Social Distribution Principles: A Formal Analysis of Short - and Long - Term Effects Soziale Verteilungsprinzipien: Eine formale Analyse kurz- und langfristiger Effekte

This is a theoretical paper that relies heavily on formal methods to derive deductions. Strictly defined, our study is not a simulation. A simulation is usually specified as ``... formulating a stochastic model to describe a real phenomenon'' (Ross 1990, vii; Gentle 1985, p. 616). For our topic, the real phenomena are not jet known in sufficient detail. We claim that the deductions we derive are bound to occur as explicated, given certain situational constraints and the descriptions of behavior by distribution principles. The interaction between these principles and the constraints for short time and long time intervals is modeled mainly as a set of interdependent difference equations. The results thus are, in principle, deductions and explications based on formal methods. They provide a framework for empirical studies - on the one hand preventing substantial interpretations of logical necessities as empirical results, but on the other hand guiding research how to empirically test the appropriateness of fundamental conceptions of this paper. An experiment by Flament and Apfelbaum is used to introduce a research program on social distribution (Flament, C. & Apfelbaum, E. 1966. Elementary processes of communication and structuration in small groups. Journal of Experimental and Social Psychology 2, 376 - 386.) The basic conceptualizations and the main results of our interpretations and extensions are summarized in eight statements: 1. The distribution situation is a specific situation of social interaction. In particular, we argue that it is not identical with ``exchange''. 2. One possibility to act in distribution situations is to apply principles as strategic guidelines on how to allocate the resources available. We study ``equality'' (the same for everybody), ``mutuality'' (tit for tat), ``debtor'' (same as mutuality plus consideration of one's own investments), and ``favor'' (replicate the preference shown for you by others). 3. We demonstrate how these principles can be formulated as a set of interdependent difference equations to predict how resources should or will be distributed. The equations are solved by numerical iteration. 4. Important parameters of a distribution situation and aspects of generalization are the number of participants, their roles as senders and receivers and the interlocking of these roles over trials (transmission scheme), the distribution of the resources over the participants (allocation schedules), and the range of action alternatives available to the participants. The short and longterm effects of the principles differ in interaction with these parameters. 5. If participants interact repeatedly in distribution situations, they can be understood as a system. We discuss some alternative possibilities for the participants to act and show the effects of these additional alternatives. The stability of the system is analyzed by adding random error to the equations, or to have some values in the equations deviate slightly but systematically, or to intervene grossly into the system. 6. The principles analyzed lead to large qualitative and quantitative differences in the outcome distributions. We mention as some of the remarkable results: Applying the equality principle once to the situations of Flament and Apfelbaum results in a ``revolutionary redistribution'' in which the formally poor become rich and vice versa. Furthermore, only mutuality can lead to a stable exchange in which no participant looses relative to his investment, and in which within each pair of participants everybody gets as much as he invests. But this is achieved only with a moderate allotment of resources -it fails when it is needed most, under extreme conditions. 7. The complexity of the results, i.e., the interaction of the parameters in determining the behavior of the outcome distributions, demands some sophistication when applying these principles in politics and society and when testing whether persons actually use these principles in psychological experiments. 8. Two theoretical alternatives to the idea that persons use strategic principles to distribute resources are mentioned. One possibility is to resort to tactical rules every time a specific situation arises in the distribution process. The other possibility is not to derive the outcome distributions but to model a latent psychological variable like the ``propensity'' of a to send resources to B and derive from this variable some aspects of the distribution behavior. unknown publishedVersion