Information Technology Reference
In-Depth Information
Fig. 5.
The average factor of increment for merging for the enumeration and best-of-three meth-
ods using different variances of agents' weights
is between
1
.
5
and
2
.
7
times the original power of the manipulators. Whereas, the
best-of-three method has only minor effects for the manipulators as the average fac-
tors of increment in these tests are below
1
.
3
. Similar trends between the enumeration
and best-of-three methods are observed for the case of Banzhaf index too (See Figure
4
(
b
)
). However, the average factor of increment is lower for the two methods using the
Banzhaf index. On average, merging does not appear to significantly improve power
using the best-of-three method for either the Shapley-Shubik or Banzhaf index, and in
most cases is harmful for the agents. We conclude that since improvement in power over
the best-of-three method can be achieved with only a polynomial amount of work, then,
manipulators are more likely to seek a much improved power gain in merging using the
enumeration-based approach.
Figure 5 provides further comparison of the enumeration and best-of-three meth-
ods for the two indices using different variances of agents' weights. It is clear from
both Figures 5
(
a
)
and 5
(
b
)
that irrespective of the variances in the weights of agents
in the games, the enumeration method is better in all cases. As before, the figures also
show that on average, the best-of-three method does not appear to improve average
