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Заслуживает внимания фигура лидера, основателя домена сети, владе ющего технологией актуализации доменов (относительно устойчивых мат риц рефлексивных представлений). С ее помощью генерируются скачки (переходы) от одного состояния полисистемы к другому, при котором вол на изменений распространяется от уровня {Sx}, на котором находится акту ализатор, на уровни {Sx m} и {Sx+n}, где m и n – целые числа. Чем мощнее технологическое воздействие и чем точнее оно отвечает текущему состоя нию персонажей плацдарма, тем «выше» и «глубже» распространится вол на изменений интерференционной картины, способная не только сдвигать границы доменов на плацдарме, но и порождать новые домены на каждом уровне полисистемы сетевой природы. Открывается возможность управ ления развитием полисистемы, вообще говоря, из любой ее точки.

Важен вопрос о возможности моделирования обсуждаемых процес сов. В частности, естественный процесс образования доменов моделиру ется свободным группообразованием в организационно деятельностных играх (ОДИ) [11] и родственных им социально игровых технологиях. Ав торы полагают, что возможно построение на основе мифодизайна соци альной технологии искусственного доменообразования в системах сете вой природы.

Литература 1. Лефевр В.А. Конфликтующие структуры. М.: Сов. Радио, 1973.

2. Тупицын А. Рефлексия в кооперативных системах деятельности. Рефлексив ное управление. Тезисы международного симпозиума 17 19 октября 2000 г, М.: Изд во «Институт психологии РАН». С. 47 48.

3. Чучкевич М.М. Основы управления сетевыми организациями. М.: Изд во Ин ститута РАН, 1999.

4. Реут Д.В. Интернет политика. Рефлексивное управление. Тезисы междуна родного симпозиума 17 19 октября 2000 г. М.: Изд во «Институт психологии РАН». С. 125 127.

5. Реут Д.В. Релятивистские эффекты информационного пространства. Тезисы докладов III сессии Международной конференции «Эволюция инфосферы» памяти Н.Н.Моисеева 28.02 02.03 2001. Том. 3. М., 2003.

6. Шохов А.С. Структура социальной системы и ее пространство. Анализ систем на пороге XXI века: теория и практика. Материалы Международной научно практической конференции в 4 х томах. М., 1997. Том 3. С. 323 327.

7. Шохов А.С. Природа социального пространства. Социальные проблемы Ураль ского региона. Екатеринбург, 1994. С. 10 11.

8. Реут Д.В. Рефлексивный мифодизайн (тезисы). Сетевые организации. Мате риалы встречи ОДН 27 марта 2001 года. М.: Московская сеть консультантов по организационному развитию. 2001. С. 24.

9. Реут Д.В. От мифоложества – к мифодизайну и мифопрактике. Сетевые орга низации. Материалы встречи ОДН 27 марта 2001 года. М.: Московская сеть консультантов по организационному развитию. 2001. С. 25 29.

10. Щедровицкий Г.П. Схема мыследеятельности – системно структурное строе ние, смысл и содержание // Системные исследования. Методологические проблемы. Ежегодник 1986. М., 1987.

11. Щедровицкий Г.П. Организационно деятельностная игра как новая форма организации и метод развития коллективной мыследеятельности. Избранные труды. М.: Школа культурной политики, 1995. С. 115 142.

MODELING SOCIAL INFLUENCE WITH REFLEXIVE PROCESSES Philipp A. Djang (USA, Army Research Laboratory White Sands Missile Range) Diffusion of perceptions, opinions and ideas is an important area of social and political research. This research topic, while broad in scope, has relevance for current world situations such as the recruiting of terrorists, modeling of economic trends and control of crowds. How do ideas or influences propagate through a loosely connected social network of individuals and how do these influences affect the distribution of resources Reflexive processes have been used to simulate the propagation of influence between two individuals via two person reflexive games. We wish to expand this work by modeling the transmission of influence through groups of people.

Knoke and Kuklinksi have studied the diffusion of innovative technology and established some empirical norms based on analysis of their datasets. While traditional analytic methods have made substantial contributions to the understanding of how new concepts and technologies are disseminated, these methods, in general, fall short of analyzing fast changing complex environments, such the growth of a terrorist network, and further, fail to offer a broader view of how a collective behavior emerges from changes in individual characteristics. In addition, the underlying decision mechanism that drives an individual to adopt an idea is noticeably absent in this field. In order to address these shortfalls, we combine the powerful tools of reflexive processes and stochastic cellular automata to rigorously analyze rates of idea diffusion by conducting studies and examining assumptions in a manner not possible otherwise. In our model, a stochastic cellular automata is used to model a social network of individuals and reflexive processes act as the agent decision engine by serving as transition state rules for the stochastic cellular automata.

Stochastic Cellular Automata (CA) have been employed by a wide variety disciplines to illustrate numerous complex adaptive system principles. The foundations of CA are based upon early Systems Theory and rigorous mathematical analysis done by Russian scientists. Recently, Stephen Wolfram published a landmark book, A New Kind of Science devoted to CA theory and applications. In 1983, Wolfram published a landmark paper in Reviews of Modern Physics. Wolfram based his paper on remarkable contributions by three outstanding scientists Alan Turing, John von Neumann and Stainslaw Ulam. John Conway’s “Game of Life” (developed in 1969) was the first popular CA application.

The underlying motivation for employing cellular automata is their simplicity and minimalist approach for simulating complex phenomena.

General Systems Theory posits that whole is greater than the sum of the parts.

Many physical systems are composed of identical components that obey simple laws; however, it is the interaction of the simple components that gives rise to very complex and unexpected behavior. The laws that govern the transition dynamics of most cellular automata are simple geo spatial voting mechanisms.

Our innovation is to employ reflexive processes as the primary state transition mechanism. We select reflexive processes as a replacement for the simple voting rules because of its relevance to human decision making. Reflexive processes take into account normative concepts (ethics and morality) as well as game theoretic concepts of value and utility. Most importantly, reflexive processes have been empirical validated as decision prediction algorithms. By employing reflexive processes, our cellular automata can simulate the diffusion of perceptions, ideas and opinions in way that may prove to be a fertile ground for future research.

For an example of an application, we model the spread of popular opinion through a social network of agents. Agents are divided into two categories: politicians and voters. Politicians attempt to influence voters and convince them to vote for them by communicating with voters. Lefebrve’s continuous model of the subject:

X1 = x1+(1 – x1)(1 – x2) x3 is model the voters. Voters will vote for a politician if their intention is equal to their readiness. The model also includes a “spin glass model” component: voters also interact with other voters by observing their neighbor’s current opinion. With probability P, a voter may decide to switch their opinion so that it aligns with voters in their social network neighborhood. These two phenomena give rise to the so called percolation effect of cellular automata.

During the course of the simulation, islands of voter preference arise and dissipate as a function of politician voter interaction and voter voter interactions.

Our current efforts are concentrated primarily on understanding the dynamics of the interaction of multiple heterogeneous reflexive process agents embedded within a cellular automata for the study of valid model of the social phenomena of idea and opinion diffusion. We have applied data mining tools to gain insight into the behaviors of the agents and have begun to investigate the effects of initial condition parameter values on both short and long term outcomes. We are especially interested in macro level transient behaviors as the cellular automata transitions between states. We believe by simulating individual level decision characteristics with reflexive process, we can determine how certain psychological assumptions that underlie those very individual characteristics will determine the macro level dynamics at the cellular automata level.

REFLEXIVE MODELS IN DECISION MAKING Xenia Kramer (USA, New Mexico State University) Tim Kaiser (Germany, Darmstadt University of Technology) Vladimir Lefebvre (USA, University of California) Stefan E. Schmidt (USA, New Mexico State University) Jim Davidson (USA, New Mexico State University) We discuss a formal model and a prototypical example for automated reflexive decision making. Reflexive decisions involve sending packages of information to a recipient to increase the likelihood for determining his future behavior. In sending the (misleading) information the sender gains knowledge, i.e. he will know that the recipient received his informational packages. The difficulty in reflexive decision making lies within choosing an appropriate model of how the recipient processes this information. If such a model is available we can compute the recipients behavior and apply a counterstrategy. Automation enables us to evaluate all possible reflexive decisions within a fixed scenario. Therefore we can single out strategies having desired properties. We will explain two different basic schemes of reflexive decision making using a computer simulation of an application to counterterrorism where one party (US border defense) tries to allocate its resources optimally to block the other party (terrorists) from traversing certain edges in a graph (crossing the country’s border).

REFLEXIVE MODEL FOR TERRORIST RECRUITMENT Tim B. Kaiser (Germany, Darmstadt University of Technology), Stefan E. Schmidt (USA, New Mexico State University) The challenge in modeling terrorist recruitment activity lies in the difficulty of capturing the human psyche. Common modeling approaches understand human decision making processes primarily as optimization of utility gain based only on rationality. However, a disregard of the moral dimension within terrorist behavior makes it impossible adequately to describe this situation. For example, a suicide mission requires a high willingness for sacrifice which goes beyond the concept of a homo economicus. Reflexive Theory allows modeling the combination of external, environmental and internal, moral factors. In contrast to utilitarian optimization, the principle of reflexivity proposes that the subject attempts to reach a state of congruency between the self and the internal model of the self. Using the quadratic model we develop a computational model for terrorist recruitment.

REFLEXIVE THEORY AND MATCHING LAW Vladimir A. Lefebvre (USA, School of Social Sciences University of California, Irvine) Mentalism is a science about subjective matters that gives a living creature a niche for the inner world. Behaviorism is a science about behavior depriving a living creature of it. Both of these sciences have a common feature; in them, an organism appears as an entity. The first one focuses on a subject’s relation to the self, while the second one focuses on the relations between the subject and the environment (Tolman, 1932). For the last few decades, the border between mentalism and behaviorism has moved: a formal model of the subject has appeared which includes both its mental domain and its behavior. The model’s verification goes through its penetration into various branches of psychology, sociology, and anthropology.

Behaviorism represents the most attractive field for such a penetration, because of its strict inner discipline and methodological honesty that allows us to distinguish clearly what is understood and what is not. One of the unsolved problems in the science of behavior is the Matching Law (Herrnstein, 1961). It describes the ability of birds and mammals to regulate the ratio between a sequence of reinforcements and a sequence of responses. This ability looks strange from the point of view of the utilitarian common sense (see Williams, 1988). In this work we offer a solution to this problem with the help of Reflexive Model of the Intentional Subject (RIMS).

In creating this model we tried to understand a phenomenon of “moral choice” from a purely scientific point of view, rather than from a moralistic one.

A great number of specialists from psychiatrists to sociologists studying criminals and terrorists are interested in finding objective laws of moral choice. A human mental domain must be represented in their studies as clearly and unambiguously as behavior is represented in behaviorism.

RIMS is a special mathematical representation of a subject making a choice between two alternatives. This model reflects two aspects of the subject’s activity:

utilitarian and deontological. The utilitarian aspect relates to the behavior which is advantageous from the practical point of view, for example, obtaining money or food. The deontological aspect relates to the idealistic behavior, for example, choosing between good and evil. It may happen that the “moral” orientation of the alternative does not correspond to the utilitarian one. For example, a deal with an enemy may be more profitable than the deal with a friend. Both these aspects are connected into a single process of behavior generation by the formal model.

RIMS is a probabilistic model. It predicts probabilities with which the subject chooses the alternatives, one playing the role of the positive pole and the other that of the negative pole. The idea that the subject’s choice is probabilistic appeared early in the twentieth century and was used in many theoretical models (Thurstone, 1927; von Neuman & Morgenstern, 1944; Savage, 1951; Mosteller & Nogee, 1951; Bradley & Terry, 1952; Davidson, Suppes & Siegel, 1957; Bower, 1959;

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