State 3: The agent is known and trusted
6.3 Example Principles and Rules
6.3.1 Trust is Self-Reinforcing
“Trust, once established in some degree, is often self-reinforcing because individuals have stronger tendencies to confirm their prior beliefs than to disprove them.” (Hinde & Groebel, 1991a, Page 187). The converse is true, as below a certain trust, individuals tend to confirm their suspicions of others (Golembiewski & McConkie, 1975). This gives us a rule of two parts, based on Golembiewski and McConkie’s work, which attempts to correlate trusting and risking as self-heightening spirals. The first part of the rule is based on the idea that, if trust between two agents is initially above some threshold value (perhaps 0.00, but perhaps some other value, dependent on the agents concerned), which we callω xfor agentx(it is therefore agent-subjective), then
the trust between those two agents will not decrease below that threshold. This is because, for each member of the interaction, they will tend to look for the best in the behaviour of the other, and will tend to get it, since above the threshold, each will tend to cooperate with the other. Thus trust will increase, or at least stay constant.
The converse is true, since, if both agents trust each other below a certain threshold value, Ω (ω6= Ω), will tend not to cooperate with each other whatever the situation, thus reinforcing the other’s opinion about them as non-cooperative and unhelpful. Trust, then, is self-reinforcing. The only way out of this trap is to take a risk and co- operate (Swinth, 1967; Golembiewski & McConkie, 1975), but the further and further down the value for trust goes, the harder it becomes to justify taking that risk.
We can represent this rule using the formalism. The first part is that trust is self-heightening. Consider two agents,x and y.
If:
(Tx(y)t > ωx)∧(Ty(x)t> ωy)
Then:
(Tx(y)t+a ≥Tx(y)t)∧(Ty(x)t+a ≥Ty(x)t)
Informally, this says that if x trusts y more than a threshold value, and y trusts x more than a threshold value, then the amount of trust they have in each other at a later time will be greater than or equal to the amount of trust they have in each other at this time. The second part of the rules is that trust is self-reinforcing downwards also.
If:
Then:
(Tx(y)t+a ≤Tx(y)t)∧(Ty(x)t+a ≤Ty(x)t)
This is the converse of that given above. Note that ω and Ω are not necessarily the same value for each agent, neither is ω x necessarily equal to ωy. Assuming a
pessimistic point of view for a moment, we could suggest that in the second case, the following would happen:
(Tx(y)t+a < Tx(y)t)∧(Ty(x)t+a < Ty(x)t)
In other words, the trust would inevitably decrease. This is, however, unnecessary and constrains the modification formulæ given in section 4.9.2 too much. We leave the final values to those formulæ. It is sufficient to say that, when both agents do not trust each other enough, they are unlikely to at any time. A final note: for any agent x to be rational, Ω x ≤ ωx, not the other way around. This notation should
ideally contain consideration of the agent concerned, since the thresholds may well be different for different agents (i.e., perhaps we should use ω x(y) instead).
The above considerations beg a question as to how trust behaves when the value for agents is within (Ω, ω), i.e., when the trust value is not above or below the respective threshold values for self-reinforcement. We suggest that such a state is not unlike starting points for relationships, and for interactions with agents not known, or not known too well (see Boon and Holmes (1991) for a discussion of the former). In the former, the trust will tend to build up, for example as with romantic love. To build trust, risks have to be taken (Swinth, 1967). Thus, the agent who is more disposed to take risks is more likely to build trusting relationships (Swinth, 1967; Deutsch, 1962). In the formalism, this amounts to the agent who has a higher situational trust in others, since this tends to offset high risks in the cooperation threshold. In order to build trust, then, we have to trust, both our initial judgements, and other agents. An example may help. Considerx and y who have never met (¬K x(y) and¬Ky(x)). If x is trusting, he may assign a value equal to T x, which is likely to be high in any
case (x is trusting) to the measure T x(y). This being the case, it is likely that the
resultant situational trust will exceed the cooperation threshold. Take the example for yconsidering xin the previous chapter, for instance. If this is so,xwill cooperate with y, and y will increase trust inx, and so on. Conversely, if T x is very low, the chances
of cooperation are lower, thus the chances are that the resultant trust between the two will drop rather than rise. This simple example may help to make the situation more clear. In between values of Ω andω then, anything can happen.
6.3.2 An Increase in Trust Increases Societal Knowledge
Considering a society where information is of value, such as our own, the societal knowledge can be characterised by the amount of knowledge that the members of the society know collectively (i.e., that the majority of members of that society know). It follows that, if the only way information is disseminated is for agents to share it, that when agents trust each other more they will share more information, thus the amount of disseminated knowledge in the society will increase. The converse does not hold — if suddenly all agents stopped sharing information, the amount of societal knowledge would not decrease as suddenly, rather it would stay static, perhaps stagnating. It
would not, however, increase. See Bok (1978) for a discussion. Briefly, the following may hold:
K(S) = X
a∈S
K(a)
Thus the total knowledge in society is a summation of the knowledge of all agents in that society. If agents share information with others, this will increase, and if not, it will remain, at best, static:
∀a, b∈S: IfTa(b)⇒Will share knowledge a(b)t
And so:
K(b)t+1 > K(b)t
In other words, conditional onbnot knowing the informationatold her before she was told, her knowledge increases, and so does that of society. This is a simple exposition of knowledge, and does not take into account the large amount of literature on the subject. Nevertheless, it does show the worth of the formalism in describing such occurrences.
6.3.3 Dissemination of Trust Knowledge
What happens if three agents are in a situation where one of them knows only one of the others, but wants to consider the third? Formally, the situation can be described as follows, so as to avoid ambiguity. We consider agents x, y, andz. Agentx knows both y and z: Kx(y) ∧ Kx(z), the same applies to y: K y(x) ∧ Ky(z). However,z
knows onlyy: ¬Kz(x) ∧ Kz(y) holds. The situation involvesz having to considerx. Because z knows (and by definition has a trust value for) y, z can ask y for help in this matter (and assumingygives it andz does ask for it). The rule we advance here concerns how muchz will trustx, the value of which will be dependent on how much z trustsy, and how much y trustsx. The following rule will hold if z is rational:
¬Kz(x)t ∧ Kz(y)t ∧ Ky(x)t →
Kz(x)t+a ∧ (Tz(x)t+a ≤Ty(x)t) ∧(Tz(x)t+a ≤Tz(y)t)
Thus,z will not trustx any more thanydid, but also, because the amount of trustz will have in xis mediated by the trustz has in y, the information giver, the resultant trust will be no greater than the amountz trustsyin the first place. A simple formula for determining trust in this kind of example is as follows:
Tz(x) = Ty(x) × Tz(y) (6.1)
Naturally, this can be extended an arbitrary number of times, forming a kind of ‘trust network.’ This brings about questions relating to how one measure of trust compares with another for another agent. Clearly, should I say I trusted someone 50%, and my friend said the same, we may not both mean the same thing — my 50% worth may mean more to me than my friend’s. This perhaps highlights one of the problems in the use of values. A discussion of why values are used can be found in chapter 2.