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1
is associated with an erroneous decision. This situation
could occur in classification problems when the agents are competitive classification
algorithms.
The agents are expected to provide the correct answer most of the time, but they
typically disagree on individual cases. One common solution is to employ a voting
process in order to yield a group decision, i.e. let
d
1
,
d
2
...
d
n
be the respective decision
of the various agents, then the group decision is written as:
−
the right decision, while
Fig. 8.
Simulation-weighted vote and debate
⎧
⎨
n
1
if
d
i
>
0
⎩
i
=1
−
1
else
For example, let the agents be 7 different classification algorithms whose success rates
equal respectively: 0.6, 0.7, 0.8, 0.8, 0.6, 0.7, and 0.6. The group success rate according
to a normal vote would thus be 0.86. A better aggregation process will achieve a higher
success rate.
Thefirstideahereistouseaweightedvote,i.e.let
α
1
,...α
n
∈
[0
,
1]
n
:
⎧
⎨
n
1
if
α
i
d
i
>
0
⎩
i
=1
−
1
else
One possible set of weights is the individual success rate of each agent; however, it is
possible to compute the Shapley-Shubik power index [9], and our example delivers a
value of
1
7
for each agent. This is exactly the same value achieved in a normal vote.
Since the weights do not differ considerably for a small number of agents, the sign of
the weighted sum is the same as that produced during the normal vote. This finding
indicates that even if some agents possess a more powerful vote, the final decision is
always shared by at least 4 agents.
If we were to use our debate model as the voting process, such an outcome would
not occur. The least agents also happen to be those who most readily change their point
