. In this case the information given from
Agn k
the formula (3) could be useful for selecting on average (with
respect to the tasks) the more performative one. ∑ ∑ Re c x,Cy,z (τ i ) / nk
x=Ag1 i=1
Agn k
(8)
∑ ∑ Re c x, y,z (τ i ) / nk (4)
that represents the value of the reputation of the category Cy (of
x=Ag1 i=1
all the agents y included in Cy) with respect the set of tasks
that represents a sort of average recommendation from the set of (τ1,...,τk), in the domain D.
agents in D, about y performing the set of tasks (τ1 , ..., τk). We
consider the expression (4) as the reputation of the agent y with
respect the set of tasks (τ1 , ...,τk), in the domain D. 2.2 Definitions of Interest for this Work
Having to assign the meta-task proposed above, the information In this paper we are in particular interested in the case in which z
given from the formula (4) could be useful for selecting on (a new agent introduced in the world) asks for recommendation to
average (with respect to both the tasks and the agents) the more x ( x ∈ D ) about an agent belonging to its domain D (the set of
performative one.
all the agents in the world) for performing the task
τ.
x will select
the best evaluated
y,
with
y ∈ Dx on the basis of formula:
2.1 Using Categories max y∈Dx (Re cx, y,z (τ ))
As described above, an interesting approach for evaluating agents
is to classify them in specific categories already pre-judged/rated (9)
and as a consequence to do inherit to the agents the properties of
their own categories. where Dx ≡ { Ag1 , Ag2 ,...., Agm } , Dx includes all the
So we can introduce also the recommendations about categories, agents evaluated by x. They are a subset of D: Dx ⊆ D .
not just about agents (we discuss elsewhere how these In general D and Dx are different because x does not necessarily
recommendations are formed). In this sense we define: know (has interacted with) all the agents in D.
Re cx,Cy,z (τ ) (5) z asks for recommendations not only to one agent, but to a set of
different agents: x ∈ Dz , and selects the best one on the basis of
the value given from the formula:
max x∈Dz (max y∈Dx (Re cx, y,z (τ ))) Of course, the trustworthiness of categories and trustees is
strongly related to the kind of requested information/task. In these
(10) simulations we use just one kind of information in which the
Dz ⊆ D , z could ask to all the agents in the world or to a categories A, B, C and D have 80, 60, 40 and 20% of average
value of trustworthiness respectively. The uncertainty value is
defined subset of it (see later).
fixed to 20% for all of them.
We are also interested to the case in which z ask for
recommendations to x about a specific agents’ category for The simulations were carried out using two different numbers of
trustee: 20 trustees for each category and 100 trustees for each
performing the task τ.
x has to select the best evaluated Cy
among
category. In both cases we used just one trustor.
the different Cy x has interacted with (we are supposing that each
agent in the world D, belongs to a category Cy in the set 3.3 How the simulations work
{Cy1 , Cy 2 ,...., Cyn } ).
Simulations are mainly composed by two main steps that repeat
In this case we have the following formulas: continuously. In the first step, called exploration phase, agents
move into the world asking to their neighbors (other agents with a
max Cy∈Dx (Re cx,Cy,z (τ )) (11) distance of less than 3 NetLogo patches) for the information P.
Then they memorize the performance of each neighbor both as
that returns the category best evaluated from the point of view of
individual element and as a member of its own category.
an agent (x). And
The performance of a agent can assume just the two values 1 or 0,
max x∈Dz (max Cy∈Dx (Re cx,Cy,z (τ ))) (12) with 1 meaning that the agent is supporting the information P and
0 meaning that it is opposing to P. For sake of simplicity, we
that returns the category best evaluated from the point of view of assume that P is always true.
all the agents included in Dz . We also choose to let agents move with a probability of 10%
(each agent moves, with a probability of 10%, one patch in a
3. COMPUTATIONAL MODEL random direction) so, on the one hand we can say that the agents
3.1 NetLogo change their neighbors after each tick, but, on the other hand this
In order to realize our simulations, we exploited the software change is quite slow and, given the number of ticks realized they
NetLogo [20]. It is an open source agent-based programming are not able to know all the other agents in the world, but they
environment written in Java, particularly suited for modeling know properly just a subset of them.
natural and social phenomena. We call the set of neighbors with whom agents interact in each
In NetLogo everything is an agent (also the patches that compose tick: their neighborhood.
the world in which the other agents move) and it is possible to The exploration phase has a variable duration, going from 100
create and model many kind of them, specifying how they relate ticks to 1 tick. Depending on this value, agents will have a better
to each other and giving individual instructions. It is also possible or worse knowledge of their neighborhoods.
to modify the world at run time, to further answer those "what if" Then, in a second step (querying phase) we introduce in the
questions that pop up while investigating the models.
world a trustor (a new agent with no knowlegde about the
It splits the programming part, in which the programmer can set trustworthiness of other agents and categories, and that has the
up the environment of the simulation and specify the behavior of necessity to trust someone reliable for a given task). It will select
turtles, and the visual part, in which the user can start the a given subset of the population and it will query them. In
simulation, control it changing its parameters and see the result at particular, the trustor will ask them for the best category and the
run time, through the view representing the world, plots and best trustee they have experienced.
output monitors. In this way, the trustor is able to collect information about the best
Although NetLogo is an excellent instrument for simulation's recommended category and agent.
tasks, it is devoid of adequate computational libraries to It is important to underline that the trustor is collecting
implement the computational model of trust on information's information from the agents considering them as equally
sources. Then it has proved necessary to expand it with a Java trustworthy with respect to the task of "providing
plug-in made by us, able to fill these gaps. In practice, this trust recommendations". Otherwise it should weigh differently these
plug-in implements all the model of trust on information's sources. recommendations.
3.2 General Setup Then it will select the nearest agent belonging to the best
In every scenario there are four general categories, called A,B,C recommended category and it will compare it, in terms of
and D, each one characterized by: objective trustworthiness, with the best recommended individual
agent (trustee).
1. an average value of trustworthiness, in range [0,100];
The possible responses are:
2. an uncertainty value, in range [0,100].
• trustee wins: the trustee selected with individual
Those two values are exploited to generate the objective recommendation is better than the one selected by the
trustworthiness of each trustee, defined as the probability that, means of category; then this method gets one point;
concerning a specific kind of required information, the trustee will
communicate the right information. • category wins: the trustee selected by the means of
category is better than the one selected with individual
recommendation; then this method gets one point;
• equal result: if the difference between the two 100 324 42 134 0,796 0,854
trustworthiness values is not enough (it is under a
50 252 93 155 0,799 0,831
threshold), we consider it as indistinguishable result. In
particular, we considered the threshold of 3%. 25 226 140 134 0,802 0,811
These two phases are repeated 500 times. 10 184 179 137 0,800 0,785
3.4 Outputs 5 189 191 120 0,780 0,756
In every simulation we use some different indexes to analyze its
3 158 227 115 0,781 0,729
results:
1. trustee wins: number of times in which the trustee 1 133 289 78 0,754 0,649
selected with individual recommendation is better than all-in-one 118 266 116 0,8 0,727
the one selected by the means of categorial
recommendation;
2. category wins: number of times in which the trustee Second scenario:
selected by the means of categorial recommendation • Trustees queried by the trustor: 50%
(the nearest agent belonging to it) is better than the one
selected with individual recommendation; Table 2. 80 trustees, 50% queried by the trustor
3. equal result: number of times in which the difference Expl. Ph. T win C win Equal C Av T Av
between the two trustworthiness values is less than 3%; 277 73 150 0,799 0,841
100
4. trustee mean: average value of trustees’ trustworthiness
50 227 127 146 0,801 0,811
chosen with individual recommendation in the 500 run;
5. category mean: average value of the trustees’ 25 182 170 148 0,796 0,782
trustworthiness chosen with the categorial 10 176 210 114 0,778 0,739
recommendation in the 500 run.
5 159 225 116 0,763 0,702
4. SIMULATIONS RESULT 3 150 243 107 0,749 0,684
In these simulations we present a series of scenarios with 145 280 75 0,723 0,618
1
different settings to show when it is more convenient to exploit
recommendations about categories rather than recommendations all-in-one 94 313 93 0,803 0,689
about individuals, and vice versa.
We also present the “all-in-one” scenario, whose peculiarity is Third scenario:
that the exploration lasts just 1 tick and in that tick every trustee
experiences all the others. Although this is a limit case, very • Trustees queried by the trustor: 25%
unlikely in the real world, it is really interesting as each trustee Table 3. 80 trustees, 25% queried by the trustor
has not a good knowledge of the other trustees as individual
elements (it has experienced them just one time), but it is able to Expl. Ph. T win C win Equal C Av T Av
get a really good knowledge of their categories, as it has 100 248 113 139 0,803 0,824
experienced them as many times as the number of trustees for
each category. So this is an explicit case in which the 50 218 158 124 0,790 0,787
recommendations of the trustees about categories are surely more 193 192 115 0,779 0,755
25
informative than the ones about individuals.
10 159 222 119 0,756 0,705
Simulations’ results are presented in a tabular and graphical way.
In particular, we have chosen to highlight in tables, with a yellow 5 160 244 96 0,717 0,651
color, cases in which category’s performance overtakes or
equalizes individual’s one. 3 145 264 91 0,712 0,637
1 169 255 76 0,667 0,587
4.1 First Simulation
In this first set of simulations we use 20 trustees for category and all-in-one 83 336 81 0,803 0,656
analyze what happens when both the duration of exploration
phase and the percentage of queried trustees change.
Tables’ legend:
• leg : cases in which category’s performance overtakes
or equalizes individual’s one.
First scenario:
• Trustees queried by the trustor: 100%
Table 1. 80 trustees, 100% queried by the trustor
Expl. Ph. T win C win Equal C Av T Av
Fourth scenario:
• Trustees queried by the trustor: 10%
Table 4. 80 trustees, 10% queried by the trustor
Expl. Ph. T win C win Equal C Av T Av
100 209 156 135 0,794 0,784
50 184 197 119 0,774 0,742
25 159 248 93 0,754 0,685
10 175 230 95 0,691 0,642
5 176 241 83 0,671 0,614
Figure 2. Category wins when there are 20 trustees for
3 169 247 84 0,661 0,600 category.
1 170 259 71 0,615 0,548 In the first graph it is easy to see how the value of “trustee wins”
decreases when decreases the number of ticks in the exploratory
all-in-one 83 346 71 0,796 0,619 phase, that is when is reduced the number of interactions among
the agents before being queried; on the contrary, the value of
“category wins” increases proportionally with this reduction (first
Fifth scenario: effect).
• Trustees queried by the trustor: 5% At the same time, there is a direct proportionality between the
Table 5. 80 trustees, 5% queried by the trustor value of “trustee wins” and the number of trustees queried in the
querying phase; while the value of “category wins” increases
Expl. Ph. T win C win Equal C Av T Av proportionally with the reduction of the number of trustees
100 189 184 127 0,772 0,757 queried (second effect).
50 188 225 87 0,751 0,709 In practice, both these effects seem suggest how the role of
categories becomes relevant when either decreases and degrades
25 174 220 106 0,700 0,649 the knowledge within the analyzed system (before the interaction
10 188 219 93 0,659 0,616 with the trustor) or is reduced the transferred knowledge (to the
trustor).
5 174 228 98 0,648 0,611
Let us explain better. The first effect can be described with the
3 176 248 76 0,637 0,589 fact that each agent, reducing the number of interactions with the
1 190 235 75 0,603 0,559 other agents in the explorative phase, will have relevantly less
information with respect to the individual agents. At the same
all-in-one 91 337 72 0,769 0,606 time its knowledge with respect to categories does not undergo a
significant decline given that categories' performances derive
from several different agents.
Below we synthetize these results in two graph (one for the “t
win” dimension and the other for the “c win” dimension). The second effect can be explained with the fact that reducing the
number of queried trustees, the trustor will receive with
decreasing probability information about the more trustworthy
individual agents in the domain, while information on categories,
maintains a good level of stability also reducing the number of
queried agents, thanks to greater robustness of these structures.
Resuming, the above pictures clearly show how, when the
quantity of information (about the agents' trustworthiness
exchanged in the system) decreases, it is better to rely on the
categorial recommendations rather than individual
recommendations.
This result reaches the point of highest criticality in the “all-in-
one” case in which, as expected, “trustee wins” returns the
minimal value and “category wins” returns the maximal value.
Figure 1. Trustee wins when there are 20 trustees for
category. 4.2 Second Simulation
In the second set of simulations we try to increment the number of
trustees to 100 for category. It means that each trustee has much
more neighbors than before.
Tables’ legend:
• leg : cases in which category’s performance overtakes
or equalizes individual’s one.
Sixth scenario: Ninth scenario:
• Trustees queried by the trustor: 100% • Trustees queried by the trustor: 10%
Table 6. 400 trustees, 100% queried by the trustor Table 9. 100 trustees, 10% queried by the trustor
Expl. Ph. T win C win Equal C Av T Av Expl. Ph. T win C win Equal C Av T Av
100 401 5 94 0,796 0,882 100 344 26 130 0,797 0,864
50 382 8 110 0,803 0,879 50 318 48 134 0,802 0,858
25 372 15 113 0,802 0,873 25 271 84 145 0,804 0,843
10 319 43 138 0,802 0,86 10 239 122 139 0,802 0,82
5 323 53 124 0,795 0,85 5 223 151 126 0,797 8,02
3 271 95 134 0,801 0,834 3 176 217 107 0,803 0,769
1 151 238 111 0,803 0,759 1 106 318 76 0,793 0,663
all-in-one 155 252 93 0,796 0,741 all-in-one 92 322 86 0,796 0,654
Seventh scenario: Tenth scenario:
• Trustees queried by the trustor: 50% • Trustees queried by the trustor: 5%
Table 7. 100 trustees, 50% queried by the trustor Table 10. 100 trustees, 5% queried by the trustor
Expl. Ph. T win C win Equal C Av T Av Expl. Ph. T win C win Equal C Av T Av
100 382 3 115 0,799 0,878 100 316 47 137 0,802 0,856
50 362 27 111 0,801 0,873 50 310 68 122 0,797 0,842
25 354 20 126 0,799 0,866 25 262 100 138 0,798 0,823
10 292 65 143 0,804 0,849 10 205 159 136 0,801 0,799
5 291 79 130 0,8 0,842 5 190 197 113 0,8 0,772
3 221 142 137 0,803 0,813 3 133 257 110 0,8 0,725
1 120 276 104 0,797 0,712 1 99 335 66 0,792 0,63
all-in-one 139 270 91 0,800 0,727 all-in-one 80 353 67 0,802 0,622
Eighth scenario: Again, we summarize the results into two graph.
• Trustees queried by the trustor: 25%
Table 8. 100 trustees, 25% queried by the trustor
Expl. Ph. T win C win Equal C Av T Av
100 367 14 119 0,797 0,872
50 356 29 115 0,799 0,867
25 351 39 110 0,798 0,859
10 273 100 127 0,803 0,836
5 276 102 122 0,795 0,83
3 212 144 144 0,801 0,802
1 113 289 98 0,801 0,705 Figure 3. Trustee wins when there are 100 trustees for
category.
all-in-one 130 274 96 0,797 0,702
roles and reciprocal influences. In future works we have to
consider how, starting from the analysis of this study, could
change the role of knowledge about categories in a situation of
open world. In particular, we could experiment the dynamic of
this role with respect to the stability of the performances of the
different agents becoming to a category.
6. REFERENCES
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