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Conceptual Models

New Conceptual Models
(source: Final Progress Report 2006-2007)

            The stimulating interactions of our team have led to the generation of four new conceptual models which hold great promise for enhancing our understanding of basic conflict dynamics. These are outlined below:

The Crude Law Model: Development of a formal model of Deutsch’s Crude Law of Social Relations.

We have developed a formal, minimalist model of the emergence of the culture of war from a simple rule of social relations: The Crude Law. The Crude Law formulated by Deutsch provides a comprehensive summary of many years of study of the typical effects of cooperative and competitive processes (Deutsch, 1949, 1973). It states that “ the characteristic processes and effects elicited by a given type of social relationship (e.g., cooperative or competitive) tend also to elicit that type of social relationship; and a typical effect of any type of relationship tends to induce the other typical effects of the relationship”. In Deutsch’s study of conflict it was demonstrated that when conflict is viewed by the parties involved, as a mutual problem to be resolved cooperatively, it mainly leads to a constructive process of conflict resolution with mutually satisfactory outcomes. On the other hand, a competitive, win-lose orientation to a conflict mainly leads to a destructive course of conflict resolution with both sides losing or the stronger party defeating the less powerful one. From the “crude law,” one would expect that when the typical effects of a cooperative process are introduced into a conflict situation, the conflict is likely to be characterized by a constructive process; while the typical effects of a competitive process are apt to produce a destructive process of conflict resolution.

            From the modeling point of view, Crude Law defines the relationship between three types of variables:

·         Interdependence is defined as the relatively objective relation between interests of the individuals or social groups. It characterizes the consequences of realization of the interests of one individual or group for the interests of the other individual or group.

·         Behaviors (cooperation – competition) This variable describes characteristics of the momentary behaviors of individuals.

·         Orientations (cooperative - competitive). This variable describes the tendency toward cooperation s. competition. It has many components e.g. trust, perceptions of others, etc. Its changes in time are slower than changes of behaviors. 

We can summarize the findings associated with the crude law in the list of the following principles, which will form the basis for the dynamic model:

          Type of interdependence between individuals and orientation of each individual changes the probability and intensity of cooperation/competition of the individual

          There is reciprocity such that cooperative behaviors elicit cooperative behavior of the partner and competitive behaviors elicit  competitive behaviors

          Behaviors of the individuals change orientations in the direction of congruency with behaviors.

          Orientations facilitate behaviors that are compatible with them.

In our model we have investigated the emergent consequences of the assumptions of the Crude Law as applied to interactions in a social group. We based our model on the observation that the Crude Law describes the growth or decay of several related and mutually dependent (by feedback loops) sets of variables.  We will thus adopt for our model the generic formalism of growth: the formalism of the Alphabet Model (Nowak & Solomon 2006)

In a series of simulations we varied the parameters to learn under what conditions islands of conflict were created. One result was quite trivial. For the islands of conflict to be created the coefficient of reciprocity must be larger then the rate with which behaviors decays. The other result was much more surprising. The parameter that most strongly prevented the creation of sustainable islands of conflict involved the mobility of elements of conflict. This involves both the type of interdependence, and behaviors. The local exponential growth of behaviors in the model is possible only because the new behaviors are created exactly in the location where the facilitating factors (interdependence or orientations) are present. They can in turn multiply, because there is the facilitating factor.

If behaviors migrate outside the location where the negative interdependence exists, or if the elements of orientations migrate fast enough to escape the islands of negative behaviors, the behaviors and the conditions for their  proliferation do not exist together in the same place long enough to lead to the exponential proliferation of negative behavior. Islands of behaviors cannot be formed, and thus the behaviors decay.  Preservation of local concentration is thus critical for the emergence and maintenance of conflict. In general our simulations show the critical role of local conditions and local dynamics. According to the model, even large scale intractable conflicts are maintained by high local reciprocal behaviors and frozen conditions. If the elements move, if the behaviors are not returned to those who are under condition to reciprocate them the conflict is likely to dissolve.

Dynamics of Two-Actor Cooperation-Competition Conflict Models.

A mathematical model for conflict can give us insight into which mechanisms are the most important in maintaining or resolving a conflict.  We developed a nonlinear model of the interactions in time between two actors (which could be individuals, groups, or nations) based on the theoretical and experimental insights of Deustch, Pruitt, Gottman, Murray, Swanson, Tyson, and Swanson, and Coleman, Vallacher, Nowak, and Bui-Wrzosinska.  In this model, the state of each actor at a given moment in time depends on its own state in isolation, its previous state in time, its inertia to change, and the influence from the other actor.  We analyzed this model using analytical methods and numerical computer simulations.  We determined how the dynamics of the actors depends on whether they influence each other through positive feedback (cooperation), negative feedback (competition), or mixed positive and negative feedback.  This model gives us insight into the dynamics of conflicts and is the starting base for more complex simulations that will model the interactions between many actors at once.

            A paper on this model was one of three papers nominated for the best theoretical paper at the International Association for Conflict Management conference in July, 2007, in Budapest Hungary, and has been submitted for publication to Negotiation and Conflict Management Research. 

A Dynamical Model of Conflict in Asymmetrical Power Relations.

Deutsch’s theory of conflict resolution (1973, 2006a) is one of the most important and influential theoretical advances for the study of conflict of the last century. Based on his earlier work on cooperation and competition in groups (Deutsch, 1949a, 1949b), it specified the basic conditions and processes involved in constructive versus destructive conflict. However the original formulation of the theory assumed equal power between the parties in conflict. This assumption constrains both the theoretical scope and practical implications of the theory. This research project will empirically validate and refine a new social-psychological model of the dynamics of power and conflict, thus extending Deutsch’s theory into situations of asymmetrical power. It combines prior work on interdependence and social power and integrates them through the lens of dynamical systems theory, a new paradigm for the study of social conflict. A conceptual article is being submitted to Journal of Conflict Resolution and empirical studies of the main propositions are planned for Fall, 2007.

Intractability in Conflict: A Network Simulation Model.

The formalism of knowledge networks was used to model the development of intractability in conflict. The catastrophic versus linear dynamics of escalation, in the model, are a result of the network structure (groups, relations, semantic structure). The model was tested empirically (see description of empirical study of escalation in close relationships above for details). Nodes correspond to issues and links to relations between issues. Closeness was modeled as the degree to which different issues were interrelated and relevant to each other, i.e. as the strength of connections between the issues. The outcomes of computer simulations proved to be remarkably similar to empirical results. Attractor tendencies were clearly visible in the model’s dynamics. The model replicated the non-linear character of the change of attractors in close relations, and the linear escalation pattern in distant relationships. Furthermore, the simulation could illustrate more general laws of escalation resulting from the model, where the pattern of escalation of a given conflict is strongly linked to its structure. The application of the model to social networks illustrates how the social structure (dense versus dispersed, coherent versus chaotic…) determines a social system’s behavior in conflict (linear conflict escalation versus unpredicted outbreaks).