The development and interaction of terrorist and fanatic groups

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to extend the theoretical framework of organizing and self-organizing social groups and communities, including terrorist groups. The main goal of our work is to gain insight into the role of recruitment and retention in the formation and survival of social organizations. Understanding the underlining mechanisms of the spread of ideologies under competition is a fundamental component of this work. Here contacts between core and non-core individuals extend beyond its physical meaning to include indirect interaction and spread of ideas through phone conversations, emails, media sources and other similar mean. This work focuses on the dynamics of formation of interest groups, either ideological, economical or ecological and thus we explore the questions such as, how do interest groups initiate and co-develop by interacting within a common environment and how do they sustain themselves? Our results show that building and maintaining the core group is essential for the existence and survival of an extreme ideology. Our research also indicates that in the absence of competitive ability (i.e., ability to take from the other core group or share prospective members) the social organization or group that is more committed to its group ideology and manages to strike the right balance between investment in recruitment and retention will prevail. Thus under no cross interaction between two social groups a single trade-off (of these efforts) can support only a single organization. The more efforts that an organization implements to recruit and retain its members the more effective it will be in transmitting the ideology to other vulnerable individuals and thus converting them to believers.     

The Social Embeddedness of Academic Online Groups in Offline Networks as a Norm Generating Structure: An Empirical Test of the Coleman Model on Norm Emergence

This paper analyzes two questions. First, under which conditions does a norm emerge in academic online groups that prescribes members to help others during group discussions? Second, what effects does such a norm, and other social conditions, have on the contributing behavior of researchers during online discussions? It is argued that the Coleman model (1990) on the emergence of norms points to an important condition that facilitates the realization of such a norm. According to the Coleman model (1990) a dense network among members of a group tends to strengthen a group norm. The paper makes a distinction between different kinds of academic online groups. The criterion of the distinction is the extent to which within the membership a highly integrated research community exists. An online group with a highly integrated research community is called to have a high degree of social embeddedness of its online communication in offline networks. It is hypothesized that a high degree of embeddedness has a number of effects. A higher degree of embeddedness leads to a stronger help-prescribing norm. The stronger the norm the more researchers send online answers to questions of their co-members during public online discussions. Furthermore, a high degree of embeddedness increases the answering behavior of researchers directly because it provides opportunities to gain reputation within the academic community through contributing to the discussion. The study makes use of data that consist of a combination of survey data and observed data of the communication behavior of researchers in about 50 international academic emailing lists. The results provide evidence for the expected effect of embeddedness on the strength of the norm and for the effect of embeddedness on the answering behavior of researchers. The strength of the help-prescribing norm indirectly influences the answering behavior.     

Faciliated Work Groups: Theory and Practice

This paper concerns the facilitation of working groups whose general aims are to achieve a shared understanding of issues, a sense of common purpose and a mutual commitment to action. We see the main role of the facilitator in such a group as contributing to process and structure, not content. This view is coloured by our assumptions about groups and how their work can be facilitated: that groups have an emotional life which influences and is influenced by each participant who experiences a tension between what is best for the group and what is personally desired, and that the facilitator's main tasks are to see and understand the group life, intervening only to help the group maintain a task orientation to its work. To understand the group the facilitator observes verbal and non-verbal behaviour, attends to relationships between participants and maintains awareness of his or her own feelings. For some work groups, the facilitator can be helped by computers, which provide an effective means externalizing many aspects of group work. By assigning to the computer the information manipulation and communication tasks, group members can concentrate their attention on the judgmental tasks, and the facilitator can attend better to group processes. Effectively used, computers can help a group maximize the creative and minimize the destructive aspects of its life.     

Survey study and experimental investigation on the local behavior of pedestrian groups

Current research on pedestrian dynamics mainly focuses on the interactions among isolated individuals, the impact of the presence of groups is not fully considered. In recent 5 years, researchers have started to investigate pedestrian group movement. The aim of this work is to explore the local behavior of pedestrian groups by questionnaires and field observation. Survey study focused on pedestrians' psychology when walking in groups, which included five parts: group size, interpersonal distance, spatial relationship among group members, speed adjustment of group members, information transmission, and acid action among group members. Meantime a field observation was carried out to study group movement characteristics, which contained speed, step frequency, offset angle and interpersonal distance. The survey results show that group members have a closer interpersonal distance, faster information transmission and plenty of acid action. Conversely, group walking has a negative influence on pedestrian's speed, step frequency by comparing with the way isolated pedestrian walks. In addition, it is found that for a certain group, the group members are able to keep movement consistent. Also there exists obvious movement diversity among different group types (male dyads, female dyads, couple groups, and ordinary‐friend groups) because of different gender and social relationship. Ultimately the results will be more promising for helping to model the movement of pedestrian groups. © 2014 Wiley Periodicals, Inc. Complexity 20: 87–97, 2015     

The cultural Red King effect

Why do minority groups tend to be discriminated against when it comes to situations of bargaining and resource division? In this article, I explore an explanation for this disadvantage that appeals solely to the dynamics of social interaction between minority and majority groups—the cultural Red King effect (Bruner, 2017). As I show, in agent-based models of bargaining between groups, the minority group will tend to get less as a direct result of the fact that they frequently interact with majority group members, while majority group members meet them only rarely. This effect is strengthened by certain psychological phenomenon—risk aversion and in-group preference—is robust on network models, and is strengthened in cases where preexisting norms are discriminatory. I will also discuss how this effect unifies previous results on the impacts of institutional memory on bargaining between groups.     

A theory of liberal churches

There is a counterintuitive gap in the club theory of religion. While it elegantly accounts for the success of strict sectarian religious groups in recruiting members and maintaining commitment, it is less satisfactory when attempting to account for groups requiring neither extreme nor zero sacrifice. Moderate groups are always a suboptimal choice for rational, utility maximizing agents within the original representative agent model. The corner solutions of zero and absolute sacrifice, however, are rarely observed empirically compared to the moderate intermediate. In this paper, we extend the original model to operate within an agent-based computational context, with a distribution of heterogeneous agents occupying coordinates in a two dimensional lattice, making repeated decisions over time. Our model offers the possibility of successful moderate groups, including outcomes wherein the population is dominated by moderate groups. The viability of moderate groups is dependent on extending the model to accommodate agent heterogeneity, not just within the population of agents drawn from, but heterogeneity within groups. Moderate sacrifice rates mitigate member free riding and serve as a weak screening device that permits a range of agent types into the group. Within-group heterogeneity allows agents to benefit from the differing comparative advantages of their fellow members.     

Information acquisition and transparency in committees

We study an intertemporal model of committee decision-making where members differ in their levels of efficiency. They may acquire costly information that enhances their ability to make a correct decision. We focus on the impact of transparency. We show that the principal’s initial utility is higher under transparency, because members exert more effort, which makes correct decisions more likely. The principal also benefits from transparency later, unless transparency leads to an alignment of the signal qualities of highly efficient and less efficient committee members. In general, committee members are harmed by transparency. Together with the insights from the literature, our results may help to decide when transparency in committees is desirable.     

How to bid in unified second-price auctions when requests are duplicated

In display advertising auctions, a unique display opportunity may trigger many bid requests being sent to the same buyer. Bid request duplication is an issue: programmatic bidding agents might bid against themselves. In a simplified setting of unified second-price auctions, the optimal solution for the bidder is to randomize the bid, which is quite unusual. Our results motivate the recent switch to a unified first-price auction by showing that a unified second-price auction could have been detrimental to all participants.     

Optimizing time limits in retail promotions: an email application

Most marketing managers know intuitively that once a customer delays a purchase decision, the potential is high that the purchase may be put off indefinitely. In response, marketing managers usually set ‘deadlines’ or time limits for how long an offer is available. However, research has shown that, while time limits can help motivate customers to buy now rather than later (or not at all), time limits that are over/under restrictive may actually hurt response more than help. We consider two opposing forces of time, namely awareness and urgency. Longer time limits allow for greater awareness of an offer, which, everything else being equal, should lead to a larger response. At the same time, longer time limits also reduce the urgency of an offer leading consumers to delay their purchase (perhaps) indefinitely and thus, everything else being equal, lead to a lower response. Using decision calculus, we model the optimal time limit for promotional offers and demonstrate its use in an email marketing application. Email marketing has emerged as a profitable tool for companies like Amazon and JCrew who regularly use email to communicate promotional offers to their customers because of its low cost to implement and its relatively high response rates. This research contributes to the field by providing marketing managers a methodology for determining superior choices for time limit in promotional offers.     

Social comparison,group composition,and incentive provision

This article analyzes the optimal composition of groups of arbitrary size according to the social preferences of group members in a situation of moral hazard. We focus on rivalry, pure self-interest and altruism to show that in a situation where every group member compares his or her remuneration to the average remuneration of all members in the same group, ideally there should be as many extreme altruists as there are extreme rivals. If, by contrast, every member of the group compares his or her own remuneration to that of a focal agent, ideally, this focal agent should be a strong altruist, while all other group members should be highly competitive. Our results show that it is important to foster heterogeneity in the social preferences of the members of a group in order to maximize the profitability of the firm.     

Root Systems for Asymmetric Geometric Representations of Coxeter Groups

Results are obtained concerning root systems for asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg and Eriksson, and generalize the standard geometric representation of a Coxeter group in such a way as to include certain restrictions of all Kac–Moody Weyl groups. In particular, a characterization of when a nontrivial multiple of a root may also be a root is given in the general context. Characterizations of when the number of such multiples of a root is finite and when the number of positive roots sent to negative roots by a group element is finite are also given. These characterizations are stated in terms of combinatorial conditions on a graph closely related to the Coxeter graph for the group. Other finiteness results for the symmetric case which are connected to the Tits cone and to a natural partial order on positive roots are extended to this asymmetric setting.     

The problem of highly constrained tasks in group decision support systems

Most experimental uses of group decision support systems (GDSS) are associated with relatively unrestricted domains, for example, idea generation and preference specification, where few restrictions on potential solutions exist. However, an important GDSS task is that of resource allocation across functional areas of the organization, including supply chain applications. These types of tasks, such as budget planning and production planning, are typically highly constrained and difficult to solve optimally, necessitating the use of decision aids, such as those found in GDSS.We use a model based on adaptive search of a genetic algorithm as the analogy for the group decision making process. We apply this model to experimental data gathered from GDSS groups solving a production planning task. The results indicate very low estimated crossover rates in the experimental data. We also run computational experiments based on adaptive search to mimic the GDSS data and find that the low estimated crossover rate might be due to the highly constrained search space explored by the decision making groups. The results suggest further investigation into the presumed beneficial effects of group interaction in such highly constrained task domains, as it appears very little true information exchange occurs between group members in such an environment. Furthermore, the simulation technique can be used to help predict certain GDSS behaviors, thus improving the entire GDSS process.     

Structural Learning: Attraction and Conformity in Task-Oriented Groups

This study extends previous research that showed how informal social sanctions can backfire when members prefer friendship over enforcement of group norms. We use a type of neural network to model the coordination of informal social control in a small group of adaptive agents confronted with a social dilemma. This model incorporates two mechanisms of social influence, informal sanctions and imitation. Both mechanisms vary with the strength of the social tie between source and target. Previous research focused on the effects of social sanctions. Here, we demonstrate a curvilinear effect of imitation on compliance with prosocial norms. Moderate doses of imitation reduce the coordination complexity of self-organized collective action and help the network achieve satisfactory levels of cooperation. High doses, however, undermine the agent-based learning required to find cooperative solutions. Increasing group size also diminishes compliance due to increased complexity, with larger groups requiring more imitation to overcome the coordination problem.     

A two-phase algorithm for consensus building in AHP-group decision making

Group decision making through the AHP has received significant attention in contemporary research, the primary focus of which has been on the issues of consistency and consensus building. In this paper, we concentrate on the latter and present a two-phase algorithm based on the optimal clustering of decision makers (members of a group) into sub groups followed by consensus building both within sub groups and between sub groups. Two-dimensional Sammon’s mapping is proposed as a tool for generating an approximate visualization of sub groups identified in multidimensional vector space, while the consensus convergence model is suggested for reaching agreement amongst individuals in and between sub groups. As a given, all decision makers evaluate the same decision elements within the AHP framework and produce individual scores of these decision elements. The consensual scores are obtained through the iterative procedure and the final scores are declared as the group decision. The results of two selected numerical examples are compared with two sets of results: the results obtained by the commonly used geometric mean aggregation method and also the results obtained if the consensus convergence model is applied directly without the prior clustering of the decision makers. The comparisons indicated the expected differences among the aggregation schemes and the final group scores. The matrices of respect values in the consensus convergence model, obtained for cases when the decision makers are optimally clustered and when they are not, show that in the latter case the decision makers receive lower weights of respect from other members in the group. Various tests showed that our approach is efficient in cases when no clusters can be visually and undoubtedly identified, especially if the number of group members is high.     

Problem structuring methods for large group interventions

Problem structuring methods (PSMs) aim to build shared understanding in a group of decision makers. This shared understanding is used as a basis for them to negotiate an agreed action plan that they are prepared to help implement. Engaging in a social process of negotiation with a large number of people is difficult, and so PSMs have typically focused on small groups of less than 20. This paper explores the legitimacy of deploying PSMs in large groups of people (50–1000), where the aim is to negotiate action and build commitment to its implementation. We review the difficulties of facilitating large groups with PSMs, drawing heavily on our experience of working with over 25 large groups. We offer a range of lessons learned and suggest concrete approaches to facilitating large groups to achieve the objectives of PSMs. This paper contributes to the evaluation and development of PSMs.     

Mathematical modeling of church growth

The possibility of using mathematics to model church growth is investigated using ideas from population modeling. It is proposed that a major mechanism of growth is through contact between religious enthusiasts and unbelievers, where the enthusiasts are only enthusiastic for a limited period. After that period they remain church members but less effective in recruitment. This leads to the general epidemic model which is applied to a variety of church growth situations. Results show that even a simple model like this can help understand the way in which churches grow, particularly in times of religious revival.     

Limit theorems for queueing systems with infinite number of servers and group arrival of requests

We consider an infinite-server queueing system where customers come by groups of random size at random i.d. intervals of time. The number of requests in a group and intervals between their arrivals can be dependent. We assume that service times have a regularly varying distribution with infinite mean. We obtain limit theorems for the number of customers in the system and prove limit theorems under appropriate normalizations.     

Affine mappings in the geometries of algebras

Modules and algebras over a commutative ring R and the geometry associated with an algebra are studied. The non-homogeneous members of a module, for which no maximal ideal of R contains every co-ordinate, the generators of a module, for which polynomials in the co-ordinates take arbitrary values and the non-singular members of an algebra are investigated in relation to the group G of non-singular R-linear transformations. Particular attention is given to bi-quadratic extensions of fields. Geometrical isomorphisms are proved to be exactly those transformations that can be written as the composition of a translation, a member of G and a co-ordinate-wise extension to the algebra of an automorphism of R.The author gratefully acknowledges the help and advice of Prof. Walter Benz of the University of Waterloo and the financial support of the University of Waterloo and the National Research Council of Canada.     

Group decision making in a multiple criteria environment: A case using the AHP in software selection

This paper reports the results of a case study where the analytic hierarchy process (AHP) technique was employed to support the selection of a multi-media authorizing system (MAS) in a group decision environment. Three MAS products were identified and ultimately ranked using the AHP. Six software engineers, who are technically competent and experienced, participated in our study. These engineers were trained to use the AHP and asked to apply this technique to select the most appropriate MAS product for adoption. A post-study survey and interview were conducted with all the engineers to collect further feedback on the use of the AHP, as compared to their frequently used Delphi technique, in supporting group decisions. The experiment results and survey findings indicated that the AHP is preferable to Delphi as the AHP helps group members center a discussion around objectives, rather than alternatives. We also found the AHP to be more conducive to consensus building in group decision settings.