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One of the conclusions drawn in [3] concerns the integration of dynamic aspects
into the influence model. The authors' framework is indeed a decision-making process
activated after a single step of mutual influence. In reality, such mutual influence does
not necessarily stop after just one step but may actually become iterative. This paper
proposes a possible extension of the results presented in [3] for use in the dynamic
case. The evolution of agents' beliefs throughout the debate either change or reinforce
the agents' convictions relative to their initial preference. Intuitively, as well as from
other standpoints, an agent's social influence depends on the relative strength of other
agents' convictions. The idea for our model therefore is to define influence as a time-
dependent variable.
In [7], the concepts of influence and conviction during the simulation of a debate are
introduced. This article will follow up on the prior work proposed in [1]. Our main im-
provement here over previous efforts relates to the fact that in [7], coalitions of agents
were modeled using capacities, and the change in conviction during a debate was com-
puted with a symmetric Choquet integral, which is in fact an aggregation function typi-
cally introduced in multicriteria decision making [2]. The main drawback in [7] pertains
to a lack of semantic justifications.
Reference [3] provides a formal framework to define the notion of influence, while
[7] introduces the revision equations relative to agents' convictions and preferences.
Moreover, [6] suggests a cybernetic interpretation to merge both of these models. The
present paper is intended as a continuation of [7], with [6] also used for guidance.
The main contribution of this paper is to propose the state equations of the cybernetic
interpretation in order to describe the way agents' convictions may evolve over time.
To achieve this goal, a capacity will be introduced to model the relative importance of
agents in the debate; such a capacity is based on the decisional power of agents using
the generalized Hoede-Bakker index [3,5]. Consequently, a number of simulations will
be proposed to illustrate the collective decision-making process.
The paper will be organized as follows. Section 2 will briefly recall the main con-
cepts of the models presented in [7] and [3]. From this formal framework, Section 3
will establish the state equations that serve to model the dynamic relationships between
convictions and influences when a speaker-agent / listener-agent pair is isolated. Fol-
lowing a presentation of preference changes, Section 4 will offer a few illustrations.
Lastly, Section 5 will provide the conclusion and outlook for future research.
2
Concepts and Notations
2.1
Notion of Influence in a Debate
The assumption behind our model is that an agent's influence is correlated with his
capacity to alter the group decision. It addresses the concept of the ”weight” of an
agent's choice in a collective voting procedure. This ”weight” parameter cannot be static
since it needs to evolve with agent preferences, which in turn allow for the formation of
certain coalitions that are more likely than others.
It is common experience that during the discussion phase, some agents will change
their initial opinions. The reasons for this change, in assuming that it is not a random
occurrence, may be of different types. The most natural reason is that they have been
