توازن تاثیر-متقاطع: استفاده از سیستم های اثر متقابل زوج و چند ارزشی شبکه های کافمن به تجزیه و تحلیل سیستم های چند رشته ای

Cross-impact analysis is the name for a familiar method for multidisciplinary systems analysis in social sciences and management sciences, especially in technology foresight, technology assessment and scenario planning. A recently proposed form of cross-impact analysis, CIB, may be of interest for physicists, sociophysicists and complex network researchers because the CIB concept reveals considerable relations to some concepts of these research fields. This article describes the basics of CIB analysis framework, its applications in the social sciences, and its relations to the equilibrium points of pair interaction systems, random graphs, and generalized Kauffman nets. Therefore CIB can be seen as a merger of concepts originating in utterly different scientific fields. This may prove to be fruitful for both sides: For sociophysicists as an example of the application of complex network concepts in the social sciences and for cross-impact practitioners as a source of theoretical insights in the background of their tool.

The application of mathematical simulation methods in a social science context is fraught with difficulty. Probably the most critical aspect is that essential knowledge about economic, technological, social, and political systems and their interdependence is often restricted to qualitative insights and implicit mental models produced by experts. On the other hand, there is clearly a need for a suitable mathematical approach, because the state of extreme interdependence inside and between these systems frequently excludes the possibility of intuitive systemic understanding. In the past, several techniques have been developed to meet the needs of interdependence analysis under the special conditions of multidisciplinary systems that include social systems. One of the most popular is a group of techniques denoted as cross-impact analysis. In these techniques, expert judgements about the interdependence of the main system variables are collected in a matrix scheme, and a more or less heuristic evaluation procedure is used to compute scenarios of probable system behaviour. Section 2 provides a short overview of the basics of cross-impact analysis. Cross-impact analysis achieved considerable popularity among those concerned with projecting and analysing scenarios to do with political, economic, technological, or social change. However, the method has also been the focus of criticism. One major criticism was based on the fact that over the decades cross-impact research did not succeed in constructing a clear theoretical foundation for the different evaluation procedures used by this method. This begs the question whether the results of cross-impact analysis contain arbitrariness to an unknown degree. In this context it should be noted that a recently proposed cross-impact method (cross-impact balance analysis, in short CIB analysis, cf. Section 3), shows considerable affinity with various mathematical objects well known in mathematical systems theory, physics, complexity research, and theoretical biology. The main purpose of this paper is to make the method known to physicists and sociophysicists because it can be understood as a fruitful application of theoretical concepts to social sciences and management sciences. It will be shown in Section 4 that cross-impact data can be related to generalized forces, and the solutions of a CIB matrix can be associated with equilibrium states of a pair interaction system. Furthermore, CIB can be understood as an automata network with close links to well known automata net classes, such as INCAs (inhomogeneous cellular automata) and Boolean (Kauffman) nets (cf. Section 5).

In this paper the cross-impact balance analysis (CIB analysis), a method for developing future scenarios by analysing qualitative expert statements on the interdependences of multidisciplinary systems, was presented and the theoretical background of the method was discussed. This revealed considerable links to well-established methods in systems theory, automata research and complexity research. The solutions of CIB may therefore be understood as a finite state approximation of the equilibrium points of a non-linear pair interaction system, as well as being interpreted as attractors of an automata network. The exploration of the relationships between CIB and its mathematical background brings various benefits. The orientation on mathematical concepts of system analysis protects the CIB framework (initially a heuristic approach) from being arbitrary in its analysis procedures. Furthermore it helps to interpret the elements and the results of the method in a consistent and well-founded way. Finally, the available information on the properties and overall behaviour of the theoretical relatives of CIB also provides insight into the behaviour of CIB. In the view of sociophysics and complexity research, CIB may be understood as an example of a network analysis method which builds a bridge to well-established analysis concepts in social sciences and management sciences. Furthermore CIB approaches Roth’s [86] recent demand for more empiricism in network models because the method’s data are completely gained by expert elicitation.