Analysing the Relationship
between Risk and Trust
By Audun Jøsang and Stéphzne Lo Presti
Roadmap
• Risk-Trust in Literature
• Measuring Risk-Trust
• Decision via Risk
• Balancing Trust and Risk
• Conclusion
Risk-Trust in Literature
• Concept uncertainty
of Trust
subjectivity
risk
• Trust is the extent to which one party is willing to depend on somebody, or something, in a
given situation with a feeling of relative security, even though negative consequences are
possible.
• Concept of Risk
• Anticipated hazard, measurable
• Trust vs. Risk
• Both difficult to scale
• Both upon uncertainty and unpredictability
• Relationship between them (antecedent, alternative, outcome)?
Risk-Trust in Literature
• A risk-trust model by fuzzy logic [Manchala1998]
• (trans_history, cost) -> trust
Measuring Risk-Trust : Decision via Risk
• Expected Monetary Value (EV)
• 𝐸𝑉 = 𝐼
𝑛
𝑖=1 𝑝𝑖 𝐺𝑖
• Expected Utility (EU)
• 𝐸𝑈 =
• 𝐼: the monetary investment/bet
• 𝑝𝑖 : the probability of the 𝑖th
outcome
• 𝐺𝑖 : the gain factor of the 𝑖𝑡ℎ
outcome, given 𝐼
𝑛
𝑖=1 𝑝𝑖 𝑢
𝐼𝐺𝑖
• 𝑢(⋅): non-linear utility function of
monetary value
• 𝑢 𝐼𝐺 < 𝐼𝐺: risk averse
• 𝑢 𝐼𝐺 > 𝐼𝐺: risk seeking
• 𝑢 𝐼𝐺 = 𝐼𝐺: risk-neutral
• Risk-Neutral Case
(𝐸𝑉 = 𝐸𝑈 = 𝐸𝐺 ⋅ 𝐼)
𝐸𝐺: Expected Gain
Measuring Risk-Trust : Decision via Risk
• 𝐸𝐺 For Decision
• 𝐸𝐺 = 𝑝𝐺𝑠 + 1 − 𝑝 𝐺𝑓 = 𝑝 𝐺𝑠 − 𝐺𝑓 + 𝐺𝑓
• 𝑝: probability of successful transaction
• 𝐺𝑠 : gain factor to a successful transaction 𝐺𝑠 ∈ [0, ∞]
• 𝐺𝑓 : loss factor to a failed transaction 𝐺𝑓 ∈ [−1,0]
• 𝐸𝐺 ≔ 𝑓(𝑝, 𝐺𝑠 , 𝐺𝑓 )
Measuring Risk-Trust : Decision via Risk
• 𝐼 For Decision
• 𝐼 = 𝐹𝐶 𝐶
• 𝐶: the total capital
• 𝐹𝐶 : fraction of the total capital
• 𝐹𝐶 ≔ 𝑓(𝑝, 𝐺𝑠 )
• 𝐹𝐶 varies in the same direction of 𝐺𝑠 and 𝑝
𝜆
𝐺𝑠
• E.g. 𝐹𝐶 = 𝑝
• 𝜆: factor moderating the influence of 𝐺𝑠 , or risk attitude
• Low 𝜆 – risk-taking; high 𝜆 – risk-aversion;
Measuring Risk-Trust : Balancing Trust - Risk
• “The outcome of the transaction depends on somebody or
something and that the relying party is uncertain about the outcome
of the transaction.”
• Paraphrase 𝒑: the reliability of 𝑥 for producing a successful outcome
• Reliability Trust: the trusting party’s probability estimate 𝑝 of success
of the transaction
Measuring Risk-Trust : Balancing Trust - Risk
• Decision Trust
• to normalize different between 𝑥’s reliability and the cut-off probability on an
agent’s decision surface (risk attitude), given (1) risk attitude defined by a
decision surface, and (2) transaction outcome upon 𝑝, 𝐺𝑠 , 𝐹𝐶 and 𝑝𝐷
• 𝑇=
𝑝−𝑝𝐷
𝑝𝐷
0
𝑝−𝑝𝐷
1−𝑝𝐷
𝑝 < 𝑝𝐷
𝑝 = 𝑝𝐷
𝑝 > 𝑝𝐷
𝑇 ∈ [−1,1]
• 𝐷: decision surface
• 𝑝: probability 𝑥 producing a successful outcome, given 𝐺𝑠 and 𝐹𝐶
• 𝑝𝐷 : cut-off probability on 𝐷 for the same 𝐺𝑠 and 𝐹𝐶
Measuring Risk-Trust : Balancing Trust - Risk
• Decision Trust
•
•
•
•
•
(0,-1), (𝑝𝐷 ,0), and (1,1)
Decision trust depended on a distance between 𝑝 and 𝑝𝐷
𝑇 > 0, trusting 𝑥 for the transaction
𝑇 = 0, undecided
𝑇 < 0, not trusting 𝑥
Conclusion
Summary
Shortcomings:
• To derive a computational model
for risk-trust
• Reliability trust: probability of
success of the transaction
• Decision trust: considering risk
attitude, complete the notion of
trust
• Success of an operation is more
complex than reliability of 𝑥
• Behavior modelling
Thank You