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of view. More precisely, we can run the debate with identity as the
B
function and as
success rates for convictions. It is assumed that 7 competitive classification algorithms
are available and moreover that the correct solution is supposed to be alternative
+1
.
As said above, the initial probability of the 7 algorithms to choose alternative +1 are:
0.6, 0.7, 0.8, 0.8, 0.6, 0.7, and 0.6. The debate stops when all classification algorithms
are in agreement. We will assume then that their answers are independent random vari-
ables and that 10,000 cases are studied by each agent. For each case, the agent's answer
is inferred according to his probability of being correct.
Next, for each of these 10,000 cases, we compute the group decision according to 3
methods:
-
the choice with a majority vote procedure,
-
the choice with a weighted majority vote procedure,
-
the decision derived using our debate model.
While simple and weighted majorities yield the correct answer at a rate of 86
%
, our
method produced a 94
%
rate. Hence, the aggregation by a debate significantly increases
success rate.
In order to verify this good result, we tried using different situations of the same
model. For 7 agents, several values for the probability of making the right decision were
randomly generated, and the 3 corresponding rates computed (results are presented in
Figure 8). In this figure, both the weighted voting rate and our debate output vs. this
rate are plotted. Note that the same rate for the simple vote can be obtained with very
different sets of probabilities. The debate always yields a better rate, although its pref-
erences change according to the specific probability profile. The weighted vote success
rate is quite close to that of the simple vote, except for very unique probability sets
where several agents (algorithms) perform much better than the others.
5
Conclusions and Outlook
The state equations derived in this paper allow simulating macroscopically the outcome
of a debate according to the initial inclinations of agents and the social influences taking
place within the group (whereby the influence function is a priori known). The deliber-
ation outcome depends not only on the order in which the agents intervene in the debate
to explain their opinions, but also on the influence an agent is able to exert on a social
network.
The model formalism proposed in this paper is close to the one used in control theory
to model the dynamic behavior of technical systems. Guiding a debate might then be
seen as a control problem, whose aim could, for example, be how to reach a consensus
as quickly as possible or how to reinforce one alternative over the other, etc.
A debate is thus seen as a continuous dynamic system: a state equation representa-
tion has been preferred to the multicriteria decision-making framework in [7] given
that time explicitly appears in the revision of convictions. The model semantic has
also been inspired from the game theory concepts proposed in [3]: influence and deci-
sional power in a social network. In our dynamic extension, decisional power is a time-
varying variable itself and may be used as the actuator signal in the debate control loop.
