Socio-Cognitive Model of Trust: Quantitative Aspects - Trust Theory: A Socio-Cognitive and Computational Model - page 102

H perceived

DoT XY τ

σ 1

H

0

H max

Figure 3.6 Degree of Trust and Hazard Threshold: the case of the Delegation Branch. (Reproduced
with kind permission of Springer Science+Business Media C

2001)

for decision. However, we believe that this is not enough. A specific risk policy seems necessary
for the trust decision and bet; and we should aim to capture this aspect explicitly.
The equation (3.4) - that basically follows classical decision theory - introduces the degree
of trust instead of a simple probability factor. In this way, it permits one to evaluate when to
delegate rather than to do it herself in a rigid, rational way. The importance of this equation
is to establish what decision branch is the best on the basis of both the relative (success and
failure) utilities for each branch and the probability (trust based) of each of them. In this
equation no factor can play a role independently from the others. Unfortunately, in several
situations and contexts, not just for the human decision makers but - we think - also for good
artificial decision makers, it is important to consider the absolute values of some parameter
independently from the values of the others. This fact suggests that some saturation-based
mechanism, or threshold, by which to influence the decision, needs to be introduced.
For example, 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 is independent either from the probability of
the failure (even if it is very low) or from the possible payoff (even if it is very high). In other
words, that danger might seem to the agent an intolerable risk. In this paragraph we analyze
(just in a qualitative way) different possible threshold factors that must play an additional role
when choosing between alternatives like in Figure 3.5.
First, let us assume that each choice implies a given failure probability as perceived by X
(and let's call this: 'hazard' or 'danger'), and a given 'threat' or 'damage': i.e. a negative utility
due to both the failure (the cost of a wasted activity and a missed reward) and the possible
additional damages. 13
Second, we assume that X is disposed to accept a maximum hazard ( Hmax ) in its choices,
in a given domain and situation. In other words, there is a 'hazard' threshold over which X is
not disposed to pursue that choice .
We are considering the case of delegation branch ( DoT XY τ , U(X) d − , U(X) d + ), but the same
concepts are valid in the case of X 's performance (substituting DoT XX τ , U(X) p − , U(X) p + ). In
Figure 3.6 we have:

H perceived is the failure hazard perceived by X ;
H max is the maximum failure hazard acceptable by X ;
σ H is the hazard threshold.

13 Thus here we will use the term 'risk' as the result of the entity of losses (damage or threat) and of its probability
(hazard or danger). Risk theory (Kaplan and Garrik, 1980) calculates the risk as the product of uncertainty (subjective
probability) and damage; other authors propose - for the objective risk - the product of frequency and magnitude
of the danger. We are interested in the subjective dimension, so risk should be in our terminology hazard ∗ damage.
(Common sense would prefer to call 'risk' the probability, and 'danger' the global result of probability and damage).