  An opinion leader-follower model (OLF) is a two-action collective
decision-making model for societies, in which three kinds of actors are
considered: "opinion leaders", "followers", and "independent actors". In OLF
the initial decision of the followers can be modified by the influence of the
leaders. Once the final decision is set, a collective decision is taken
applying the simple majority rule. We consider a generalization of \OLF, the
gOLF models which allow collective decision taken by rules different from the
single majority rule. Inspired in this model we define two new families of
collective decision-making models associated with cooperative influence games.
We define the "oblivious" and "non-oblivious" influence models. We show that
gOLF models are non-oblivious influence models played on a two layered
bipartite influence graph.
  Together with OLF models, the Satisfaction measure was introduced and
studied. We analyze the computational complexity of the satisfaction measure
for gOLF models and the other collective decision-making models introduced in
the paper. We show that computing the satisfaction measure is #P-hard in all
the considered models except for the basic OLF inwhich the complexity remains
open. On the other hand, we provide two subfamilies of decision models in which
the satisfaction measure can be computed in polynomial time.
  Exploiting the relationship with influence games, we can relate the
satisfaction measure with the Rae index of an associated simple game. The Rae
index is closely related to the Banzhaf value. Thus, our results also extend
the families of simple games for which computing the Rae index and the Banzhaf
value is computationally hard.
