Interpersonal Trust Model Ing. Arnoštka Netrvalová DSS - seminar, 8.12.2008.

Interpersonal Trust Model

Ing. Arnoštka Netrvalová

DSS - seminar, 8.12.2008

2DSS-seminar, 8.12. 2008

Interpersonal trust model

Why? Where? What? Trust definition Trust values Trust types Mapping functions Trust representation Personal trust factors Personal trust design Personal trust forming Aggregation and transformation Model behaviour study Personal trust effect Conclusion

Fide, sed qui fidas, vide.

It is an equal failing to trust everybody, and to trust nobody.

[ChangingMinds.org]

/33


WHY? WHERE?

Phenomenon of everyday life Internet

e-banking – credibility e-commerce – trustworthiness of partners e-service – quality, promptness

PC and computing

/33




WHERE? WHAT?

Computing and trust P2P systems – security (working together of nodes) GRID computing – security (reliability of sources, users) AD HOC networks – message integrity (node =server, router,

client, malicious nodes, special protocols, cryptographic codes) MAS – security dependability (malicious agent detection, migrating,

selection of „the best“ agent, system’s optimization) Semantic web – credibility of sources (machine information

collection)

/33



Trust definition

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 an action (or independently of our capacity of ever to be able to monitor it) and in a context in which it affects our own action.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Gambetta's definition was derived as a summary of the contributions to the symposium on trust in Cambridge, England, 1988.

/33


THE TRUSTTHE TRUST in an individual is a commitment to an action based on a belief that the future actions of that individual will be make for a good outcome.


Trust values

1 0. 5 0.025

0

Blind trust

High trust

Low trust

Absolute distrust

Ignorance

Low distrust

High distrust

0.95 0.7 0.3 0.05

/33



Trust types

personalpersonal – trust between entity

- unilateral - reciprocal

phenomenalphenomenal – trust to phenomenon (products of phenomenon)

/33



Mapping function

/33


0

0,5

1

0 0,5 1

Interval

Trust

Blind trust

Complete distrust

Strong trust

Weak trust

Ignorance

Strong distrust

Weak distrust

non-linear

asymmetrical


Personal trust description

Group of n autonomous individuals X ={x1, x2, … , xn}

Measure of the interpersonal trust (between two individual xi and xj)

Reciprocal trust: xi →xj and xj →xi [ ]

Trust representation (in the group)

The interpersonal trust in the group - directed weighted graph vertices - the individuals directed edge with weight - measure of interpersonal trust

Complete distrustComplete distrust - edge with zero weight No contactNo contact - no edge

ji , n, jixxtt jiij and 1 ,,1,0,

jiij tt ;

/33



Group trust representation

A

B

C

0.9

0.60.8

0.5

/33


Example:

Representation of personal trust in three individual’s group (A, B, and C)

118.0

5.016.0

19.01

T

Trust (adjacency) matrix


Basic personal trust factors

Initial trustInitial trust – is defined as the initial trust value

ReputationReputation of an entity - is an expectation of its behavior based on information about the entity’s past behavior within a specific context at a given time

RecommendationRecommendation – is based on expectation given by other entities’ observations by communication

ContactContact – represents direct trust experience

DispositionDisposition – acceptation intensity of acquired information

/33



Personal trust factors representation

/33


Initial trust matrix Reputation matrix Contact matrix Recommendation matrix Disposition matrix


Personal trust design

/33


Subject

Knowledge Base

Communication

Reputations

RecommendationsTrust

Evaluation

Contacts

Disposition

Initial trust

Group of subjects

Context


Personal trust forming

- personal trust i-th entity to j-th entity - number of reciprocal contacts i-th and j-th entities - number of recommendations of j-th entity to i-th from others - reputation of j-th entity at i-th entity - randomness, where 0≤<1

,G

ijdijcijt

ijr

,,,,,, GrdcttFT ijijijjiijij

ijijij ttT

0 ijT 1

/33



- weight (effect) of reputation (constant / number of steps)- weight (sum of contacts of i-th subject)- weight (sum of recommendations of j-th subject to i-th one

igir

ij

id

ij

ic

ijjiijijij

w

G

w

r

w

d

w

ctttT ,

Personal trust forming

irw

irw

icwidw

n

jijijic cw

,1

n

jijijid dw

,1

n

cc lij

lij

1-

n

dd lij

lij

1-

ijc ijd

/33




Aggregation function

/33


0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

0,55

0,60

0,65

0,70

0,75

0,80

0,85

0,90

0,95

1,00

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,000,000,100,200,300,400,500,600,700,800,901,00

Dílčí hledisko "v"

Agr

ega

ce o

bo

u h

led

ise

k

Dílčí hledisko "u"

1010 ijij tt

ijijijij ttAtt ,,max

ijijijijijijijijij tttttttttA 1,

1,min,,max ijijijijijij ttttAtt


Transformation – logistic S-curve Interpersonal trust model

/33

Transformation bounded interval 0, 1 b

ax

exu

1

1

minmax

minmax6,41,9

1

1

x

exu 99,0maxand01,0min uu

Option:Option:

min, max weights

0,000,050,100,150,200,250,300,350,400,450,500,550,600,650,700,750,800,850,900,951,00

-2 -1 0 1 2 3 4 5 6

Lineární transformace při známých maximech a minimech Univerzální transformace min=-1, max=5Linear transformation (min, max known ) Universal transformation


Model behavior study

Personal trust forming Number of contacts influence Number of recommendations influence Initial trust influence Reputation influence Trust disposition influence Weight of contacts effect Weight of recommendations effect Weight of reputation effect

/33



Personal trust – study

/33


0,790,740,84

0,34

0,140,27

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

reputation

reputace r2→s1 r4→s1 r5→s2 r2→s3 r4→s3 r4→s5

relationship

si sj

Selected subjects - reputation of partners



0

1

2

3

4

0 1 2 3 4 5 step

number of contacts

s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4

0

1

2

3

4

0 1 2 3 4 5 step

number of recommendations

s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4

/33


Trust

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5

step

trust

t12

t14

t25

t32

t34

t54



/33


0

1

2

3

4

0 1 2 3 4 5 step

number of contacts

s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4

Influence of number of contacts (reputation=0,5 ; number of recommendation=0)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5

step

trust

t12 t14 t25

t32 t34 t54



/33


0

1

2

3

4

0 1 2 3 4 5 step


s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4

Influence of number of recommendations (reputation=0.5; number of conntacts=0)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5

step

trust

t12 t14 t25

t32 t34 t54



/33


Influence of initial trust (s1 s2)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5

step

trust

0,15 0,35 0,55 0,75 0,95


Personal trust – studyInfluence of reputation (s1 s4, r 41)

0,3

0,35

0,4

0,45

0,5

0,55

0 1 2 3 4 5step

trust

0,200,350,500,650,80

Reputation values:

0

1

2

3

4

0 1 2 3 4 5 step

number of contacts

s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4

/33


0

1

2

3

4

0 1 2 3 4 5 step


s1→s2

s1→s4

s2→s5

s3→s2

s3→s4

s5→s4



Influence of disposition - trust for six selected relationships (for 5 steps, 1-10 runs)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5 6 7 8 9 10

run

trust

t12

t14

t25t32

t34

t54

/33




/33


Number of contacts - weight influence (s1-->s4 )

0,34

0,35

0,36

0,37

0,38

0,39

0,4

0 1 2 3 4 5step

trust

w =0,2 w =0,5 w =1 w =2 w =5



/33


Influence "aditional" weight of recomendation (s1 s2 )

0,6

0,65

0,7

0,75

0,8

0,85

0,9

0,95

1

0 1 2 3 4 5

step

trust

w =0,2 w =0,5 w =1 w =2 w =5



/33


Weight of reputation influence (s3 s2, r23)

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 1 2 3 4 5

step

trust

w =0,5 w =1 w =2 w =5 w =10


Information effect model

Transformation – joint initial and effective probability distribution

Initial probability distribution p(x)

(Input) Effective probability

distribution r(x)

Final probability distribution q(x)

(Output)

);||()||()||( rqpDrpDqpD

)( )()1()( xrxpxq 10

Convenient measure of intensity effect evaluation:

Potential solution:

/33



Example: Symmetrical divergenceInterpersonal trust model

/33

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

1 9 17 25 33 41 49 57 65 73 81 89 97 105

113

121

129

137

145

153

161

169

177

185

0

5

10

15

20

25

30

35

40

45

J ablk a-1k g S ym e tr ic k á dive rg e nc e pok le s ů a vz růs tů

Z adaná % m e z i-týde nní tole ranc e :=0,05% C e ny Č RCommodity: Apples

Given % inter-weeks tolerance = 0,05%

Symmetrical divergence (incr., decr.)

Price CZK/kg, 2004-2007


Personal trust effect

λ 0, 1 - effect intensityE(α, ), 0≤α< ≤1 - effect distribution

,1 EtT ijijijij

11

n

jij

/33

n – number of subjects, i-th subject, i-th subject



Conclusion

/33


Cooperation – selection of partners (published)Cooperation – selection of partners (published) Personal trust modelPersonal trust model ( (submittedsubmitted)) Phenomenal trust modelPhenomenal trust model ( (simultaneous verificationsimultaneous verification)) Trust model with interventionTrust model with intervention byby agent agent technology technology

application application (JADE)(JADE)

Available information:http://www.kiv.zcu.cz/~netrvalo/publikace/publikace.html

Thank you for your attention.

Questions?

Interpersonal Trust Model Ing. Arnoštka Netrvalová DSS - seminar, 8.12.2008.

Documents

interpersonal trust

group trust representation

x j reciprocal trust

trust p2p systems security

individual x

asymmetrical slide

particular action

malicious nodes