In MAS studies on Trust building and dynamics the role of direct/personal experience and of recommendations and reputation is proportionally overrated; while the importance of inferential processes in deriving the evaluation of trustees' trustworthiness is underestimated and not exploited. In this paper we focus on the importance of generalized knowledge: agents' categories. The cognitive advantage of generalized knowledge can be synthesized in this claim: "It allows us to know a lot about something/somebody we do not directly know". At a social level this means that I can know a lot of things on people that I never met; it is social "prejudice" with its good side and fundamental contribution to social exchange. In this study we experimentally inquire the role played by categories' reputation with respect to the reputation and opinion on single agents: when it is better to rely on the first ones and when are more reliable the second ones. Our claim is that: the larger the population and the ignorance about the trustworthiness of each individual (as it happens in an open world) the more precious the role of trust in categories. This powerful inferential device has to be strongly present in WEB societies supported by MAS.
Categories and Subject Descriptors I.2.11 [Artificial Intelligence] : Intelligence - multiagent systems Distributed
Artificial 1.
In MultiAgent Systems (MAS) and Online Social Networks (OSN) studies on Trust building and dynamics the role of direct/personal experience and of recommendations and reputation (although important) is proportionally overrated; while the importance of inferential processes in deriving the evaluation of trustee's trustworthiness is underestimated and not sufficiently exploited (a part from the so called “transitivity”, which is also, very often, wrongly founded).
In particular, generalization and instantiation from classes and
categories [
At a social level this means that I can know a lot of things on people that I never met; it is social "prejudice" with its good side and fundamental contribution to social exchange. How can I trust (for drugs prescription) a medical doctor that I never met before and nobody of my friends knows? Because he is a doctor! Of course we are underlining the positive aspects of generalized knowledge, its essential role for having information on people never met before and about whom no one gave testimony. The more rich and accurate this knowledge is, the more it is useful. It offers huge opportunity both for realizing productive cooperation and for avoiding risky interactions. The problem is when the uncertainty about the features of the categories is too large or it is too wide the variability of the performers within them. In our 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 about the trustworthiness of each individual the more precious the role of trust in categories. If I know (through signals, marks, declaration, ...) the class of a given guy/agent I can have a reliable opinion of its trustworthiness derived from its class-membership. It is clear that the advantages of such cognitive power provided by categories and prejudices does not only depend on recommendation and reputation about categories. We can personally build - by generalization - our evaluation of a given category from our direct experience with its members (this is fact happens in our experiments for the agents that later have to propagate their recommendation about). However, in this simulation we have in the trustor (which has to decide whom rely on) only a prejudice based on recommendations about that category and not its personal experience.
After a certain degree on direct experiences and circulation of recommendations, the performance of the evaluation based on classes will perform better; and in certain cases there will be no alternative at all: we do not have any evaluation on that individual, a part from its category; either we work on inferential instantiation of trustworthiness or we loose a lot of potential partners. This powerful inferential device has to be strongly present in WEB societies supported by MAS. We simplify here the problem of the generalization process, of how to form judgement about groups, classes, etc. by putting aside for example inference from other classes (higher or sub); we build opinion (and then its transmission) about classes on the bases of experience with a number of subjects of a given class. 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 distinguish that specific group of people.
Knowing the stereotype of an agent could be expensive and time consuming. Here we are just interested in the fact that an agent belongs to a category: it has not to be a costly process and the recognition must be well discriminative and not-cheating. There should be visible and reliable "signals" of that membership. In fact, the usefulness of categories, groups, roles, etc. makes fundamental the role of the signs for recognizing or inferring the category of a given agent. That's why in social life are so important coats, uniforms, titles, badges, diplomas, etc. and it is crucial their exhibition and the assurance of their authenticity (and, on the other side, the ability to falsify and deceive). In this preliminary model and simulation let us put aside this crucial issue of indirect competence and reliability signaling; let us assume that the membership to a given class or category is true and transparent: the category of a given agent is public, common knowledge.
Differently from [2][
Similarly to [3], we give agents the possibility to recommend categories and this is the key point of this paper.
In the majority of the cases available in the literature, the concept
of recommendation is used concerning recommender systems [1].
These ones can be realized using both past experience
(contentbased RS) [
Focusing on collaborative filtering, the concepts of similarity and
trust are often exploited (together or separately) to determine
which contributes are more important in the aggregation phase
[
Even in [
Another example is [6] where authors use information regarding social friendships in order to provide users with more accurate suggestions and rankings on items of their interest.
A classical decentralized approach is referral systems [
Information sources come into play in FIRE [
The described solutions are quite similar to our work, although we contextualized this problem to information sources. However we do not investigate recommendations with just the aim of suggesting a particular trustee, but also for inquiring categories’ recommendations. 2. RECOMMENDATION AND REPUTATION: DEFINITIONS Let us consider a set of agents Ag1, ..., Agn in a given world (for example a social network). We consider that each agent in this world could have trust relationships with anyone else. On the basis of these interactions the agents can evaluate the trust degree of their partners, so building their judgments about the trustworthiness of the agents with whom they interacted in the past.
The possibility to access to these judgements, through
recommendations, is one of the main sources for trusting agents
outside the circle of closer friends. Exactly for this reason
recommendation and reputation are the more studied and diffused
tools in the trust domain [
1 and 0 ≤ Re cx,y,z (τ ) ≤ 1 τ, as established in the trust model of [4], is the task on which the recommender expresses the evaluation about y.
In words: Re cx,y,z (τ ) is the value of x’s recommendation about y performing the task τ, where z is the agent receiving this recommendation. In this paper, for sake of simplicity, we do not introduce any correlation/influence between the value of the recommendations and the kind of the agent receiving it: the value
Re cx,y,z (τ ) (1) of the recommendation does not depend from the agent to whom it is communicated.
So (1) represents the basic expression for recommendation. We can also define a more complex expression recommendation, a sort of average recommendation: of Agn x=Ag1 ∑ Re cx,y,z (τ ) / n in which all the agents in the domain express their individual recommendation on the agent y with respect the task τ and the total value is divided by the number of agents.
We consider the expression (2) as the reputation of the agent y with respect to the task τ in the domain D.
Of course the reputation concept is more complex than the
simplified version here introduced [5][
It is in fact the value that would emerge in the case in which we receive from each agent in the world its recommendation about y (considering each agent as equally reliable).
In the case in which an agent has to be recommended not only on one task but on a set of tasks (τ1 , ..., τ k), we could define instead of (1) and (2) the following expressions: k i=1 ∑ Re cx,y,z (τ i ) / k that represents the x’s recommendation about y performing the set of tasks (τ1,...,τk), where z is the agent receiving this recommendation.
Imagine having to assign a meta-task (composed of a set of task) to one of several agents. In this case the information given from the formula (3) could be useful for selecting on average (with respect to the tasks) the more performative one.
Agn ∑ x=Ag1 i=1 k ∑ Re cx,y,z (τ i ) / nk that represents a sort of average recommendation from the set of 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.
Having to assign the meta-task proposed above, the information given from the formula (4) could be useful for selecting on average (with respect to both the tasks and the agents) the more performative one.
As described above, an interesting approach for evaluating agents is to classify them in specific categories already pre-judged/rated and as a consequence to do inherit to the agents the properties of their own categories.
So we can introduce also the recommendations about categories, not just about agents (we discuss elsewhere how these recommendations are formed). In this sense we define: Re cx,Cy,z (τ ) (2) (3) (4) (5) where x ∈ {Ag , Ag2,...., Agn } and
1 Cy ⊆ {Ag1 , Ag2,...., Agn } , 0 ≤ Re cx,Cy,z (τ ) ≤ 1 In words: Re cx,Cy,z (τ ) is the value of x’s recommendation about the agents included in category Cy when they perform the task τ, (as usual z is the agent receiving this recommendation). We again define a more complex expression of recommendation, a sort of average recommendation:
Agn x=Ag1 ∑ Re cx,Cy,z (τ ) / n (6) in which all the agents in the domain express their individual recommendation on the category Cy with respect the task τ and the total value is divided by the number of agents.
We consider the expression (6) as the reputation of the category Cy with respect the task τ in the domain D.
Now we extend to the categories, in particular to Cy, the recommendations on a set of tasks (τ1, ...,τk): k ∑ Re cx,Cy,z (τ i ) / k i=1
(7) that represents the value of x’s recommendation about the agents included in category Cy when they perform the set of tasks (τ1,...,τk).
k Agn ∑ x=Ag1 i=1
(8) ∑ Re cx,Cy,z (τ i ) / nk that represents the value of the reputation of the category Cy (of all the agents y included in Cy) with respect the set of tasks (τ1,...,τk), in the domain D. 2.2 Definitions of Interest for this Work In this paper we are in particular interested in the case in which z (a new agent introduced in the world) asks for recommendation to x ( x ∈ D ) about an agent belonging to its domain D (the set of 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: max y∈Dx (Re cx,y,z (τ ))
(9) where Dx ≡ {Ag1 , Ag2,...., Agm } , Dx includes all the agents evaluated by x. They are a subset of D: Dx ⊆ D . In general D and Dx are different because x does not necessarily know (has interacted with) all the agents in D. 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 ))) Dz ⊆ D , z could ask to all the agents in the world or to a defined subset of it (see later).
We are also interested to the case in which z ask for recommendations to x about a specific agents’ category for performing the task τ. x has to select the best evaluated Cy among 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 {Cy1 , Cy 2,...., Cyn } ).
In this case we have the following formulas: maxCy∈Dx (Re cx,Cy,z (τ )) that returns the category best evaluated from the point of view of an agent (x). And max x∈Dz (maxCy∈Dx (Re cx,Cy,z (τ ))) that returns the category best evaluated from the point of view of all the agents included in
Dz .
3. COMPUTATIONAL MODEL
3.1 NetLogo
In order to realize our simulations, we exploited the software
NetLogo [
In NetLogo everything is an agent (also the patches that compose the world in which the other agents move) and it is possible to create and model many kind of them, specifying how they relate to each other and giving individual instructions. It is also possible to modify the world at run time, to further answer those "what if" questions that pop up while investigating the models.
It splits the programming part, in which the programmer can set up the environment of the simulation and specify the behavior of turtles, and the visual part, in which the user can start the simulation, control it changing its parameters and see the result at run time, through the view representing the world, plots and output monitors.
Although NetLogo is an excellent instrument for simulation's tasks, it is devoid of adequate computational libraries to implement the computational model of trust on information's sources. Then it has proved necessary to expand it with a Java plug-in made by us, able to fill these gaps. In practice, this trust plug-in implements all the model of trust on information's sources.
In every scenario there are four general categories, called A,B,C and D, each one characterized by: 1. 2.
an average value of trustworthiness, in range [0,100]; an uncertainty value, in range [0,100].
Those two values are exploited to generate the objective trustworthiness of each trustee, defined as the probability that, concerning a specific kind of required information, the trustee will communicate the right information. (11) (12)
Of course, the trustworthiness of categories and trustees is strongly related to the kind of requested information/task. In these simulations we use just one kind of information in which the categories A, B, C and D have 80, 60, 40 and 20% of average value of trustworthiness respectively. The uncertainty value is fixed to 20% for all of them.
The simulations were carried out using two different numbers of trustee: 20 trustees for each category and 100 trustees for each category. In both cases we used just one trustor. 3.3
Simulations are mainly composed by two main steps that repeat continuously. In the first step, called exploration phase, agents move into the world asking to their neighbors (other agents with a distance of less than 3 NetLogo patches) for the information P. Then they memorize the performance of each neighbor both as individual element and as a member of its own category. The performance of a agent can assume just the two values 1 or 0, 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 assume that P is always true.
We also choose to let agents move with a probability of 10% (each agent moves, with a probability of 10%, one patch in a random direction) so, on the one hand we can say that the agents change their neighbors after each tick, but, on the other hand this change is quite slow and, given the number of ticks realized they are not able to know all the other agents in the world, but they know properly just a subset of them.
We call the set of neighbors with whom agents interact in each tick: their neighborhood.
The exploration phase has a variable duration, going from 100 ticks to 1 tick. Depending on this value, agents will have a better or worse knowledge of their neighborhoods.
Then, in a second step (querying phase) we introduce in the world a trustor (a new agent with no knowlegde about the trustworthiness of other agents and categories, and that has the necessity to trust someone reliable for a given task). It will select a given subset of the population and it will query them. In particular, the trustor will ask them for the best category and the best trustee they have experienced.
In this way, the trustor is able to collect information about the best recommended category and agent.
It is important to underline that the trustor is collecting information from the agents considering them as equally trustworthy with respect to the task of "providing recommendations". Otherwise it should weigh differently these recommendations.
Then it will select the nearest agent belonging to the best recommended category and it will compare it, in terms of objective trustworthiness, with the best recommended individual agent (trustee).
The possible responses are: • • trustee wins: the trustee selected with individual recommendation is better than the one selected by the means of category; then this method gets one point; 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; These two phases are repeated 500 times.
In every simulation we use some different indexes to analyze its results: equal result: if the difference between the two trustworthiness values is not enough (it is under a threshold), we consider it as indistinguishable result. In particular, we considered the threshold of 3%. trustee wins: number of times in which the trustee selected with individual recommendation is better than the one selected by the means of categorial recommendation; category wins: number of times in which the trustee selected by the means of categorial recommendation (the nearest agent belonging to it) is better than the one selected with individual recommendation; equal result: number of times in which the difference between the two trustworthiness values is less than 3%; trustee mean: average value of trustees’ trustworthiness chosen with individual recommendation in the 500 run; category mean: average value of the trustees’ trustworthiness chosen with the categorial recommendation in the 500 run. 4. SIMULATIONS RESULT In these simulations we present a series of scenarios with different settings to show when it is more convenient to exploit recommendations about categories rather than recommendations about individuals, and vice versa.
We also present the “all-in-one” scenario, whose peculiarity is that the exploration lasts just 1 tick and in that tick every trustee experiences all the others. Although this is a limit case, very unlikely in the real world, it is really interesting as each trustee has not a good knowledge of the other trustees as individual elements (it has experienced them just one time), but it is able to get a really good knowledge of their categories, as it has experienced them as many times as the number of trustees for each category. So this is an explicit case in which the recommendations of the trustees about categories are surely more informative than the ones about individuals.
Simulations’ results are presented in a tabular and graphical way. In particular, we have chosen to highlight in tables, with a yellow color, cases in which category’s performance overtakes or equalizes individual’s one.
In this first set of simulations we use 20 trustees for category and analyze what happens when both the duration of exploration phase and the percentage of queried trustees change.
leg : cases in which category’s performance overtakes or equalizes individual’s one.
T win C win Equal C Av T Av all-in-one
100 •
T win C win Equal 155 134 137 120 115 78 116 150 146 148 114 116 107 75 93 139 124 115 119 96 91 76 81 0,799 0,802 50 25 10 5 3 1 50 25 10 5 3 1 50 25 10 5 3 1 252 226 184 189 158 133 118 277 227 182 176 159 150 145 94 248 218 193 159 160 145 169 83 93 140 179 191 227 289 266 73 127 170 210 225 243 280 313 113 158 192 222 244 264 255 336 all-in-one
100 •
100 •
100 all-in-one 156 197 248 230 241 247 259 346 184 225 220 219 228 248 235 337 135 119 93 95 83 84 71 71 127 87 106 93 98 76 75 72 C Av 0,794 0,774 0,754 0,691 0,671 0,661 0,615 0,796 C Av 0,772 0,751 0,700 0,659 0,648 0,637 0,603 0,769 T Av 0,784 0,742 0,685 0,642 0,614 0,600 0,548 0,619 T Av 0,757 0,709 0,649 0,616 0,611 0,589 0,559 0,606 •
Below we synthetize these results in two graph (one for the “t win” dimension and the other for the “c win” dimension).
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 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 effect).
At the same time, there is a direct proportionality between the value of “trustee wins” and the number of trustees queried in the querying phase; while the value of “category wins” increases proportionally with the reduction of the number of trustees queried (second effect).
In practice, both these effects seem suggest how the role of categories becomes relevant when either decreases and degrades the knowledge within the analyzed system (before the interaction with the trustor) or is reduced the transferred knowledge (to the trustor).
Let us explain better. The first effect can be described with the fact that each agent, reducing the number of interactions with the other agents in the explorative phase, will have relevantly less information with respect to the individual agents. At the same time its knowledge with respect to categories does not undergo a significant decline given that categories' performances derive from several different agents.
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-inone” case in which, as expected, “trustee wins” returns the minimal value and “category wins” returns the maximal value.
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. leg : cases in which category’s performance overtakes or equalizes individual’s one. Again, we summarize the results into two graph.
In this second set of simulations, are confirmed the two effects detected in the first simulations. However it is possible observe a greater difficulty of recommendations about categories to prevail on the recommendations about individuals: just strongly reducing the trustees queried by the trustor it is possible value a role for categories' recommendations.
This result could be explained with the fact that increasing the number of the agents in the neighborhood of each agent, it increases the possibility to have in it highly trustworthy agents and as a consequence more agents reporting information about them.
In other works [
In this paper we have investigated the different roles that can play recommendations about individual agents and about categories of agents.
In this case the new agent introduced (called trustror) has a whole
world of agents completely unknown to it, and ask for
recommendations to a (variable) subset of agents for selecting an
agent to whom delegate a task. The information received regards
both individual agents and agents' categories. The informative
power of these two kinds of recommendations is dependent from
the previous interactions among the agents and also from the
number agents queried by the trustor. However, there are cases in
which information about categories is more useful that
information towards individual agents. In some sense this result
complements the results achieved in [
In this work we have in fact considered a closed world, with a fixed set of agents. This choice was based on the fact that we were interested to evaluate the relationships between knowledge about individual and knowledge about categories, for calibrating their 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.
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