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Our agents do not update their beliefs in a simple Bayesian fashion. In the most
general terms, a Bayesian agent moves through time and evidence having a set
of beliefs. Each time it learns a new fact, the agent revises its degree of belief in
each hypothesis by adapting to the new fact. For a Bayesian agent, 'confirmation'
is analogous to a new fact making a hypothesis more probable than it was before;
'disconfirmation' is analogous to new evidence making a hypothesis less probable
than before. Close analysis of scientists' behaviour suggests that they sometimes
behave as Bayesians (Gooding and Addis
2004
), however, recent evidence shows
that this is not the only factor at work.
6.9
Choosing Actions
In what we have modelled, each agent perceives the potential outcome of an experi-
ment differently because each has a different confidence profile, just as in real life.
It follows from our definition of an experiment that each agent perceives a subtly
different experiment being performed. The result of the multiplication (belief pro-
file
×
result probabilities) is then used to modify each agent's a priori confidence
value for each hypothesis. The degree of modification to the belief profile depends
upon the agent's flexibility (see Sect. 6.2.1). A similar process occurs when there
is a decision to consult another agent rather than experiment. The cycle of learning
through consultation is similar to that for an experiment, except that there is no need
to involve Bayes' Rule because the confidence values in the profiles of consulters
and consultees are already expressed in the same terms; that is belief or perceived
probability.
The Peircian, pragmatic notion of belief implies that the numerical confidence
value attached to each hypothesis by an agent represents the probability, given avail-
able each state of affairs, of its performing an action. Under certain conditions Game
Theory favours a 'mixed strategy' approach where a mix of actions are tried ac-
cording to some probability distribution (Luce and Raffia 1957, pp. 67-70). We
use an agent's belief profile to calculate personalised
entropies
for each experiment
(see Evaluating Actions). The decision mechanism deploys this profile as a set of
probabilities to act. We will illustrate this using the simple coin experiment.
Indifference represents the expected probability of an event (as implied by a
hypothesis). The gain for choosing 'correctly' would be increased confidence in
one's view of the world. If we assume the expected loss for acting on a wrong belief
is one unit and expected gain is zero then we can express the payoff in a two person
zero sum matrix (Table
6.1
,
6.2
).
•
h
is the expected 'belief' that some hypothesis represents a particular state of
affairs. It does not matter which hypothesis, since this represents an average.
−
−
−
=
−
•
I
h
).
The equations in Table
6.1
can be generalized for any number of hypotheses and
actions.
Expected Gain in Exp1 is I
h
* (0)
(1
I
h
)*(
1)
(1
