In this paper we extend some recent results on an operatorial approach to the
description of alliances between political parties interacting among themselves
and with a basin of electors. In particular, we propose and compare three
different models, deducing the dynamics of their related {\em decision
functions}, i.e. the attitude of each party to form or not an alliance. In the
first model the interactions between each party and their electors are
considered. We show that these interactions drive the decision functions
towards certain asymptotic values depending on the electors only: this is the
{\em perfect party}, which behaves following the electors' suggestions. The
second model is an extension of the first one in which we include a rule
which modifies the status of the electors, and of the decision functions as a
consequence, at some specific time step. In the third model we neglect the
interactions with the electors while we consider cubic and quartic interactions
between the parties and we show that we get (slightly oscillating) asymptotic
values for the decision functions, close to their initial values. This is the
{\em real party}, which does not listen to the electors. Several explicit
situations are considered in details and numerical results are also shown.Comment: To appear in Physica
