Slide #1.

The Beta Reputation System A. Jøsang and R. Ismail 15th Bled Electronic Commerce Conference, Bled, Slovenia, June 2002, pp. 1-14
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Slide #2.

Outline • Introduction • Building Blocks in the Beta Reputation System • Belief Discounting in the Beta Reputation System • Performance of the Beta Reputation System • Conclusion 2
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Slide #3.

Introduction Reputation systems • • • • Encouraging good behavior and adherence to contracts Fostering trust amongst strangers in e-commerce transactions Providing incentive for honest behavior and helping people make decisions about who to trust. Without a reputation system taking past experiences into account, strangers might prefer to act deceptively for immediate gain instead of behaving honestly. 3
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Slide #4.

Introduction • Fundamental aspects • Reputation engine • Take reputation ratings from various inputs including feedback about other users • Use mathematical operations to compute a reputation score • Propagation mechanism • Two approaches: • Centralized (e.g., eBay) • Reputation data are stored in a central server • Users send a query to the central server for the reputation score • Decentralized • Everybody keeps and manages reputation of other users • Users can ask others for feedbacks 4
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Slide #5.

Contribution A reputation engine (called Beta Reputation System) is proposed based on the beta probability density function which can be used to represent probability distributions of binary events (1/0 for success/failure or satisfactory/unsatisfactory) • Posteriori probabilities of binary events can be represented as beta distributions • A sound basis in the theory of statistics • Applicable to both centralized and distributed systems 5
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Slide #6.

Building Blocks in the Beta Reputation System The Beta Reputation System: • The beta-family of probability density functions is a continuous family of functions indexed by the two parameters α and β . 6
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Slide #7.

Building Blocks in the Beta Reputation System “When observing binary processes with two possible outcomes , the beta function takes the integer number of past observations of and to estimate the probability of , or in other words, to predict the expected relative frequency with which will happen in the future.” 7
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Slide #8.

Building Blocks in the Beta Reputation System Initially α=1 and β=1 yielding the initial reputation score of 0.5, meaning no information 8
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Slide #9.

Building Blocks in the Beta Reputation System Example: • • A process with two possible outcomes • Produced outcome 7 times • Produced outcome 1 time The Beta function is plotted below: 9
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Slide #10.

Building Blocks in the Beta Reputation System Example (cont’): • represents the probability of an event • represents the probability that the first-order variable has a specific value • The curve represents the probability that the process will produce outcome during future observations • The probability expectation value -> the most likely value of the relative frequency of outcome is 0.8 8 / (8 + 2) 10
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Slide #11.

Building Blocks in the Beta Reputation System • In e-commerce, an agent’s perceived satisfaction after a transaction is not binary - not the same as statistical observations of a binary event. • Beta reputation system can be extended to non-binary events by representing positive and negative feedbacks as a pair (r, s) of continuous values. Degree of dissatisfaction (a real number) Degree of satisfaction (a real number) 11
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Slide #12.

Building Blocks in the Beta Reputation System . Compact notation: 12
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Slide #13.

Building Blocks in the Beta Reputation System • T’s reputation function by X is subjective (as seen by X) Superscript (X): feedback provider (the trustor) Subscript (T): feedback target (the trustee) 13
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Slide #14.

Building Blocks in the Beta Reputation System • A reputation rating is how an entity is expected to behave in the future • When the reputation rating is within a range [0, 1], from Definition 1: • When the reputation rating is within a range [-1, 1], 14
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Slide #15.

Building Blocks in the Beta Reputation System One can combine positive and negative feedback from multiple sources, e.g., combine feedback from X and Y about target T Combine positive feedback Combine negative feedback Operation is both commutative and associative 15
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Slide #16.

Belief Discounting in Beta Reputation System • Belief discounting is done by varying the weight of the feedback based on the agent’s reputation • Jøsang’s belief model uses a metric called opinion to describe beliefs about the truth of a proposition • • • interpreted as probability that proposition x is true interpreted as probability that proposition x is false interpreted as uncertainty 16
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Slide #17.

Belief Discounting in Beta Reputation System Y: a recommender who provides a feedback to X about T X: a trustor who has its opinion about Y Objective: X wants to form an opinion about T, taking into account its opinion about Y Y’s opinion about T 17
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Slide #18.

Belief Discounting in Beta Reputation System • The opinion metric can be interpreted equivalently to the Beta function by mapping: • Inserting (b,d,u) defined above into the three equations in Definition 4, one can obtain T’s discounted reputation function by X through Y, , as follows: Associative but not commutative 18
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Slide #19.

Belief Discounting in Beta Reputation System Q: Prove or show by example on slide #18 19
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Slide #20.

Belief Discounting in the Beta Reputation System Q: Prove or show by example (Continuation from slide #19) 20
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Slide #21.

Providing and Collecting Feedback • • • • Feedback is received and stored by a feedback collection center C Assume that all agents are authenticated and that no agent can change identity Agents provide feedback about transactions C discounts received feedback based on providers reputation and updates the target’s reputation function and rating accordingly • C provides updated reputation ratings to requesting entities 21
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Slide #22.

Performance: Effect of Discounting Center C receives a sequence of n identical feedback values (r=n, s=0) from X about T Blue line is (r=1000, s=0) meaning no discounting at all, i.e., C takes X’s feedback as is Varying X’s reputation function parameters Pink line is (r=0, s=0) under which T’s rating is not influenced by X’s feedback at all. i.e., C ignores X’s feedback Conclusion: As X’s reputation function gets weaker, T’s rating is less influenced by the feedback From X 22
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Slide #23.

Conclusions • The Beta reputation system uses beta probability density function to combine feedback and derive reputation ratings, with a strong foundation in the theory of statistics • Belief discounting can deal with bad-mouthing or ballotstuffing attacks when trust is accurate (i.e., when Center C is accurate in assessing a recommender X’s reputation). • Discounted feedbacks are combined by Center C to yield the reputation score of a target node. • Flexibility and simplicity make it suitable for supporting electronic contracts and for building trust between players in e-commerce applications (centralized or distributed). 23
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