Information Technology Reference
In-Depth Information
Global level
(macro)
group preferences
Intermediate level
(meso)
conditional preferences
Local level
(micro)
individual preferences
Fig. 2.
Flow of social influence
The group welfare function provides a complete
ex post
description of the relation-
ships between the members of a multiagent system as characterized by their
ex ante
conditional utilities. Unless the members of the system are praxeologically indepen-
dent, the
ex post
utility is not simply an aggregation of individual utilities, as is the
case with classical social choice theory. Rather, it constitutes a meso to macro to micro
propagation of preferences: from the intermediate, or meso, level, derived from local
influences between the agents in the form of conditional preferences, up to the global,
or macro, level and down to the individual, or micro, level, as illustrated in Figure 2.
We define the
maximum group welfare
solution as
(
a
1
,...,a
n
) = argmax
a
∈
A
w
X
1
···
X
n
(
a
1
,...,a
n
)
.
(26)
Also, the
maximum individual welfare
solution is
a
i
=argmax
a
i
∈A
i
w
X
i
(
a
i
)
.
(27)
If
a
i
=
a
i
for all
i
, the action profile is a
consensus
choice. In gen-
eral, however, a consensus will not obtain, and negotiation may be required to reach a
compromise solution.
The existence of group and individual welfare functions provides a rational basis for
meaningful negotiations; namely, that any compromise solution must at least provide
each agent with its security level; that is, the maximum guaranteed benefit it could
receive regardless of the decisions that others might make. The security level for
X
i
is
∈{
1
,...,n
}
s
X
i
=max
a
i
min
∼
a
i
U
X
1
···
X
n
(
a
1
,...,
a
n
)
.
(28)
∼
a
i
In addition to individual benefit, we must also consider benefit to the group. Although
a security level, per se, for the group cannot be defined in terms of a guaranteed bene-
fit (after all, the group, as a single entity, does not actually make a choice), a possible
rationale is that the benefit to the group it should never be less than the smallest guaran-
teed benefit to the individuals. This approach is consistent with the principles of justice
espoused by [14], who argues, essentially, that a society as a whole cannot be better
off than its least advantaged member. Accordingly, let us define a security level for the
group as
s
X
1
···
X
n
=min
i
{
/n
, where we divide by the number of agents since the
utility for the group involves
n
players.
s
X
i
}