Subjectivity handling of ratings for Trust and Reputation systems: An Abductive Reasoning Approach

Subjectivity handling of ratings for Trust and Reputation systems: an Abductive Reasoning Approach

1Mozhgan Tavakolifard, 2Kevin C. Almeroth, 3Pinar Ozturk

1Centre for Quantifiable Quality of Service in Communication Systems1*, Department of Telematics, Norwegian University of Science and Technology (NTNU), E-mail:

[email protected] 2Department of Computer Science, University of California, Santa Barbara (UCSB), E-mail:

[email protected] 3Department of Computer and Information Science, Norwegian University of Science and

Technology (NTNU), E-mail: [email protected]

Abstract The majority of trust models consider two types of knowledge in estimating the trustworthiness of a

trustee in an interaction: experiences and recommendations. However, this leads to a nested trust problem; how could we trust the recommendations? Even when the recommenders are not deceptive, there is still a trust related problem due to the subjectivity of human judgment. This paper describes a missing part of the existing trust management models: handling the subjectivity of recommendations. Our approach is based on the idea that a recommender's judgment method can be inferred and the recommended entity can be (re)evaluated according to the value system of the truster who is about to make a decision. Extraction of the judgment method involves abductive reasoning which is implemented in the proposed account using subjective logic. This approach has been quantitatively compared with two other methods. Our experiments show that our proposed solution outperforms an extended version of the “Beta trust model”, a trust model without subjectivity elimination. Our suggested method for trust and reputation systems may also be applied to other systems that include a rating mechanism such as recommender systems.

Keywords: Abductive reasoning, Rating, Recommender, Subjectivity, Trust 1. Introduction

A steadily increasing number and variety of virtual social networks create problems that diminish the advantages the Web may provide. A major problem with an open and distributed environment is that users lack sufficient information about the quality of the e-services and their providers. Conventional security mechanisms cannot handle the trust phenomenon in the way the new information systems need. Therefore, the growth of services such as online transactions and information exchange is conditioned on the development of new trust management models.

The recent trust management models mimic the behavior that people exhibit independent of the Internet. That is, if a person does not know about the person she is considering doing business with, she uses other people in her social network to find out whether the candidate business partner has a good reputation. In a corresponding recommendation system there are three roles: The trustee is the service provider; the truster is interested in the provided service and needs to judge the trustworthiness of the provider; and the recommender can provide a rating to the truster about a trustee. An agent can play more than one role. For example, a truster often rates (hence, the recommender role) the trustee after a transaction in which she was involved. The truster normally relies on her own experiences if she has them [1, 2], and uses others’ recommendations if she does not feel that she has enough experience with the trustee herself [3-5]. Hence, the majority of trust models consider two types of knowledge in estimating

*``Centre for Quantifiable Quality of Service in Communication Systems, Centre of Excellence'' appointed by The Research Council of Norway, funded by the Research Council, NTNU and UNINETT. http://www.q2s.ntnu.no

Subjectivity handling of ratings for Trust and Reputation systems: an Abductive Reasoning Approach Mozhgan Tavakolifard, Kevin C. Almeroth, Pinar Ozturk

International Journal of Digital Content Technology and its Applications(JDCTA) Volume5,Number11,November 2011 doi:10.4156/jdcta.vol5.issue11.45

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the trustworthiness of a trustee in an interaction: experiences and recommendations. Recommendations about a trustee are derived from word-of-mouth and are frequently based on ratings about the trustee given by recommenders.

Ratings of a pessimistic and skeptical person may result in a completely different pattern than those of an optimistic person, i.e., ratings are highly subjective. The meaning of a trust value provided by a recommender may be distorted due to differences in the perceptions of the two persons. For example, a rating value of 0.7 may mean a very high value of trust for one recommender, but it is possible that the receiver perceives the same value as only average. Despite the existence of a significant number of trust management models [3, 6-10, 19], surprisingly few (e.g., [11-13]) have investigated the subjectivity problem.

We present an approach to handle the subjectivity problem in the evaluation of recommendations. The main idea underpinning our proposed subjectivity handling approach is that the judgment method of a recommender can be inferred. The judgment method is a function that maps a property/attribute (e.g., delivery time is late) of the trustee to the rating-value the recommender attached to that property. In our proposed model, extraction of the judgment method of a recommender relies on abductive reasoning [14-16]. Abductive reasoning is a general approach to finding the hypotheses that would best explain a given set of evidence. In the trust domain, properties of the trustee correspond to the hypotheses and the recommender’s rating is the evidence. We have implemented abductive reasoning using subjective logic [17]. Subjective logic, described in Section 3, enables the representation of a specific belief calculus by taking both the uncertainty and individuality of beliefs into account. In general, subjective logic is suitable for modeling and analyzing situations involving uncertainty and incomplete knowledge.

We provide an evaluation through examples representing usage of our proposed model and through simulations comparing an extended version of the “Beta trust model” [7] and the basic version of the model without subjectivity elimination. The results indicate our extension is useful in dealing with subjectivity. Furthermore, we compared our method with two methods proposed by Farez Abdul-Rahman [6] and Regan et al. [14].

The remainder of the paper is organized as follows. Section 1 describes our view of the subjectivity problem and the proposed solution while Section 2 briefly explains subjective logic. Our proposed model to handle subjectivity during trust inference is described in Section 3. Two expressive examples are given in Section 4 to demonstrate uses of our model. The evaluation plan and the results are presented in Section 5. Section 6 provides an overview of related work. Finally, Section 7 provides concluding remarks and future research directions. 2. Subjectivity and its Elimination in the Trust Domain

A universally accepted definition of trust is still lacking despite extensive studies from philosophers, sociologists, and psychologists. One of the most commonly accepted definitions is from the sociologist Diego Gambetta [18]: “... trust (or, symmetrically, distrust) is a particular level of the subjective probability with which an agent will perform a particular action, both before [we] can monitor such action (or independently of his capacity of ever be able to monitor it) and in a context in which it affects [our] own action”. As stated in this definition, some of characteristics of trust are: subjectivity, context-dependency, and dynamicity.

Recommenders communicate a rating-number (to the requesting truster) that captures how the recommenders perceive and interpret a transaction situation (e.g., trustee properties), which in turn invokes emotions, which then forms a rating number. Emotions and their quantified representations amount to the ‘subjectivity’ of the judgment of the recommender. The truster, upon receiving such a number, should map this value to the information about the properties of the truster, which she needs in order to judge the trustee. However, since the judgment of these two persons is likely different, the truster needs to know more than just the ratings of recommenders in order to infer properties of the trustee correctly. She needs to know about the recommender’s rating behavior, or judgment process.

The subjectivity issue is different from the deception problem. With subjectivity, the agent’s evaluation is different because it is based on a different trust model. With deception, the agent has malicious intentions. Models for dealing with unreliable information, however, deal with both situations in the same manner: the information is discarded. In this way, useful


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information might be discarded and the information-giver’s reputation might be negatively impacted. If the agents can align their notions, such communications can be translated and used as reliable information.

The problem of subjectivity arises because of the difference between internal contexts (judgment methods and trust models) of the recommender (sender of the rating) and the truster (receiver of the rating). In other words, the truster receives only the recommender’s rating about the trustee, which is subjective, and she has to use this rating in her own trust model, which is not necessarily the same as the recommender’s trust model. The key idea of our approach is that the truster may reduce if not eliminate the subjectivity of the recommender if she can infer the actual2 properties of the trustee from the ratings of the recommender. Then, the truster will be able to use this information as if a rating resulted from her direct experience with the trustee rather than from recommenders.

We envision that the truster can infer the judgment method of the recommender by observing the recommender’s ratings and corresponding trustee’s properties. For example, in cases where a recommender is known to consistently bias its ratings (e.g. always exaggerating positively or negatively, or always reporting the opposite of what it thinks), it is in fact possible to “re-interpret” the ratings. This can be done by extraction of the conditional relation between the trustee’s properties as antecedents and the recommenders’ ratings as consequences from the history of interactions3. Based on this information, the truster will be able to translate a new rating provided by the recommender into the actual properties of the trustee by employing abductive reasoning. Figure 1(a) shows the trust value computation by the truster without considering the subjective difference. The recommender sends a rating about the trustee to the truster based on his own observations of the trustee’s properties and the truster simply uses this rating in her own trust model (decision making model) as if she had generated the rating herself. Figure 1(b) shows the same process; however, the truster considers the subjective differences and re-interprets the rating from the recommender by inferring the judgment method of the recommender from historical data.

Trustee propertees

Recommender Decision taking

RatingTruster

Trust value

Recommender

Learning

Interpretation

Decision taking

Truster

Rating

Recommender's judgement method

Trustee properties

Trust value

(a) (b)

Trustee propertees

History

Figure 1. Trust value computation (a) without and (b) with subjectivity consideration.

2 The reference here is the truster, that is, the actual/true value of a trustee property is the reasoner/truster’s own judgment. 3The history contains two kinds of information for each interaction: the rating that the truster received from the recommender regarding the trustee before an interaction and the truster’s own observation of the trustee’s properties after the completion of the interaction.


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In a later transaction, given the rating of the recommender about the current trustee, the truster can infer the actual properties of the trustee, using the recommender’s judgment method and then employing its own trust estimation method on these properties to make a decision. In this way, the effects of subjectivity in trust communication can be reduced, if not eliminated. 3. Subjective Logic

Subjective logic [17] is a type of probabilistic logic that allows probability values to be expressed with degrees of uncertainty. Probabilistic logic combines the strengths of logic and probability calculus, meaning that it has the capability of binary logic to express structured argument models, and it has the power of probabilities to express degrees of truth about those arguments. Subjective logic makes it possible to express uncertainty about the probability values themselves, meaning that it is possible to reason with argument models in the presence of uncertain or partially incomplete evidence.

Subjective logic enables the representation of a specific belief calculus in which trust is expressed by a belief metric called an “opinion.” Subjective opinions express subjective beliefs about the truth of propositions with degrees of uncertainty. A multinomial opinion is defined over X = {xi | i = 1..k} which is a set of exhaustive and mutually disjoint propositions, , and

is denoted by . is a vector of belief masses over the propositions of , is the uncertainty mass, and is a vector of base rate values over the propositions of . These

components satisfy , , and as well as

.

An element is interpreted as a belief mass over . This value is the amount of

positive belief that is true. The uncertainty mass, , can be interpreted as the lack of belief

mass in the truth of any of the propositions of . In other words, the uncertainty mass reflects that the belief owner does not know which of the propositions of , in particular, is true, only that one of them must be true. The base rate vector, , will play a role in determining probability expectation values over and represents a non-informative a priori probability distribution over X before any evidence has been received. Given a frame of cardinality, , the default base rate for each element in the frame is , but it is possible to define arbitrary base rates for all the mutually exclusive elements of the frame, as long as the additivity constraint is satisfied.

Each observation over the propositions of takes the form of a trivial vector denoted by with elements where only one element (corresponding to the observed proposition) has value 1, and all other elements have value 0. The aggregate observations are stored as a cumulative vector and is denoted by . The simplest way to update an observation vector as a result of a

new observation is by adding the newly received vector, , to the previously stored vector, . Sometimes, it is desirable to give relatively greater weight to more recent observations. This weighting can be achieved by introducing a longevity factor [0, 1] which controls the rate at which old observations are aged and discounted as a function of time. With , observations are completely forgotten after a single time period. With , observations are never forgotten.

(1)

The corresponding opinion, , of observation vector, , is calculated as follows:


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(2)

is the non-informative prior weight expressed as a constant and should be equal to the

cardinality of the frame for an a priori uniform distribution. The aggregated trust value, the probability distribution over the disjoint elements of a state

space, is determined by the Beta distribution [7] in the case of a binary state space and by the Dirichlet distribution in the general, multinomial case.

Jøsang introduces a set of operators to be used for computations with subjective opinions [17]. We will use only the abduction operator in our model. Jøsang denotes the ‘abduction’ operator as . Let and be frames. Assume that

an observer perceives a conditional relationship between the two frames and where plays the role of consequent and plays the role of antecedent.

By using the notation for conditional abduction, the expression for subjective logic conditional abduction can be defined as:

(3)

where is a set of different multinomial opinions

conditioned on each respectively.

The notation denotes that the antecedent opinion, , is derived as a function of the

consequent opinion, , together with the conditional opinion . The expression

thus represents a derived value, whereas the expression represents an input argument.

Naturally, the information about conditional opinions of the form is available (from

antecedent to consequent), however, abduction requires conditional opinions of the form .

A method is given for the inversion of into [17].

Abduction allows inferring as an explanation of . Because of this relationship, abduction allows the precondition to be inferred from the consequence .

In the next section, we introduce our model, which is based on a subjective logic implementation of abductive reasoning and discuss how it interprets information from recommenders about trustees in a more inclusive and effective manner. 4. The Proposed Abductive Model

In this section, we describe an abductive reasoning approach to handle subjectivity. We assume that the ratings resulting from an interaction is a function of multiple aspects of the interaction and which are determined by intrinsic properties of the trustee in general. The set of properties that the trustee exhibits in a given interaction is denoted by , for example, shipping time or quality of products, in a seller-buyer scenario. The information given by a recommender about a trustee takes the form of a rating, , chosen from a finite number of discrete values or a number on a scale of 1 to (e.g., a rating of stars up to a maximum of 5).

We consider a conditional relation between opinions of the trustee’s properties, , ,

, and opinions of the recommender’s rating, , where is the antecedent and is the consequence. For the sake of simplicity, we assume that the trustee has just one property,

, e.g., quality of products, which can take on a finite number of discrete values referred as


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, e.g., poor, moderate, and high . The procedure is the same when there is more than one property.

The truster learns about the subjectivity of the recommender from the history of interactions. The history contains two kinds of information for each interaction: the recommender’s rating about the trustee whom the truster received before the interaction, and the truster’s own judgment about the trustee after completion of the interaction. A single past experience in the history is represented as an ordered pair where is the recommender’s rating and p is the truster’s assessment of the trustee’s property from direct experience. is a trivial vector where only one element, the element with index equal to the rating level, has value 1. For example, (rating = (0, 0, 1, 0, 0), quality of product = ) corresponds to an interaction when the recommender’s rating for quality of product of a seller (trustee) was 3-stars and the truster observed this property as poor in a direct experience. The cumulative vector of observations, , for each property value is the sum of all ratings

received from the recommender when the observed trustee’s property had the value . Here, we treat all interactions as they occur at the same time and we assess the dynamic behavior (the chronological sequence of interactions) in Section 4.1.

(4)

For instance, means 9 1-star ratings and one 5-star rating have been

recommended when the property had the value of . The corresponding subjective logic

opinion and the cumulative observation vector are calculated using Equation 2. The

conditional opinion, , represents the recommender’s judgment method and essentially encodes the correlation between the recommender’s ratings and the trustee properties. The truster calculates (learns) this conditional opinion/judgment method from the history of interactions. Thus the truster will be able to translate the next recommender’s rating (eliminating its subjectivity) based on what she has learned. She considers the next rating from the recommender as the consequent and uses the abduction operator to convert it to an opinion about the antecedent, which is the actual property of the trustee from the truster’s own view. Then, she estimates the trustworthiness of the trustee using her own personal method of trust estimation.

In order to use the abduction operator (see Equation 3), opinions of the form should be

inverted into opinions of the form . For this purpose, we use the suggested method by Jøsang [17], however, because of space limitation, we do not give the details of the method here. The abduction operator can be used to derive opinions about the trustee properties :

(5)

The whole process is illustrated in Figure 2. As this figure shows, both the recommender and

the truster generate ratings about the trustee that are uninfluenced by their own internal contexts. Using abduction, the truster translates the rating provided by the recommender (conclusion) back to the trustee property (hypothesis) and then generates her own rating for the trustee using her own trust model (influenced by her own internal context). 4.1. Dynamic Trustees and Recommenders


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So far, we have treated all interactions as if they occurred at the same time. In this section, we consider dynamic behavior for the trustee and the recommender and a chronological order for their interactions. By “dynamic behavior,” we mean that the behavior of trustees and recommenders may shift over time. The judgment method of a recommender may change as a result of a change in her internal context or perhaps because she suddenly feels like being misleading. The truster can handle such a change in a recommender/trustee behavior by incorporating the general assumption that recent evidence is more representative of a trustee property or using the recommender judgment method compared to past observations. Therefore, we use the previously mentioned longevity factor (see Equation 1) to update observations. If the truster has learned a trustee property with high certainty and the property changes afterwards, a significant amount of new evidence would be necessary to change the truster’s belief about this trustee property. We use the following formula to update with the outcome of a new

interaction .

(6)

Recommender

Truster

Trustee

Learning of the recommender's

judgement method

Subjectivity elimination by interpretation of the recommender's rating

(Abduction)

Decision taking by the truster's own trust evaluation method

Own judgement of the trustee

Internal context

History of interactions

Internal context

: Trustee property

: Interpreted trustee property(hypothesis)

: Recommender's judgement method (conditional opinion)

: Recommender's rating(conclusion)

:(recommender rating, trustee property)

Figure 2. Subjectivity handling process.

Furthermore, we propose to adjust after each interaction based on similarity ( )

between the estimated and real outcome.

(7)


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If and are the same, then will be equal to 1,

otherwise it will be between 1 and 0. The maximum value of their difference is where is the number of rating levels. In this case, will be equal to 0. Then the value of is adjusted as follows:

(8)

is a constant and a natural number greater than or equal to 2. The value is decided based

on the application. For example, in risky applications, after a change in the behavior of the trustee, the value of should be decreased sharply; therefore, a greater value of m would be needed. If then would increase by . On the other hand, when

, would decrease. These formula avoid being below zero and above one. The initial value of should be zero, although it would be increased quickly when there was any success in the estimation of interactions. 4.2. Discussion

The necessary computation scales linearly with respect to the number of recommenders and trustees in the system, since the truster learns about properties of each trustee and judgment method of each recommender individually. We can construct a theoretical bound on the amount of computation necessary in terms of the number of trustee properties, , and number of

values for each trustee property, . The model for a trustee includes properties while the

model for the recommender includes judgment methods. It takes order to update a single trustee property after each rating. After observing a rating for a single trustee from a

single recommender it would take order time to update the trustees’ properties and time to update the recommender’s judgment method. The computations do not necessarily scale well as the number of trustee properties and trustee property values grow; however, it may be reasonable to create models with a small fixed number of trustee properties and values.

In our model, the greater the correlation between the trustee properties and the recommender’s ratings, the higher their mutual information and the easier it is to infer the value of one given the value of the other. The stronger the correlation, the more deterministic the learned judgment method will be (the uncertainty values of conditional opinions will be less). Consequently, if a recommender tends to report a unique rating for each value of a trustee property, then it is possible to infer the trustee properties. For instance, if a recommender tends to report five-star rating for one trustee when the truster has established that the trustee is usually poor, our approach will exploit the correlation between poor and 5-star rating to allow the truster to interpret a 5-star rating from this recommender as meaning poor. Hence a truster can equally make use of ratings from honest and dishonest recommenders as long as they are consistent (i.e. use a fairly deterministic judgment method).

If a recommender’s judgment method is quite stochastic and completely random, then it will be more difficult to infer trustee properties. Note that a truster is not adversely affected when ratings are weakly correlated with the trustee properties, since the algorithm does not try to infer a single trustee property for a given rating, but rather a subjective logic opinion about the trustee property in the form of which contains a distribution of beliefs over possible values of the trustee property and the uncertainty value. Hence, when a recommender gives random ratings, the algorithm will simply infer that some values of the property are only slightly more likely than others with a high value of uncertainty, which can be interpreted as providing only a little information.


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In general, our method extracts just the “right” amount of information from each rating based on the amount of correlation between ratings and trustee properties. The value of uncertainty helps the truster to determine whether she should rely on this result for decision making or not. Thus, the truster is able to model the subjectivity of the recommender from the first interaction. As the number of direct experiences increases, the value of uncertainty decreases and the truster will be more certain about the inferred judgment method.

We can imagine some cases in which a recommender colludes with a trustee, deviating from its standard judgment method to offer inflated ratings for that particular trustee. The recommender could most effectively collude by reporting ratings that are highly correlated with trustee properties for every trustee except the colluding trustee. However, it is reasonable to assume that the ratings of many recommenders will be used to model each trustee’s properties and thus a colluding recommender will have a minimal impact.

5. Application Scenarios

In this section two scenarios, similar to ones mentioned by Regan et. al [14], have been presented to demonstrate the operation of our model. The scenarios include one with consistent recommenders and one with inconsistent recommenders to illustrate that our model performs successfully in both cases. By a consistent recommender, we mean that the recommender is consistent in providing rating for the truster and there is a strong correlation between the trustee properties and the recommender’s ratings. 5.1. A consistent recommender

Consider a scenario involving one truster, one trustee, and one recommender. The trustee has a single property, , which can take the values poor, moderate, or high, and the recommender will offer 5-stars ratings, . This example will walk through how, given some information about the trustee, the truster can learn the judgment method of the recommender and use this information to translate her rating to the actual property of trustee (eliminating as much as possible the impact of subjectivity of the recommender).

We begin by assuming that the truster has already had 10 interactions with the trustee where she was high 9 times and poor only once. The recommender has reported that she is usually unsatisfied by providing 8 1-star ratings when the trustee was high, one 5-stars rating when the trustee was moderate, and one 5-stars rating when the trustee was poor. For the sake of simplicity, the default base rate is assumed for all opinions in this example and all opinions are demonstrated by the simpler form rather than the form . The following is an example history for this scenario regardless of the sequence of interactions,

(9)

The cumulative vectors are calculated as,

(10)

The following are the corresponding conditional opinions which are calculated according to

Equation 2.

(11)

The opinion of is obtained from by inversion:


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(12)

Assume that the same recommender expresses that she is unsatisfied with a new trustee and

gives a recommendation of one 5-stars and 9 1-star ratings:

(13) Because the truster had learned the recommender’s judgment method, , the truster

would be able to interpret/translate this rating to the opinion of the truster about the property of the trustee using abduction (see Equation 5):

(14)

That is, the new trustee’s property value is probably high. Note that the example illustrated

in this section is one in which the truster is able to identify a strong correlation between the recommender’s 1-star rating and the trustee being high. If the recommender has responses that are more weakly correlated, for example, reporting 2-star ratings 3 times when the trustee was poor, 4-stars ratings 4 times when the trustee was moderate, and 2-star ratings 3 times when the trustee was high. The equation set 7 shows the results of this case.

(15)

As seen in , the inference model about the trustee property is rather uncertain (i.e.,

0.9441).

5.2. An inconsistent recommender We modify the previous scenario to demonstrate that a recommender who provides

inconsistent ratings (i.e., ratings which do not correlate with observed trustee properties) cannot mislead the truster and these ratings are naturally discounted within the model in a principled way.

Let us assume a new recommender who uses a judgment method that is essentially random, providing ratings from a uniform distribution, providing 1-star ratings, , 5-stars ratings evenly, independent of the trustee property. We now explain how ratings provided by the recommender would affect the truster’s model of this recommender’s judgment method. We begin by assuming that this recommender has provided a set of ratings consisting of 2 ratings at each level of ratings(1-star, , 5-stars).


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(16)

It can be seen that the truster is completely uncertain about what to believe is the value of the

trustee’s property, and the truster has learned that there is an equal chance of the recommender reporting any of the ratings values regardless of whether the trustee’s property is poor, moderate, or high.

We assume that this recommender provides a set of ratings for a new trustee, which again are evenly distributed among 1-star, , 5-stars ratings. The truster takes into account the model of the recommender’s judgment method when she updates its model of the trustee property for the new trustee. As a result, the recommender’s ratings have less impact on determination of the trustee property. It is the lack of certainty about this recommender’s judgment method that naturally downplay the impact of the ratings provided by her in our model. Thus, recommenders for whom uncertainty exists will not overly impact the truster’s representation of the trustee properties. 6. Evaluation

In this section, we show through simulated scenarios how effectively the Beta trust model [7] is able to cope with subjectivity once it has been enhaced with our approach. Moreover, we compare our approach to the implementation of another method proposed by Farez Abdul-Rahman [6] and a probabilistic trust and reputation model which is able to handle subjectivity called “BLADE” by Regan et al. [14]. We briefly explain these two methods here.

In the Farez method, the truster stores the difference between the truster’s observation of the trustee property and the recommender’s rating after completion of each interaction. The most common value in this set (called semantic distance) is added to the next rating from the recommender in order to translate it into the truster’s semantic space. In the BLADE model, a trustee’s unknown properties are modeled as random variables in a Bayesian Network and a Bayesian learning approach is used to learn these random variables. As part of our evaluation, we hypothesize that: a) The Beta trust model combined with our approach for subjectivity handling outperform the

original Beta trust model as well as the Beta trust model with a simple subjectivity handling method such as the Farez method in situations where there is consistent subjectivity.

b) The extended Beta trust model will perform approximately as good as the BLADE model in consistent subjectivity situations.

c) The Beta trust model with our subjectivity handling method does not perform worse than the original model when the subjectivity is inconsistent.

d) Our method is able to cope with change in recommender or trustee behavior over time. Based on the results of our evaluation, we conclude that extension of the Beta trust model

with our proposed subjectivity handling mechanism improves its predictions.

6.1. Methodology Data is produced manually by simulation and is not taken from a real working system. The

evaluation consists of 1 truster, 22 trustees, and 20 recommenders. The trustees are assumed to have only one property and recommenders provide binary ratings unsatisfied or satisfied. Therefore, the Beta distribution can be used to model these binary transactions and the trust value is estimated as the probability expectation value of the Beta distribution.


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In the simulation, the recommenders are truthful by default. That is, they directly report on the trustee property they observe. The set of trustees are divided into a set of 11 known trustees with which the truster interacted directly, and 11 unknown trustees about which the truster gains information only through recommenders. In the first step the truster interacts with the set of known trustees and records the outcome. Then, the truster collects a set of opinions from each recommender about a randomly drawn subset of the known trustees, where each opinion represents a recommender-trustee interaction randomly determined by the trustee’s trustworthiness. Each trustee is assigned an intrinsic trustworthiness probability

Pr(P = satisfied ) from the set . The information in this first step forms the history of interactions and is used to estimate the recommender’s judgment method (conditional opinions).

Next, the truster collects opinions about the unknown trustees (once again based on 20 recommender-trustee interactions) and estimates the aggregated trust value for them. We have used three generic scenarios in our evaluation: (i) consistent subjectivity scenario in which recommenders report the opposite of the trustee property they observe, (ii) inconsistent subjectivity scenario in which recommenders report their observations erroneously at random, and (iii) dynamic behavior scenario in which the behavior of the recommender and/or the trustee’s property may change over time. The metric

is computed over all N = 11 unknown trustees for evaluation of the three models.

As the results is Sections 1.2-1.4 illustrate, our system learns, in general, any judgment method as long as the recommender provides enough consistent ratings (i.e., conditional opinions with low uncertainty values) allowing the truster to establish a strong correlation between the trustee properties and the ratings generated by the recommender’s judgment method.

6.2. Consistent Subjectivity

The purpose of this scenario is to compare the performance of the four models (the original Beta model, the Beta model with our method, the Beta model with Farez method, and the BLADE model) when there is consistent subjectivity. This test contributes to validating our hypotheses (a) and (b). In this scenario, there are some recommenders who may consistently report their observations with subjectivity in addition to the truthful recommenders. As there is only a single trustee property and two judgment methods, there is only one reasonable judgment method for subjective recommenders that maps satisfied to unsatisfied, which is, reporting the opposite of the trustee property they observe. We call these recommenders deceptive recommenders. This experiment was run with a varying number of these deceptive recommenders from zero to 20 and it has been studied how well these models handle these deceptive recommendations. Figure 3 illustrates the change in the mean error of each model as the percentage of deceptive recommenders grows.


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0 2 4 6 8 10 12 14 16 18 200.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Number of the deceptive recommenders

mea

n er

or

The Beta trust model without subjectivity handlyingThe Beta trust model with the proposed subjectivity handlyingThe Beta trust model with Farez subjectivity handlyingThe Blade model

Figure 3. Effect of subjectivity handling method on the Beta trust model when there are deceptive

recommenders.

The mean error of the aggregated trust values constructed by the models without subjectivity

handling and with the Farez method increase as the percentage of the deceptive recommenders grows, although the error is less when the Farez method is used. This result occurs because the number of deceptive recommenders increases as the amount of information useful decreases. On the contrary, the results indicate that the Beta trust model with our proposed subjectivity handling method and the BLADE model were able to correctly interpret the opinions of the deceptive recommenders and the percentage of deceptive recommenders has less impact on the mean error of the aggregated trust values. The BLADE model outperforms our proposal in this scenario and is more stable. Nevertheless, the average mean error of these two models is 0.15 (the optimal mean error is zero). Although our method is not aimed at addressing the deception problem, it is able to cope with deception when a majority of recommenders provide deceptive, yet consistent ratings. Therefore, the mean error decreases a little bit as the number of deceptive recommender increases. This graph does not answer the question of how these models perform when the subjectivity of the recommenders is not consistent. This case is shown in the next scenario.

One of the advantages of our approach over the BLADE model, which is a purely probabilistic approach, is that degrees of uncertainty can be explicitly included as an input during the analysis. This allows advanced types of conditional reasoning to be performed in the presence of uncertainty and incomplete information. This will also allow us to understand the relative proposition of firm evidence and uncertainty as contributing factors to the derived probabilistic likelihoods. Furthermore, our approach is based on feedback from personal experience while the BLADE model relies on modeling with one single distribution. 6.3. Inconsistent Subjectivity

The goal of this test is to compare the output of the four models when subjectivity is not consistent. It contributes to validating our hypothesis (c) that the Beta trust model with our subjectivity handling method does not perform worse than the original model when the recommenders has inconsistent subjectivity. The same experimental setup as in Section 6.2 was used. Instead of deceptive recommenders, we introduced inconsistent recommenders. Inconsistency was added to information provided by these recommenders by adding a Gaussian


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error with a standard deviation of 0.75 to the distribution of ratings. Then, we varied the percentage of the inconsistent recommenders in the scenario from zero to 20. The results are illustrated in Figure 4.

0 2 4 6 8 10 12 14 16 18 200.06

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Figure 4. Effect of subjectivity handling method on the Beta trust model when there are inconsistent

recommenders.

As expected, in all four cases the mean error increases in proportion with the inconsistency

due to the increasing percentage of inconsistent advisors. From an information theoretic perspective, there is no information in completely random ratings, so it is normal that none of the techniques do well. However, the mean error is less in the Beta trust model with our method and in the BLADE model. It makes sense to ignore random ratings, which is what our model intrinsically does. In these two tests the behavior of the recommenders and the trustees do not change. In the next test we assume that their behavior may change over time.

6.4. Dynamic Behavior

This test validates our hypothesis (d). To verify the effectiveness of our mechanism in incorporating the change in behavior (see Section 4.1) we focus on the trustee’s property, keeping the technique of changing the recommender’s judgment method the same. A simple scenario was simulated in which a sequence of ratings is reported by a recommender and at the midpoint of this sequence the actual trustee property generating the ratings was changed. We compare how well the truster is able to initially learn the trustee property and adjust what she has learned after the actual trustee property has changed.

To focus on how a change in the distribution over the actual trustee property affects the truster’s learning of this property, we assume that the truster has already learned the recommender’s judgment method with high a high degree of certainty. In our evaluation, the system learned a binary trustee property with values and whose actual distribution was

and . During the first half of the sequence, our recommender would report ratings derived from observing the trustee property drawn from the actual distribution. Half way through the sequence, the actual distribution of the trustee property was shifted to and .


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After each reported rating, we recorded the probability expectation value (as an estimate for the trust value) of the parameter representing the trustee property and compared this with the actual trustee property distribution to generate the ; we then averaged this error over 50 runs. This evaluation was run using the standard model without any forgetting method and was repeated after incorporating the static and dynamic forgetting method to adjust for change. In the static forgetting method, the value of is constant and in the dynamic forgetting method, the value of is adjusted according to Equation (8).

Figure 5 illustrates the mean error at each time step when a rating was reported. We can see that when the actual trustee properties are shifted, the mean error immediately goes up, but the rate at which this mean error then drops is far greater when the forgetting methods are incorporated. Besides, the drop is smaller with the dynamic forgetting method. Also note that the initial learning of the trustee property is not as stable when we incorporate possible trustee change. This result is due to the increase of uncertainty.

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Figure 5. Effect of incorporating the forgetting method on the Beta trust model when there are

dynamic trustees.

7. Related Work on Subjectivity

This section gives a brief overview of the sparse but highly relevant research on subjectivity. We summarize the related work in Table 1.

Table 1. Related Work

Related Work Shortcoming - Stratification and qualitative labels [6, 10] - Weighted majority of the ratings for each recommender [4] - Determination of disposition based on past trust values and communication of percentiles (relative perception about trustee) instead of absolute trust values [11] - Bayesian networks and Bayesian learning approach [14]

-Different meaning of qualitative labels for different persons -Heuristic -Loss of useful information -Not a sound solution in several cases -Requires a large number of trust value assignments in the past -Difficult to get the probability knowledge and the uncertainty value. -Cannot scale up easily to more complex environments -Does not allow for the use of background knowledge


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- Communication of the objective facts of the experiences instead of subjective opinions or ratings by using ontologies [8, 20] - Forming communities with similar interests using super-agents [2] - Neighborhood lists and implicit communities [3]

-Requires agents to either learn complicated models of the others or represent their experiences using ontologies. -Not suitable for completely decentralized environments -Not always easy to find like-minded recommenders in sparse networks -Difficulty of forming accurate communities in the beginning -Demands much effort and time

Some proposals divide the span of trust into strata and assign qualitative labels to them

[6,10]. For example, the stratification is given as the set of Very Trustworthy, Trustworthy, Untrustworthy, and Very Untrustworthy [6,10]. The use of strata with qualitative labels may initially be considered as a good solution to the problem of subjectivity, because it seems to provide a clear semantics and avoids the ambiguity associated with numerical values. Nevertheless, in order for it to have the claimed effect, a qualitative label such as “trustworthy” should hold the same meaning for one person as it does for another. This is not necessarily the case because persons with different personality cultures may associate the same experience with different strata. For example, based on his or her own perception of trust, what is viewed by someone as “very trustworthy” may be judged as hardly “trustworthy” by another person.

Abdul-Rahman and Hailes' reputation model [6] approaches the problem from another direction, by using a heuristic based on prior experiences, called the semantic distance, to “bias” received recommendations. The semantic distance is an average of all previous experiences. The problem with this, however, is that it is incomplete: firstly it assumes all other agents in the system use the same model, which in a heterogeneous environment will hardly ever be the case. Secondly, they do not differentiate between recommendations of different agents, which are based on different types of interactions.

In another work, deception and subjectivity are addressed by taking a weighted majority of the ratings of each recommender according to how successful each recommender has been at estimating the trustee reputations [4]. This work rates accuracy of the opinion source based on subsequent observations of trustee behavior. While these models are grounded in principled theories, they still make use of heuristics to deal with unreliable ratings. By weighting, discounting or eliminating ratings, useful information may be thrown away. For instance, when a recommender offers a consistent yet a subjective advice, it may be possible to interpret the rating rather than diminishing its importance or throwing it away all together.

Hasan et al. presented a statistical solution [11] for the elimination of subjectivity from trust recommendations. They conceive trust as a value relative to the disposition of the recommender rather than an absolute score, where disposition to trust is an inherent propensity of an individual to trust or distrust others. Disposition is a stable characteristic of the personality that governs how a person views the trustworthiness of other persons and is determined on the basis of trust values that a person has assigned in the past. For instance, a person who has a tendency of assigning high values of trust may have a high disposition to trust. A trust value is re-represented as a percentile which is the perception of the trustee relative to the other trustees that have been rated in the past by the same recommender. The receiver can convert the percentile to a local absolute score by reading the value (at the given percentile) in the collection of trust values that she herself has assigned to others. The main drawback of this work is that it requires a large number of trust value assignments in the past for a close approximation of their disposition to trust. Besides, there are several cases for which this method does not give correct results.

Another approach that aims to explore subjective differences was proposed by Regan et al. [14]. The authors proposed modeling e-market services as Bayesian networks and use a Bayesian learning approach to estimate distribution of the model parameters. More specifically, they model trustee properties and recommender’s evaluation function as dynamic random variables. As a result, receiver of the recommendations can progressively learn a probabilistic model that calibrates the interpretation of trustee evaluations. In other words, a correlation between the reported ratings and the known trustee’s properties are established and used to


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learn the recommender’s subjective evaluation function, which can in turn be used to infer the trustee’s properties. However, it is difficult to get the probability knowledge and the uncertainty value in this approach and this solution does not scale up easily to more complex environments. In addition, the Bayesian learner does not allow for the use of background knowledge and thus any contextual information needs to be encoded in the interactions.

Sensoy et al. [8] develop an approach for distributed service selection that allows consumers to represent their experiences with the service providers using ontologies. An experience is a record of what service the customer has requested and received in return. In this way, the experience-based approach allows the objective facts of the experiences (other than subjective opinions, i.e. ratings) to be communicated to the other party and thus eliminates subjective differences among consumers. However, this approach requires consumer agents to either learn complicated models of other consumers or represent their experiences using ontologies. Moreover, Trust is an inherently personal phenomenon and has subjective components, which cannot be captured in ontology.

Wang et al. [2] propose a community-based reputation for Web service selection based on the opinions from all community members that have similar interests and judgment criteria. However, it is not always easy to find like-minded recommenders in real applications.

Alternatively, communities can be built automatically during the process of agents’ interactions. If agents interact more often with other agents that are like-minded, gradually, communities will be formed. For example, in Yu and Singh’s model [3], implicit communities are formed, where each agent keeps a list of neighbors from which it can gain good services or referrals. However, it may take a long time and requires much effort for agents to learn each other and form effective communities. Furthermore, Consumer agents do not have much experience with services in the beginning and the communities built by them are therefore not very accurate.

Our approach can be characterized in three ways. First, we assume a completely decentralized environment, heterogeneous trust models, various rating schemes, and no common data such as ontologies. Second, our model does not require many previous interactions. The prediction can be started with only one interaction. Furthermore, it provides an uncertainty value along with its estimation. As the number of interactions decreases, the higher the uncertainty value will be and this helps the agent to decide whether to rely on this prediction or not. And finally, ratings are not discarded or discounted; therefore, there is no information loss. 8. Conclusions and Future Work

We have introduced an approach that explicitly addresses the problem of subjectivity arising from the inherent difference in the value systems of any two agents. The fundamental idea that underpins the approach is to learn the judgment method (which maps the rating values provided by a recommender about a trustee to the actual properties of the trustee) of each recommender. Subjectivity can be learned by using abductive reasoning to unravel how each recommender interprets and conveys the trustee properties in form of rating values. Subsequently, the learned judgment method of a recommender can be used to plausibly infer the true properties of a new trustee unknown to the truster, on the basis of the rating value this recommender provides, The truster, in turn, uses her own trust model to determine the expected value of a possible new interaction with a trustee having the inferred such properties.

Our evaluation shows that integrating subjectivity handling into a trust management system leads to performance improvements. The real strength of our approach is that any subjectivity differences between the recommender’s and the truster’s interpretation of trustees do not adversely affect the truster’s decision making. Moreover, the approach treats any consistent deception on the part of a recommender in a similar way as the subjective difference is treated. In addition, it is able to address possible dynamic changes in a trustee’s behavior by giving more weight to recent information, allowing the older and inaccurate information to fade into the past.

Our model is designed with the challenges inherent in trust management in mind, in which trusters identify and avoid underperforming trustees while allowing recommenders to have the edibility of using their own standards to evaluate these trustees. However, it can be added to other systems such as recommender systems. The method is easy to implement for recommender


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https://www.researchgate.net/publication/1961197_Learning_Nested_Agent_Models_in_an_Information_Economy?el=1_x_8&enrichId=rgreq-89953a394640502504a6f51bc4643bcb-XXX&enrichSource=Y292ZXJQYWdlOzIzNzA4MTU2NTtBUzoxMDM1MzczODQwOTk4NDNAMTQwMTY5NjY0NDE3Ng==




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Subjectivity handling of ratings for Trust and Reputation systems: An Abductive Reasoning Approach

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