The Beta Reputation System Audun Jsang and Roslan

The Beta Reputation System Audun Jøsang and Roslan Ismail [1] Presented by Hamid Al-Hamadi CS 5984, Trust and Security, Spring 2014

Outline • Introduction • Building Blocks in the Beta Reputation System • Performance of the Beta Reputation System • Conclusion 2

Introduction • Many existing reputation systems • Applicability in e-commerce systems: • Enforcement is needed in order for contracts and agreements to be respected • Traditionally rely on legal procedures to rectify disagreement. • Hard to enforce in e-commerce • unclear which jurisdiction applies • cost of legal procedures 3

Introduction • Reputation systems • As a substitute to traditional Reputation systems can be used to encourage good behavior and adherence to contracts • Fostering trust amongst strangers in e-commerce transactions • Gathers, distributes, and aggregates feedback about participants behavior • Incentive for honest behavior and help people make decisions about who to trust. • Without a reputation system taking account past experiences, strangers might prefer to act deceptively for immediate gain instead of behaving honestly. 4

Introduction • Online auction sites were the first to introduce reputation schemes e. g. e. Bay. com • Others include company reputation rating sites such as Biz. Rate. com, which ranks merchants on the basis of customer ratings • The internet is efficient in capturing and distributing feedback, unlike the physical world. • Some challenges: • An entity can attempt to change its identity to erase prior Feedback • Restart after it builds a bad reputation • Not enough feedback provided by surrounding entities • Negative feedback hard to elicit • Difficult to ensure feedback is honest 5

Introduction • Example of dishonesty through reputation systems: • Three men attempt to sell a fake painting on e. Bay for $US 135, 805 • Two of the fraudsters actually had good Feedback Forum ratings as they rated each other favorably and engaged in honest sales prior to fraudulent attempt. • Sale was abandoned just prior to purchase, buyer became suspicious 6

Introduction • Fundamental aspects: • Reputation engine • Calculates users’ reputation ratings are from various inputs including feedback from other users • Simple or complex mathematical operations • Propagation mechanism • Allows entities to obtain reputation values • Two approaches: • Centralized (e. g. e. Bay) • Reputation values are stored in a central server • Users forward their query to the central server for the reputation value whenever there is a need • Decentralized • Everybody keeps and manages reputation of other people themselves • Users can ask others for the required reputation values 7

Introduction • Authors propose a new reputation engine based on the beta probability density function called the beta reputation system • strongly based on theory of statistics • paper describes centralized approach, but the reputation system can also be used in a distributed setting 8

Building Blocks in the Beta Reputation System • The Beta Density Function • Can be used to represent probability distributions of binary events • The beta-family of probability density functions is a continuous family of functions indexed by the two parameters α and β. 9

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. ” 10

Building Blocks in the Beta Reputation System 11

Building Blocks in the Beta Reputation System • Example: • process with two possible outcomes • Produced outcome 7 times • Produced outcome 1 time • Will have beta function as plotted below: 12

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 • Curve represents the uncertain probability that the process will produce outcome during future observations • probability expectation value -> the most likely value of the relative frequency of outcome is 0. 8 8 / (8 + 2) 13

Building Blocks in the Beta Reputation System • The Reputation Function In e-commerce an agent’s perceived satisfaction after a transaction is not binary - not the same as statistical observations of a binary event. • Let positive and negative feedbacks be given as a pair of continuous values. Degree of satisfaction Degree of dissatisfaction 14

Building Blocks in the Beta Reputation System • Compact notation : • 15

Building Blocks in the Beta Reputation System • T’s reputation function by X is subjective (as seen by X) Superscript (X): feedback provider Subscript (T): feedback target 16

Building Blocks in the Beta Reputation System • The Reputation Rating • Simpler representation to communicate to humans that a reputation function • Given as a probability value – within a range • Neutral value is in middle of range • Scale the rating to be in the range [-1, +1] • A measure of reputation and how an entity is expected to behave in the future 17

Building Blocks in the Beta Reputation System • Combining Feedback • 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 18

Building Blocks in the Beta Reputation System • Discounting • Used to vary the weight of the feedback based on the agents reputation • Described in the context of belief theory • Jøsang’s belief model uses a metric called opinion to describe beliefs about the truth of statements • • • interpreted as probability that proposition x is true interpreted as probability that proposition x is false interpreted as inability to assess the probability value of x 19

Building Blocks in the Beta Reputation System • Y has opinion about T, gives it to X • X has opinion about Y Then X can express its opinion about T taking into account its opinion about Y’s advice , as follows: Given by Y (its opinion about T) Apply X’s opinion about Y 20

Building Blocks in the Beta Reputation System • The opinion metric can be interpreted equivalently to the beta function • mapping between the two representations defined by: • Using previous eq. , discounting operator for reputation functions is obtained: Associative but not commutative 21

Building Blocks in the Beta Reputation System • Forgetting • Old feedback less relevant for actual reputation rating • Behavior changes over time • Old feedback is given less weight than new feedback • Can use an adjustable forgetting factor Order of feedback processing matters • If λ=1 -> no forgetting factor, nothing is forgotten • If λ=0 -> only last feedback, all others forgotten 22

Building Blocks in the Beta Reputation System • Forgetting (cont’) • To avoid saving all of the feedback tuples (Q) forever, a recursive algorithm can be used instead: 23

Building Blocks in the Beta Reputation System • Providing and collecting feedback: • After each transaction, a single agent can provide both positive and negative feedback simultaneously: • Feedback can be partly satisfactory, and given as a pair • The sum can be interpreted as the weight of the feedback • Minimum weight of feedback is r + s = 0, equivalent to not providing feedback • Alternatively, define a normalization weight denoted by so that the sum of the parameters satisfy • Feedback can be provided as a single value with values within a specified range • If we have such that then the can be derived using and as follows: • Weight can reflect importance of transactions (high importance -> high ) 24

Building Blocks in the Beta Reputation System • Feedback is received and stored by a feedback collection centre C • Assumed that all agents are authenticated and that no agent can change identity • Agents provide feedback about transaction • 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 25

Performance • Example A: Varying Weight • This example shows how the reputation rating evolves as a function of accumulated positive feedback with varying weight w • Let C receive a sequence Q of n identical feedback values v=1 about target T • Then: Reputation parameters: Reputation rating: Derived from previous equations: 26

Performance w=1 w=0 27

Performance • Example B: Varying Feedback • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying feedback value v V=1 • For v=1 the rating approaches 1, and for v=-1 the rating approaches -1. V=-1 28

Performance • Example C: Varying Discounting • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying discounting • C receives a sequence Q of n identical feedback values v =1 about target T • Forgetting is not considered • Each feedback tuple with fixed value (1, 0) is discounted based on the feedback provider’s reputation function defined by Reputation parameters: Reputation rating: 29

Performance • Example C: Varying Discounting (cont’) practically equivalent to no discounting at all Varying Feedback provider’s reputation function parameters • As X’s reputation function gets weaker T’s rating is less influenced by the feedback From X • with r=0, s=0 , T’s rating not influenced by X’s rating 30

Performance • Example D: Varying Forgetting Factor • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying forgetting factor λ • C receives a sequence Q of n identical feedback values v =1 about target T • Discounting is not considered Using previous equations, the reputation parameters and rating can be expressed as a function of n and λ according to: 31

Performance • Example D: Varying Forgetting Factor (cont’) 32

Performance • Example E: Varying Feedback and Forgetting Factor • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1. • Let there be a sequence Q of 50 feedback inputs about T, where the first 25 have value , and the subsequent 25 inputs have value • Using previous equations, the reputation parameters and rating can be expressed as a function of n, v, and λ according to: In more explicit form: 33

Performance • Example E: Varying Feedback and Forgetting Factor (cont’) In more explicit form: 34

Performance • Example E: Varying Feedback and Forgetting Factor (cont’) v=1 • Two phenomena can be observed when the forgetting factor is low (i. e. when feedback is quickly forgotten): • Firstly the reputation rating reaches a stable value more quickly, and • secondly the less extreme the stable reputation rating becomes. v=-1 35

Conclusion • Reputation systems can be used to encourage good behavior and adherence to contracts in e-commerce • Authors propose a beta reputation system which is based on using beta probability density functions to combine feedback and derive reputation ratings • Strong foundation on theory of statistics • Assumed a centralized approach, although it is possible to adapt the beta reputation system in order to become decentralized • flexibility and simplicity makes it suitable for supporting electronic contracts and for building trust between players in e-commerce 36

References [1] A. Josang, and R. Ismail, "The Beta Reputation System, ” 15 th Bled Electronic Commerce Conference, Bled, Slovenia, June 2002, pp. 1 -14. 37