Coalition analysis with preference uncertainty in group decision support

Coalition analysis is extended to incorporate uncertain preference into three stability concepts, general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ) under the paradigm of the graph model for conflict resolution. As a follow-up analysis in the graph model, coalition analysis aims to assess whether equilibriums under individual calculations are vulnerable to coalition moves and countermoves and, hence, become unstable under coalition stabilities. Coalition analysis has been considered for transitive graph models with simple preference under four stabilities, Nash, GMR, SMR, and SEQ, as well as general graph models with uncertain preference for the Nash stability. This paper introduces preference uncertainty into coalition stabilities under GMR, SMR, and SEQ for general graph models that can be transitive or intransitive. Depending on the focal coalition’s different attitudes towards preference uncertainty, four different extensions are presented. Interrelationships of coalition stabilities are investigated within each extension and across the four extensions. A case study is carried out to illustrate how to apply the proposed coalition stabilities

Attitudes and Coalitions in Brownfield Redevelopment and Environmental Management

Conflict analysis tools are applied to brownfield negotiations in order to investigate the impacts of coalition formation and a decision maker’s (DM’s) attitudes upon the successful resolution of brownfield disputes. The concepts of attitudes within the Graph Model for Conflict Resolution (GMCR) is defined and subsequently are used, along with coalition analysis methods, to examine the redevelopment of the Kaufman Lofts property and the resolution of a post-development dispute involving Eaton’s Lofts, both located in downtown Kitchener, Ontario, Canada. Within the model of the Kaufman Lofts redevelopment, the project is broken down into three connected project conflicts: property acquisition, remediation selection and redevelopment; with the graph model applied to all three conflict nodes. The application of attitudes shows the impact of cooperation between local governments and private developers in the formation of a coalition that mutually benefits all parties. Coalition analysis, applied to the redevelopment selection conflict between Heritage Kitchener and the private developer in the Kaufman Lofts project, illustrates the importance of close collaboration between the local government and the developer. Systems methodologies implemented here for the examination of brownfield redevelopments are examined and contrasted with the economic and environmental tools commonly used in the redevelopment industry. Furthermore, coalition formation within GMCR is used to examine the negotiation of the Kyoto Protocol, to demonstrate that formal conflict resolution methods can be utilized in other areas of environmental management

Matrix Representations and Extension of the Graph Model for Conflict Resolution

The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, two critical components of which are status quo analysis and coalition analysis. In stability analysis, an equilibrium is a state that is stable for all decision makers (DMs) under appropriate stability definitions or solution concepts. Status quo analysis aims to determine whether a particular equilibrium is reachable from a status quo (or an initial state) and, if so, how to reach it. A coalition is any subset of a set of DMs. The coalition stability analysis within the graph model is focused on the status quo states that are equilibria and assesses whether states that are stable from individual viewpoints may be unstable for coalitions. Stability analysis began within a simple preference structure which includes a relative preference relationship and an indifference relation. Subsequently, preference uncertainty and strength of preference were introduced into GMCR but not formally integrated. In this thesis, two new preference frameworks, hybrid preference and multiple-level preference, and an integrated algebraic approach are developed for GMCR. Hybrid preference extends existing preference structures to combine preference uncertainty and strength of preference into GMCR. A multiple-level preference framework expands GMCR to handle a more general and flexible structure than any existing system representing strength of preference. An integrated algebraic approach reveals a link among traditional stability analysis, status quo analysis, and coalition stability analysis by using matrix representation of the graph model for conflict resolution. To integrate the three existing preference structures into a hybrid system, a new preference framework is proposed for graph models using a quadruple relation to express strong or mild preference of one state or scenario over another, equal preference, and an uncertain preference. In addition, a multiple-level preference framework is introduced into the graph model methodology to handle multiple-level preference information, which lies between relative and cardinal preferences in information content. The existing structure with strength of preference takes into account that if a state is stable, it may be either strongly stable or weakly stable in the context of three levels of strength. However, the three-level structure is limited in its ability to depict the intensity of relative preference. In this research, four basic solution concepts consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined at each level of preference for the graph model with the extended multiple-level preference. The development of the two new preference frameworks expands the realm of applicability of the graph model and provides new insights into strategic conflicts so that more practical and complicated problems can be analyzed at greater depth. Because a graph model of a conflict consists of several interrelated graphs, it is natural to ask whether well-known results of Algebraic Graph Theory can help analyze a graph model. Analysis of a graph model involves searching paths in a graph but an important restriction of a graph model is that no DM can move twice in succession along any path. (If a DM can move consecutively, then this DM's graph is effectively transitive. Prohibiting consecutive moves thus allows for graph models with intransitive graphs, which are sometimes useful in practice.) Therefore, a graph model must be treated as an edge-weighted, colored multidigraph in which each arc represents a legal unilateral move and distinct colors refer to different DMs. The weight of an arc could represent some preference attribute. Tracing the evolution of a conflict in status quo analysis is converted to searching all colored paths from a status quo to a particular outcome in an edge-weighted, colored multidigraph. Generally, an adjacency matrix can determine a simple digraph and all state-by-state paths between any two vertices. However, if a graph model contains multiple arcs between the same two states controlled by different DMs, the adjacency matrix would be unable to track all aspects of conflict evolution from the status quo. To bridge the gap, a conversion function using the matrix representation is designed to transform the original problem of searching edge-weighted, colored paths in a colored multidigraph to a standard problem of finding paths in a simple digraph with no color constraints. As well, several unexpected and useful links among status quo analysis, stability analysis, and coalition analysis are revealed using the conversion function. The key input of stability analysis is the reachable list of a DM, or a coalition, by a legal move (in one step) or by a legal sequence of unilateral moves, from a status quo in 2-DM or $n$-DM ($n > 2$) models. A weighted reachability matrix for a DM or a coalition along weighted colored paths is designed to construct the reachable list using the aforementioned conversion function. The weight of each edge in a graph model is defined according to the preference structure, for example, simple preference, preference with uncertainty, or preference with strength. Furthermore, a graph model and the four basic graph model solution concepts are formulated explicitly using the weighted reachability matrix for the three preference structures. The explicit matrix representation for conflict resolution (MRCR) that facilitates stability calculations in both 2-DM and $n$-DM ($n > 2$) models for three existing preference structures. In addition, the weighted reachability matrix by a coalition is used to produce matrix representation of coalition stabilities in multiple-decision-maker conflicts for the three preference frameworks. Previously, solution concepts in the graph model were traditionally defined logically, in terms of the underlying graphs and preference relations. When status quo analysis algorithms were developed, this line of thinking was retained and pseudo-codes were developed following a similar logical structure. However, as was noted in the development of the decision support system (DSS) GMCR II, the nature of logical representations makes coding difficult. The DSS GMCR II, is available for basic stability analysis and status quo analysis within simple preference, but is difficult to modify or adapt to other preference structures. Compared with existing graphical or logical representation, matrix representation for conflict resolution (MRCR) is more effective and convenient for computer implementation and for adapting to new analysis techniques. Moreover, due to an inherent link between stability analysis and post-stability analysis presented, the proposed algebraic approach establishes an integrated paradigm of matrix representation for the graph model for conflict resolution

Fuzzy Preferences in the Graph Model for Conflict Resolution

A Fuzzy Preference Framework for the Graph Model for Conflict Resolution (FGM) is developed so that real-world conflicts in which decision makers (DMs) have uncertain preferences can be modeled and analyzed mathematically in order to gain strategic insights. The graph model methodology constitutes both a formal representation of a multiple participant-multiple objective decision problem and a set of analysis procedures that provide insights into them. Because crisp or definite preference is a special case of fuzzy preference, the new framework of the graph model can include---and integrate into the analysis---both certain and uncertain information about DMs' preferences. In this sense, the FGM is an important generalization of the existing graph model for conflict resolution. One key contribution of this study is to extend the four basic graph model stability definitions to models with fuzzy preferences. Together, fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability provide a realistic description of human behavior under conflict in the face of uncertainty. A state is fuzzy stable for a DM if a move to any other state is not sufficiently likely to yield an outcome the DM prefers, where sufficiency is measured according to a fuzzy satisficing threshold that is characteristic of the DM. A fuzzy equilibrium, an outcome that is fuzzy stable for all DMs, therefore represents a possible resolution of the conflict. To demonstrate their applicability, the fuzzy stability definitions are applied to a generic two-DM sustainable development conflict, in which a developer plans to build or operate a project inspected by an environmental agency. This application identifies stable outcomes, and thus clarifies the necessary conditions for sustainability. The methodology is then applied to an actual dispute with more than two DMs concerning groundwater contamination that took place in Elmira, Ontario, Canada, again uncovering valuable strategic insights. To investigate how DMs with fuzzy preferences can cooperate in a strategic conflict, coalition fuzzy stability concepts are developed within FGM. In particular, coalition fuzzy Nash stability, coalition fuzzy general metarationality, coalition fuzzy symmetric metarationality, and coalition fuzzy sequential stability are defined, for both a coalition and a single DM. These concepts constitute a natural generalization of the corresponding non-cooperative fuzzy preference-based definitions for Nash stability, general metarationality, symmetric metarationality, and sequential stability, respectively. As a follow-up analysis of the non-cooperative fuzzy stability results and to demonstrate their applicability, the coalition fuzzy stability definitions are applied to the aforementioned Elmira groundwater contamination conflict. These new concepts can be conveniently utilized in the study of practical problems in order to gain strategic insights and to compare conclusions derived from both cooperative and non-cooperative stability notions. A fuzzy option prioritization technique is developed within the FGM so that uncertain preferences of DMs in strategic conflicts can be efficiently modeled as fuzzy preferences by using the fuzzy truth values they assign to preference statements about feasible states. The preference statements of a DM express desirable combinations of options or courses of action, and are listed in order of importance. A fuzzy truth value is a truth degree, expressed as a number between 0 and 1, capturing uncertainty in the truth of a preference statement at a feasible state. It is established that the output of a fuzzy preference formula, developed based on the fuzzy truth values of preference statements, is always a fuzzy preference relation. The fuzzy option prioritization methodology can also be employed when the truth values of preference statements at feasible states are formally based on Boolean logic, thereby generating a crisp preference over feasible states that is the same as would be found using the existing crisp option prioritization approach. Therefore, crisp option prioritization is a special case of fuzzy option prioritization. To demonstrate how this methodology can be used to represent fuzzy preferences in real-world problems, the new fuzzy option prioritization technique is applied to the Elmira aquifer contamination conflict. It is observed that the fuzzy preferences obtained by employing this technique are very close to those found using the rather complicated and tedious pairwise comparison approach

Preference Uncertainty and Trust in Decision Making

A fuzzy approach for handling uncertain preferences is developed within the paradigm of the Graph Model for Conflict Resolution and new advances in trust modeling and assessment are put forward for permitting decision makers (DMs) to decide with whom to cooperate and trust in order to move from a potential resolution to a more preferred one that is not attainable on an individual basis. The applicability and the usefulness of the fuzzy preference and trust research for giving an enhanced strategic understanding about a dispute and its possible resolution are demonstrated by employing a realworld environmental conflict as well as two generic games that represent a wide range of real life encounters dealing with trust and cooperation dilemmas. The introduction of the uncertain preference representation extends the applicability of the Graph Model for Conflict Resolution to handle conflicts with missing or incomplete preference information. Assessing the presence of trust will help to compensate for the missing information and bridge the gap between a desired outcome and a feared betrayal. These advances in the areas of uncertain preferences and trust have potential applications in engineering decision making, electronic commerce, multiagent systems, international trade and many other areas where conflict is present. In order to model a conflict, it is assumed that the decision makers, options, and the preferences of the decision makers over possible states are known. However, it is often the case that the preferences are not known for certain. This could be due to lack of information, impreciseness, or misinformation intentionally supplied by a competitor. Fuzzy logic is applied to handle this type of information. In particular, it allows a decision maker to express preferences using linguistic terms rather than exact values. It also makes use of data intervals rather than crisp values which could accommodate minor shifts in values without drastically changing the overall results. The four solution concepts of Nash, general metarationality, symmetric metarationality, and sequential stability for determining stability and potential resolutions to a conflict, are extended to accommodate the new fuzzy preference representation. The newly proposed solution concepts are designed to work for two and more than two decision maker cases. Hypothetical and real life conflicts are used to demonstrate the applicability of this newly proposed procedure. Upon reaching a conflict resolution, it might be in the best interests of some of the decision makers to cooperate and form a coalition to move from the current resolution to a better one that is not achievable on an individual basis. This may require moving to an intermediate state or states which may be less preferred by some of the coalition members while being more preferred by others compared to the original or the final state. When the move is irreversible, which is the case in most real life situations, this requires the existence of a minimum level of trust to remove any fears of betrayal. The development of trust modeling and assessment techniques, allows decision makers to decide with whom to cooperate and trust. Illustrative examples are developed to show how this modeling works in practice. The new theoretical developments presented in this research enhance the applicability of the Graph Model for Conflict Resolution. The proposed trust modeling allows a reasonable way of analyzing and predicting the formation of coalitions in conflict analysis and cooperative game theory. It also opens doors for further research and developments in trust modeling in areas such as electronic commerce and multiagent systems

Conflict Networks

Conflict parties are frequently involved into more than one conflict at a given time. In this paper the interrelated structure of conflictive relations is modeled as a conflict network where opponents are embedded in a local structure of bilateral conflicts. Conflict parties invest in specific conflict technology to attack their respective rivals and defend their own resources.We show that there exists a unique equilibrium for this conflict game and examine the relation between aggregated equilibrium investment (interpreted as conflict intensity) and underlying network characteristics. The derived results have implications for peaceful resolutions of conflicts because neglecting the fact that opponents are embedded into an interrelated conflict structure might have adverse consequences for conflict intensity.Network games, conflicts, conflict resolution

Common Representation of Information Flows for Dynamic Coalitions

We propose a formal foundation for reasoning about access control policies within a Dynamic Coalition, defining an abstraction over existing access control models and providing mechanisms for translation of those models into information-flow domain. The abstracted information-flow domain model, called a Common Representation, can then be used for defining a way to control the evolution of Dynamic Coalitions with respect to information flow

Negotiation Support System with Third Party Intervention

A flexible methodology is developed to specify how a desired outcome can be reached in a given conflict by determining the preference structures required for the decision makers to find it stable. The objective of this methodology is to provide informed collective negotiation support. This new methodology is generated by reverse engineering some Graph Model for Conflict Resolution (GMCR) procedures and is therefore called "Inverse GMCR". The essence of Inverse GMCR is to determine whether and how a strategic conflict can be ideally resolved, which may inform the mediators of strategies to achieve this resolution. Formal definitions and mathematical representations for the new Inverse GMCR methodology are formulated in this thesis. The four basic graph model stability definitions, Nash stability (R), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ) are redefined for Inverse GMCR as Nash IPS, GMR IPS, SMR IPS, and SEQ IPS, respectively where IPS stands for Inverse Preference Structure. Pattern recognition and inverse calculations are used to generate strategies that permit mediators to negotiate a desired resolution. Mediation, or third party intervention, is strengthened by utilizing the insightful information provided by the Inverse GMCR methodology and the negotiation support system. An in-depth strategic investigation and analysis of a complex water conflict in the Middle East is carried out to test and refine the algorithms developed here. This conflict occurred along the Euphrates River and had three key time points when the conflict escalated to the brink of a full scale war, in 1975, 1990, and 1998. A comprehensive analysis of the conflict is undertaken, including bilateral and trilateral negotiations both before and after mediation. Based on the new Inverse GMCR and existing algorithms, an advanced decision support system (DSS) is designed, built, and illustrated using real world conflicts. The new DSS, called GMCR+, is capable of handling a wide variety of decision problems involving two or more decision makers (DMs). Given the DMs, the options or courses of action available to each of them, and each DM's relative preferences over the scenarios or states that could occur, GMCR+ can calculate stability and equilibrium results according to a range of solution concepts that explain human behavior under conflict. Then the inverse component of the DSS, GMCR+, can determine the preference rankings of DMs that produce stable states and equilibria as specified by the user. Other features incorporated into GMCR+ include coalition analysis, graph and tree diagram visualization, narrative reporting of results, and a tracing feature that shows how the conflict could evolve from a status quo state to a desirable equilibrium or other specified outcome. The system GMCR+ has a modular design in order to facilitate the addition of further advances. The overarching purpose of this research is to provide a simple and intuitive methodology to better understand and resolve actual conflicts. The GMCR+ DSS was developed in order to implement the Inverse GMCR methodology in the context of the standard graph model functions and in a practical way. Analysis and investigation of real world examples demonstrate the applicability of the methodology in various domains