A New Approach for Trust Calculation in Social Networks

1. A New Approach for Trust Calculation in Social Networks Mehrdad Nojoumian (student) Timothy C. Lethbridge (supervisor) University of Ottawa, Canada tcl@site.uottawa.ca Trust Calculation - Nojoumian and Lethbridge

2. Objectives of this talk • Explore the behavior of various trust calculation approaches • Describe an approach that has an improved combination of characteristics. Trust Calculation - Nojoumian and Lethbridge

3. Some definitions • Social network • Nodes are actors (buyers, sellers, partners, brokers) • Arcs are relationships (buying, selling, advising, consulting, sharing, etc.) • Reputation: Perception an agent has of another’s intentions • Derived from one’s own observations and those in one’s social network • Reputation is a social quantity, but everyone has their own perception of it Trust Calculation - Nojoumian and Lethbridge

4. Trust • Personal expectation about another’s behavior in a particular encounter (Mui 2002) • Derived from reputation • Parties in a transaction must establish trust to do business effectively • If party A has low trust of party B, party A will be willing to pay party B less, and will need to consider insurance • So party B has an incentive to be trustworthy Trust Calculation - Nojoumian and Lethbridge

5. Reputation systems • Gather experiences from participants as transactions take place • Trustworthy agents increase in reputation • Untrustworthy agents drop in reputation • Reputation systems can be ‘centralized’ • E.g. in EBay, sellers receive ratings (-1, 0,1) for reliability. • Reputation can be the sum or some other function of those ratings Trust Calculation - Nojoumian and Lethbridge

6. Decentralized reputation systems • A1 can query others who have transacted with A2 • Overall reputation can be a combination of A1’s: • Direct experience with A2 • Feedback from others who have interacted with A2 • Reputation of others (A3, A4 and A5) as witnesses Trust Calculation - Nojoumian and Lethbridge

7. Trust is built up over time • Through a series of transactions • Co-operations (C) = good experiences with the agent in question • Delivery occurred in a timely manner • Merchandise was as advertised • Payment was received in full and on time • Acted as a truthful or reliable witness • Defections (D) = bad experiences • Delivery excessively late • Merchandise wrong or inferior to expectation • Payment excessively late or not received • Acted as an untruthful or unreliable witness Trust Calculation - Nojoumian and Lethbridge

8. A sample trust function from the literature • Y&S: Yu and Singh (2000) • Compute Tt+1 = f(Tt, CorD) Trust Calculation - Nojoumian and Lethbridge

9. Effect of Y&S = 0.1 and  = -0.2 Increment in trust after cooperation Decrement in trust after defection Trust value before transaction Yellow region: The better you are, the less co-operation benefits Trust value after cooperation Trust value after defection Yellow region: The worse you are, the less defection costs

10. Y&S ‘Increment’ view = 0.1 and  = -0.2 Increment on defection Increment on cooperation Trust value, Tt Trust Calculation - Nojoumian and Lethbridge

11. Y&S ‘Next value’ (Tt+1) view = 0.1 and  = -0.2 Next value on defection Next value on cooperation Trust value, Tt Trust Calculation - Nojoumian and Lethbridge

12. Y&S ‘Sequence’ view = 0.1 and  = -0.2 • Sequences of • 30 cooperates • 10 cooperates + 10 defects + 10 cooperates • 30 defects Inflection point Penalty for D after C Trust Calculation - Nojoumian and Lethbridge

13. A new proposed formula family: N&L (Nojoumian and Lethbridge) • Key changes: • As trust increases above threshold , keep increasing the reward for co-operation • Up to the maximum • As trust decreases below threshold keep increasing the cost of defection • Down to the minimum • Between  and keep cost and reward fixed Trust Calculation - Nojoumian and Lethbridge

14. The N&L trust function:In case of Cooperation • Tt in [-1, ) • Bad agent (for now): Encourage • Reward increases linearly from • Xencourage (default 0.01) to • Xgive (default 0.05) • Tt in [, ] • Agent about which you are indifferent: Give Xgive • Tt in (, +1] • Good agent: Reward • Reward increases linearly from • Xgive to • Xreward (default 0.09) Trust Calculation - Nojoumian and Lethbridge

15. The N&L trust function:In case of Defection • Tt in [-1, ) • Bad agent: Penalize • Increment increases linearly from • Xpenalize (default -0.09) to • Xtake (default -0.05) • Tt in [, ] • Agent about which you are indifferent: Take Xtake • Tt in (, +1] • Good agent (for now): Discourage • Increment increases linearly from • Xtake to • Xdiscourage (default -0.01) Trust Calculation - Nojoumian and Lethbridge

16. Comparison of ‘increment’ views = 0.1 and  = -0.2 Next value on defection Next value on cooperation Y&S N&L -1 Trust value, Tt +1 -1 Trust value, Tt +1 Trust Calculation - Nojoumian and Lethbridge

17. Comparison of ‘next value’(Tt+1) views = 0.1 and  = -0.2 Increment on defection Increment on cooperation Y&S N&L -1 Trust value, Tt +1 -1 Trust value, Tt +1 Trust Calculation - Nojoumian and Lethbridge

18. Comparison of ‘sequence’ views = 0.1 and  = -0.2 Yellow: 10C 10D 10C Y&S N&L ‘Maxed out’ Inflected asymptotic Less severe penalty for D after C, but can be adjusted

19. Effect of adjusting N&L parameters: 0.1 to 0.3 and  -0.2 to -0.4 Original Result Longer indifferent period Slight delay only

20. Effect of adjusting N&L parameters:Xencourage 0.01 to 0.015 and Xpenalize -0.09 to -0.15 Original Result Slight effect of increased encouragement Effect of increased penalty Larger D after C penalty

21. Effect of different N&L sequencesXencourage remains 0.015 and Xpenalize remains -0.15 20C10D end <0 10C10D10C end >010D20Cend <0 10C20D10D10C10D Trust Calculation - Nojoumian and Lethbridge

22. Same sequences from Y&S function 20C10D end <0 10C10D10Cend <010D20C end >0 10C20D10D10C10D Trust Calculation - Nojoumian and Lethbridge

23. Microsoft Excel formula for calculating N&L trust values =prevTrustValue+(IF(CorD="C", MIN(1-PrevTrustValue, IF(GoodOrBad="B", X_encourage+(PrevTrustValue+1)/(beta2--1)*(X_give-X_encourage), IF(GoodORBad="I", X_give, X_give+(PrevTrustValue-alpha2)/(1-alpha2)*(X_reward-X_give) ))), MAX(-1-Y50, IF(GoodORBad="B", X_penalize+(PrevTrustValue+1)/(beta2--1)*(X_take-X_penalize), IF(GoodORBad="I", X_take, X_take+(PrevTrustValue-alpha2)/(1-alpha2)*(X_discourage-X_give) ))) )) Trust Calculation - Nojoumian and Lethbridge

24. You can simplify calculations by using an approximation • Results of quadratic regression for the N&L for default parameters Trust Calculation - Nojoumian and Lethbridge

25. Varying the function for varying transaction value • E.g. You could apply the formula N=floor(Log10(V)) times where V is the transaction value • I.e. • $10-$99 - Apply once • $100-$999 - Apply twice • $1000-$9999 - Apply 3 times • Etc. • The base of the logarithm can be changed for different effects Trust Calculation - Nojoumian and Lethbridge

26. Main drawback of N&L • ‘Maxing out’ or ‘hitting rock bottom’ • No further increase in trust after you reach 1 • No further decrease in trust after you reach -1 • Asymptotic approach corresponds to ‘diminishing returns’ • Could be rectified by making the function open-ended Trust Calculation - Nojoumian and Lethbridge

27. Conclusions - • It seems reasonable to consider that trust functions should • Reward more (or same) the better an agent is • Penalize more (or same) the worse an agent is • Y&C trust function does not have these properties • But has asymptotic approach / diminishing returns

28. Conclusions - 2 • We propose a family of trust functions • Reward always increases the better an agent is, and vice-versa • Eight parameters can be adjusted to fine tune behavior • Future work: • Empirically evaluate the ability of the variously parameterized Y&C or N&L functions to predict actual trustworthiness Trust Calculation - Nojoumian and Lethbridge