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A Time-Varying Model to Simulate a Collective
Decisional Problem
A. Imoussaten
1
, J. Montmain
1
,A.Rico
2
,andF.Rico
2
1
LGI2P, Ecole des mines d'Ales, Site EERIE Parc Scientifique G. Bresse
30035 Nımes cedex, France
2
ERIC, Universite Claude Bernard Lyon 1, 43 bld Du 11 novembre
69100 Villeurbanne, France
{
abdelhak.imoussaten,jacky.montmain
}
@mines-ales.fr,
{
agnes.rico,fabien.rico
}
@univ-lyon1.fr
Abstract.
A group of agents have to decide between two alternatives. At the
begining each actor have a preference and a conviction about this preference.
During the debate the conviction and the preference of each agent can change
under the involved social influences.
The theoretical model of this paper is presented in [7], and the influence model
is the one presented in [3]. The aims is to present a new dynamical model for
collective decisional problems. Moreover the presented model offers additional
perspectives for purposes of controlling the debate.
Keywords.
Debate, Influence, Decisional power, Choquet integral, Control, Col-
lective decision, Social network.
1
Introduction
A group of agents is faced with a collective decision; in response, a debate has been
organized to identify which alternative appears to be the most relevant following a de-
liberation. This study will be limited to the binary, albeit common, situation involving
two options denoted
+1
and
−
1
. It is assumed that each agent has an inclination to
choose one of the alternatives
+1
and
1
, though due to the influence of other agents
this inclination may differ from the agent's actual decision [3]. In general terms, it can
be considered that each time a speaker intervenes in the debate, agents may change
their preference due to social influences taking place within the group. Once agents'
preferences reach a point of no longer changing, then the deliberation process ends and
a group decision is made. The aim of this debate is for every agent to hear the argu-
ments of all other agents by the end of the deliberation process and then to make a final
decision based on full knowledge of the facts.
This deliberation is viewed as a dynamic process with its own dynamics and where
agents' beliefs and preferences evolve as arguments are exchanged. The deliberation
outcome thus depends both on the order in which agents intervene in the debate to
explain their opinion and on the influence a given agent may exert on a social network.
In this context, social influence is related to the statistical notion of the decisional
power held by an individual within a social network, as proposed in [5] and [3].
−
