Information Technology Reference
In-Depth Information
In our model, the choice of an experiment is derived from its effectiveness, as
perceived by an agent, in discriminating between hypotheses. This choice is gov-
erned by the agent's initial confidence E
n
−
1
(H). We represent an agent's view of an
experiment by the entropy, represented for each experiment as:
R
e
m
H
m
{
Entropy(e)
=
E
n-1
(R
e
/
H
m
)
}∗
Log2(E
n
−
1
(R
e
/
H
m
)
}
This equation describes the confidence of a result given a hypothesis as perceived by
an agent, i.e. the choice of experiment is affected by an agent's bias. The experiment
with the lowest entropy is the experiment most likely to be chosen by the agent in
that it will have the clearest and most decisive results for supporting or negating each
of the hypotheses in the agent's confidence-profile. Thus, the choice reflects both a
property of the experiment and a property of the experimenter.
Even so, the experiment with the lowest entropy is 'most likely'to be selected. This
is because the actions of agents are governed, Monte Carlo fashion, by a probability
distribution based upon belief, and because we apply game theory in the decision
procedure (Luce and Raiffa
1957
). Suppose in our simple example we choose to
'ask' for a head or a tail. Then allowing for mishearing, we could write a table of
probabilities for H1 thus:
Hypothesis: the coin is good—H1
Head
Tail
No response
Exp1:
Ask for a Head
0.9
0.05
0.05
Exp2:
Ask for a Tail
0.05
0.9
0.05
But even with mishearings for H2 we would have:
Hypothesis:
the
coin
is
double
Head
Tail
No response
headed—H2
Exp1:
Ask for a Head
0.9
0.00
0.1
Exp2:
Ask for a Tail
0.1
0.0
0.9
The initial beliefs of the agent about the different hypotheses is as before:
Agent
E
n
−
1
(H1)
0.8
E
n
−
1
(H2)
0.2
Total
1.0
The experimental setup (here, calling for a coin to be tossed) is defined by a table of
real numbers. To obtain a vector of expectations we multiply an agent's
confidence
