Analysing the Relationship
between Risk and Trust
Audun Jøsang and Stéphzne Lo Presti
2nd International Conference on Trust Management
Oxford, UK, March 2004, pp. 135-145
Roadmap
• Risk-Trust in Literature
• Measuring Risk-Trust
• Decision and Risk
• Balancing Trust and Risk
• Conclusion
Risk-Trust in Literature
subjectivity
• Concept of Trust
uncertainty
• 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, consequences measurable
• Concept of Decision Making
• Both trust and risk affect decision making
risk
Risk-Trust in Literature
Falcone and Castelfranchi (2001)
• having high trust in a person is not necessarily enough to decide to enter into a
situation of dependence on that person.
• it is possible that the value of the damage per se (in case of failure) is too high to
choose a given decision branch, and this independently either from the
probability of the failure (even if it is very low) or from the possible payoff (even if
it is very high)
Risk-Trust in Literature
Manchala (1998)
• defining risk-trust decision matrices based on (transaction history, cost) ->
decision making whether to transact with a particular party
Measuring Risk-Trust : Decision and Risk
• Expected Monetary Value (EV)
• 𝐸𝑉 = 𝐼
• Expected Utility (EU)
𝑛
𝑖=1 𝑝𝑖 𝐺𝑖
• 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
• 𝑢(⋅): non-linear utility function of monetary
value (for propensity toward risk)
• 𝑢 𝐼𝐺 < 𝐼𝐺: risk averse (u is concave)
• 𝑢 𝐼𝐺 = 𝐼𝐺: risk-neutral
• 𝑢 𝐼𝐺 > 𝐼𝐺: risk seeking
• Risk-Neutral Case
𝐸𝑉 = 𝐸𝑈 = 𝐼 ⋅ 𝐸𝐺
(𝐸𝐺 =
𝑛
𝑖=1 𝑝𝑖 𝐺𝑖
𝐼𝐺𝑖
: Expected Gain)
Measuring Risk-Trust : Decision and Risk
Decision making based on 𝐸𝐺
• 𝐸𝐺 = 𝑝𝐺𝑠 + 1 − 𝑝 𝐺𝑓 = 𝑝 𝐺𝑠 − 𝐺𝑓 + 𝐺𝑓
• 𝑝: probability of successful transaction
• 𝐺𝑠 : gain factor to a successful transaction 𝐺𝑠 ∈ [0, ∞]
• 𝐺𝑓 : gain factor (actually loss factor) to a failed transaction 𝐺𝑓 ∈ [−1, 0]
• Left graph is for 𝐺𝑓 = −1
• If 𝐸𝐺 > 0 then
a rational, risk-neutral agent
will decide to invest
• Counter example: lottery’s
𝐸𝐺 < 0, but most people still invest
Measuring Risk-Trust : Decision and Risk
Decision making based on relationships between
gain factor, success probability, and capital, i.e.,
based on the (𝐺𝑠 , 𝑝, 𝐹𝐶 ) decision plane
𝜆
𝐺𝑠
• Left graph is for 𝐹𝐶 = 𝑝 reflecting risk attitude
with 𝐺𝑓 = −1 and 𝜆 = 10000
• 𝐹𝐶 varies in the same direction of 𝐺𝑠 and 𝑝
• 𝐹𝐶 : fraction of the total capital
• 𝐼 = 𝐹𝐶 𝐶
• 𝐶: the total capital
• 𝜆: factor moderating the influence of 𝐺𝑠 , or risk attitude
• Low 𝜆 – risk-taking (pushing the decision plane up)
• high 𝜆 – risk-aversion (pushing the decision plane down)
• Invest if a transaction data point (𝐺𝑠 , 𝑝, 𝐹𝐶 ) lies below the decision surface; otherwise, reject
Measuring Risk-Trust : Balancing Trust - Risk
• Reliability Trust: defined as the trusting party’s probability estimate 𝑝
of success of the transaction
• The outcome of the transaction depends on somebody or something and that
the relying party (trustor) is uncertain about the outcome of the transaction.
• Paraphrase 𝒑: the reliability trust for producing a successful outcome
Measuring Risk-Trust : Balancing Trust - Risk
• Decision Trust: Defined as the normalized difference in the range of [-1, 1]
between the reliability trust (p) and the cut-off probability (𝑝𝐷 ) on an
agent’s decision surface, i.e.,
𝑝−𝑝𝐷
𝑝𝐷
𝑇=
0
𝑝−𝑝𝐷
1−𝑝𝐷
𝑝 < 𝑝𝐷
𝑝 = 𝑝𝐷
𝑝 > 𝑝𝐷
𝑇 ∈ [−1,1]
• 𝐷: the (𝐺𝑠 , 𝑝, 𝐹𝐶 ) decision plane
• 𝑝: reliability trust of producing a successful outcome, given 𝐺𝑠 and 𝐹𝐶 of a transaction
• 𝑝𝐷 : cut-off probability on 𝐷 for the same 𝐺𝑠 and 𝐹𝐶
• (0,-1), (𝑝𝐷 ,0), and (1,1): three extreme decision trust values T=−1, 0, 1 when p=0, 𝑝𝐷 , 1,
respectively.
Measuring Risk-Trust : Balancing Trust - Risk
• Decision Trust
• Decision trust depends on the distance between 𝑝 (X coordinate) and 𝑝𝐷
(labeled with a solid dot in the graph below)
• 𝑇 > 0, trusting 𝑥 for the transaction
• 𝑇 = 0, undecided
• 𝑇 < 0, not trusting 𝑥
Conclusions
• A trust computational model taking risk-trust relationship into
consideration for decision making
• Reliability trust: The probability of success of a transaction in the
range of [0, 1]
• Decision trust: The normalized difference in the range of [-1, 1]
between the reliability trust (𝑝) and the cut-off probability (𝑝𝐷 ) on an
agent’s risk-attitude based decision surface defined by the
relationships between gain factor (𝐺𝑠 ), reliability trust (𝑝), and
capital of investment (𝐹𝐶 ).