Operators, Heisenberg dynamics and politics

In a series of recent papers, [1]-[4], a possible way to describe interactions between political parties has been proposed in more and more refined versions and analyzed. Each version describes a decision making procedure, deducing the time evolution of three so-called decision functions (DFs), one for each party considered in our political system. These functions describe the interest of each party to form or not an alliance with some other party. In particular, in [1, 2] these decisions are driven by the interaction of each party with the other parties, with their own electors, and with a set of undecided voters (i.e. people who have not yet decided for which party to vote (if at all they decide to vote!)). The approach adopted uses an operatorial framework described, in its general version, in [5], in which the DFs are suitable mean values of certain number operators associated to the parties. The dynamics is driven by a given selfadjoint Hamiltonian operator whose analytical expression implements the various interactions between the different actors of the system. In [3] we extend the model by admitting more possible interactions, for instance those between a given party and the electors of a different party, which were not included in the models proposed in [1, 2]. In [4] no set of electors is considered at all, and we rather focus on the interactions between the three parties, interactions which are taken to be of different forms. The interesting aspect of this approach is that, since the system lives now in some finite dimensional Hilbert space, an exact analytical solution can always be deduced. The aim of my contribution is to review the general ideas behind the cited papers, and to show in some details how these ideas works concretely in the analysis of political alliances. In particular, we will describe one of the most general model proposed so far, which describes a set of parties interacting among them, with all the electors (including those of the other parties) and with the undecided voters. The kind of interaction that we will adopt here is quadratic, since this gives rise to exactly solvable equations of motion. Hence, paying the price of simplifying the possible interactions between the actors of our game, we are able to find analytic solutions for the DFs. We will also describe a recent idea used in the context of the so-called game of life, quite efficient if we need to introduce in the description of some macroscopic system a set of rules which cannot be described by any Hamiltonian dynamics, [6].