Cybernetics and Systems Analysis, Vol. 34, No. 3, 1998
METHOD FOR MODELING
SOCIAL SYSTEMS
UDC 519.87
T. N. Pomerantseva
Efficient solution of social control problems requires appropriate information support that allows for the complex social interactions and the dependence on external disturbances in control decisions. It is accordingly necessary to develop formal mathematical models for analyzing and modeling the results of decision making. Current studies in this area rely on a number of assumptions. In general, the social environment tends to some balanced state. We assume that this state can be formally described and determined. However, to achieve an adequate description of a social system, we have to allow for numerous nonlinear relationships among its state variables, which are predominantly qualitative in nature. Moreover, the social control model should satisfy some general criteria and conditions so as to ensure adequacy of the formal theory for solving real-life social control problems [1]. Solvability. The value of the model is determined by its practical realizability and its capacity to produce adequate solutions for the relevant practical problems. Completeness of Representation. Accuracy and adequacy of the solution method is obscured by imprecise hypotheses and incomplete initial information. The model should be sufficiently complete to ensure adequate results independently of weak initial data. Deterrn|nacy. Modeling-based decisions should be endowed with good control properties limiting the model dynamics to a certain state that remains unchanged during the given control horizon. Optimizability. The model should allow optimal control by certain criteria; otherwise, the formal model is useless in practice. The area of social control is currently characterized by extensive research that focuses on qualitative modeling of social processes and uses, in particular, the theory of qualitative reasoning [1]. Yet, as shown in [2], spin information models, which in some cases have better computational and expressive properties, may also be used to solve this problem. Spin models satisfy the above-listed criteria. In particular, -- in terms of solvability, they are realizable even in cases when analytical modeling is ruled out because the modeled system has an irregular state space; -- in terms of completeness of the knowledge model, they combine conflicting qualitative views of various experts into a more adequate, self-tuning model; -- determinacy of the model is achieved by simulating a large number of random events and f'mding stable states that in reality correspond to stable paths; -- optimal control involves choosing stable paths with optimal properties, thus avoiding undesirable states and motions. The spin information models proposed in [2] are mainly intended for constructing "local" social control models and for short-term forecasting of social behavior. The construction of such models is not simple because sufficient statistical data are usually unavailable and the available data become rapidly outdated. In practice, expert views and judgments provide the only information base for construction and training of a local social model. To ensure a more efficient use of conflicting expert views, we propose to modify the methods of spin information modeling proposed in [2]. The first stage uses expert views to construct a network G(F, R) of factors and qualitative dependences reflecting relationships and interactions among certain characteristics of the modeled system. The factors F have a def'mite semantic meaning, which is shared by the entire group of experts E participating in modeling. Formally, each facTranslated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 171-173, May-June, 1998. Original article submitted March 30, 1998.
1060-0396/98/3403-0467520.00 ~
Plenum Publishing Corporation
467
/
\ t~
tt Fig. 1
tor is characterized by its spin s(F) E { t , 4' }, which reflects a qualitative change in the factor dynamics. Experts describe their views of the model by sets of cognitive maps, which are graphs ME(F, R), where F are factors and R are factor interconnections of the form r + " t t and r - = t 4'. Each cognitive map is verified to ensure that it satisfies the "triangle rule" (Fig. 1), which is an expression of logical consistency of local expert judgments. The spin model G is a superposition of cognitive maps G = U M e supplied by each expert. In general, G does not have the property of logical consistency, and it becomes impossible to construct deterministic formal models, even qualitative ones. From the point of view of formal theories, the model G is a system of inconsistent differential equations, which in principle is unsolvable. Nevertheless, the model G is not meaningless from the applied point of view, as it reflects objective contradictions in a real application domain. For practical application of the spin model, we propose to use the parameter e = f(ro. ) that takes the values e = 0 if (rij = t t, Fi t t Fj; riy = t 4', F i t J, Fj), and e = Emax = i riyl if these conditions are not satisfied (i.e., the situation is logically inconsistent), The model dynamics are described by a system of nodal equations of the form s(F)" Es(F~ < Es(F, ), where s(F), s(F') are two possible states of F with opposite spins. The spin of a factor is the minimum stun of e-values for the branches entering the given node (the relationships affecting the given factor) in the previous state of the model- Es(F~3(t) = ~,e(rij,t_ 1) = min. The model time is thus discrete, and the state change quantum of the model is equal to a unit spin change in one of the nodes. Examining the sum E = Ee(rij) for the given structure and state of the model G, we obtain the following results: 1) E = 0 (we(rij) = 0): the model is completely consistent and its behavior is describable by a system of ordinary differential equations of the form dFi/dT = j(l~, F k ..... Fro); this state is not necessarily stationary, i.e., we do not necessarily have E = 0 for various initial values of the factors; 2) E > 0 (3e(r~i) > 0)" the model is partially inconsistent and has some nonlinear behavior that depends on its initial states; the goal in this case is to find states with maximum stability characterized by E = min; 3) E > 0 (ve(rij) > 0)" the system is absolutely unstable" this state is observed when the expert judgments used for modeling are completely contradictory; in this case, the model obviously has zero adequacy. The set of stable model states with minimum E forms the model space, where we can determine the family of paths of the modeled system. Switching from one path to another is allowed at the nodal points of the model, which correspond to phase transitions. The proposed model thus has good characteristics and expressive properties for formal description of social systems: ability to reflect objective inconsistencies that prevail in social systems; ability to describe phase transitions with mass changes of integral properties of the modeled system; ability to estimate the stability of the system under nondeterministic external forces of different strength. Further developments in this area may focus on the behavior of the system in an external force field and on proper field properties of the modeled system.
REFERENCES
.
468
G. Brajnik and M. Lines, "Qualitative modeling and simulation of socio-economic phenomena," J. Artif. Soc. Social Simul., 1, No. 1 (1998). T. N. Pomerantseva, Development and Investigation of Decision Support Methods for Control of Complex Social Systems [in Russian], Dissertation, Kiev (1996).
