Grossvariable

Closed or open systems on the macroscopic level turn out to be characterized by relatively few collective macroscopic observable quantities, also denoted here as grossvariables or macrovariables. Examples are pressure, density entropy, energy- and particle-fluxes, correlation functions and further parameters characterizing the macroscopic state or dynamic space-time structure of fields and particles. 

Mean Value Equations for Grossvariables of the Socio-ConHguration... 

These grossvariables should be functions of the C socio-configuration variables Although their number should be much smaller than that of the ai - i-e. Q < C- they should be carefully chosen in order to characterize the global state of the society for the aspect under consideration. 

If the grossvariables are expected to (approximately) obey a closed subdynamics, it is self-consistently plausible that the transition probabilities p i and pj° only depend on Uai via the gross variables Gq. This assumption amounts to a specialized choice of the trend parameters... 

Evidently, only such values n i (t) of the socio-configuration are compatible with given values Gq (t) - or better mean values Gq (t) of the grossvariables at time t - which fulfill... 

The approximate closed equations for grossvariables derived in this section still have a rather complicated structure, since only relatively general assumptions have been used. In special models, however, it may be possible to find alternative and simpler derivations of grossvariable equations. Such an alternative procedure will be developed in Chap. 6 when setting up equations for certain grossvariables of political psychology in interacting societies. 

At such a point quantitative argumentation can be applied The qualities and their intensities are translated into grossvariables of the socio-configuration and of the material situation. Finally, a dynamic model in terms of equations of motion for the grossvariables is tailored which takes the qualitative model mentioned above into account. 

The decisive steps 2) and 3) of the translation into quantified grossvariables and the relation between quantitative and qualitative levels of argumentation will now be considered in more detail. 

The grossvariables of political psychology are not available in a completely evident and explicit form through a direct method of measurement, as is often the case in physics or other natural sciences, so that relevant grossvariables usually have to be defined indirectly and implicitly. Two possible procedures in defining grossvariables for introduction into a model are ... 

Conversely, grossvariables are to some extent implicitly defined by the context of their equations of motion. Arguing anew about the qualitative meaning and the quantitative dynamic behaviour of coupled grossvariables on the basis of their equations builds the qualitative/quantitative feedback level of argumentation mentioned above. 

Let the two macrosocieties be denoted by and 5 2- and are treated symmetrically in so far as the same set of grossvariables for each system is introduced and a symmetry of the general form of the equations of motion with respect to an exchange of the indices 1 and 2 belonging to Sfi and if 2 is assumed. On the other hand, an asymmetry between ifi and if2 will come about in two ways ... 

For our coarse model only three primary grossvariables for each system ifj are assumed ... 

From (6.2) and (6.14) the differential equation for the grossvariable P of political psychology... 

So far, the discussion of the equation of motion (6.28) and of the potentials formally corresponds with that of the equations (2.48) and (2.124) for the opinion formation model in Sect. 2.4. In the presently discussed model, however, Pj is a collective variable of a complex socio-configuration and, more important, the trend parameters <5y, JCy depend on further dynamic grossvariables. Hence the shape of the potentials (6.29) will vary during the motion of all grossvariables. The equations (6.28) then describe the motion of Pj in terms of time dependent potentials, whose shape is determined by the other equations of motion not yet discussed. Thus the form of the dependence of the trend parameters (5y, Kj on the other grossvariables should now be considered. 

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