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

Gestão de recursos hídricos: conflito pelo uso da água no açude Epitácio Pessoa - PB.

A gestão das águas do açude Epitácio Pessoa, popularmente conhecido como Boqueirão é de responsabilidade da ANA- Agência Nacional de Águas desde 2000. No entanto, o período de estiagem que iniciou em 2012 vem afetando drasticamente a capacidade de oferta de água deste manancial para atender a todos os usos múltiplos a qual se destina, colocando assim em questão a situação da gestão dessas águas, bem como o papel de cada ator social que depende dessas delas. Partindo-se do pressuposto de que quanto mais escassa e fundamental a água é, mais fonte de conflitos ela se torna, o objetivo deste estudo foi identificar o papel e as formas de atuação dos atores sócias envolvidos com as formas de utilização da água no Açude Epitácio Pessoa através da utilização de uma técnica de análise multicritério. A metodologia de análise de conflitos trade-off é um método que utiliza a análise multicritério para a análise de conflitos, o que a tornou apropriada para ser aplicada neste estudo. Os resultados da pesquisa identificaram 5 (cinco) tipos de conflitos envolvendo os atores sociais que utilizam essas águas e a própria gestão do manancial. Os conflitos apresentados foram de origem Legal, Institucional, Ambiental, Social e Econômico e foram identificados através da técnica de análise multicritérios. A aplicação de todas as etapas do método permitiu um diagnóstico acerca da real situação instalada às margens do açude, bem como os anseios de cada ator social envolvido com as formas de utilização dessas águas, uma vez que, todos dependem desse recurso para sobreviver. De outro lado, encontra-se a necessidade de usar de forma racional essas águas para poder garantir a segurança hídrica da região, fazendo-se necessários estudos que proponham caminhos alternativos para se amenizar esta situação. Sendo assim, o método utilizado propôs 3 alternativas possíveis: a primeira alternativa propõe a continuação das irrigações e a segunda diminuir ainda mais a área irrigada; a terceira alternativa prevê uma compensação financeira para os pequenos agricultores no caso de necessidade de total suspensão das irrigações.Water management weir Pessoa , popularly known as Boqueirao is the responsibility of the National Water Agency - ANA since 2000 . However , the drought that began in 2012 has dramatically affecting the ability of this source of water supply to meet all the multiple uses to which it is intended , thereby calling into question the status of the management of these waters , as well as the role of each social actor that relies on these them . Starting from the assumption that the more scarce and water is fundamental , source of most conflicts it becomes, the aim of this study was to identify the role and ways of acting members involved actors with ways to use the water in the weir Pessoa by using a technique of multi-criteria analysis. The methodology of conflict analysis trade-off is a method that uses multiple criteria analysis for conflict analysis , which made it suitable to be applied in this study . The survey results identified five (5 ) types of conflicts involving social actors who use these waters and the actual management of the stock . Conflicts of origin presented were legal , Institutional , Environmental , Social and Economic and were identified using the technique of multi-criteria analysis . The implementation of all the steps of the method led to a diagnosis of the real situation on the banks of the weir installed as well as the desires of each social actor involved with ways to use these waters, since all depend on that resource to survive . On the other hand , is the need to rationally use these waters in order to ensure water security in the region , making up studies that propose alternative ways to alleviate this situation. Thus , the method proposed three possible alternatives : the first alternative proposes the continuation of irrigation and the second further reduce the irrigated area , the third alternative provides financial compensation for small farmers in case of need for total suspension of irrigation

Constrained Rationality: Formal Value-Driven Enterprise Knowledge Management Modelling and Analysis Framework for Strategic Business, Technology and Public Policy Decision Making & Conflict Resolution

The complexity of the strategic decision making environments, in which busi- nesses and governments live in, makes such decisions more and more difficult to make. People and organizations with access to the best known decision support modelling and analysis tools and methods cannot seem to benefit from such re- sources. We argue that the reason behind the failure of most current decision and game theoretic methods is that these methods are made to deal with operational and tactical decisions, not strategic decisions. While operational and tactical decisions are clear and concise with limited scope and short-term implications, allowing them to be easily formalized and reasoned about, strategic decisions tend to be more gen- eral, ill-structured, complex, with broader scope and long-term implications. This research work starts with a review of the current dominant modelling and analysis approaches, their strengths and shortcomings, and a look at how pioneers in the field criticize these approaches as restrictive and unpractical. Then, the work goes on to propose a new paradigm shift in how strategic decisions and conflicts should be modelled and analyzed. Constrained Rationality is a formal qualitative framework, with a robust method- ological approach, to model and analyze ill-structured strategic single and multi- agent decision making situations and conflicts. The framework brings back the strategic decision making problem to its roots, from being an optimization/efficiency problem about evaluating predetermined alternatives to satisfy predetermined pref- erences or utility functions, as most current decision and game theoretic approaches treats it, to being an effectiveness problem of: 1) identifying and modelling explic- itly the strategic and conflicting goals of the involved agents (also called players and decision makers in our work), and the decision making context (the external and internal constraints including the agents priorities, emotions and attitudes); 2) finding, uncovering and/or creating the right set of alternatives to consider; and then 3) reasoning about the ability of each of these alternatives to satisfy the stated strategic goals the agents have, given their constraints. Instead of assuming that the agents’ alternatives and preferences are well-known, as most current decision and game theoretic approaches do, the Constrained Rationality framework start by capturing and modelling clearly the context of the strategic decision making situation, and then use this contextual knowledge to guide the process of finding the agents’ alternatives, analyzing them, and choosing the most effective one. The Constrained Rationality framework, at its heart, provides a novel set of modelling facilities to capture the contextual knowledge of the decision making sit- uations. These modelling facilities are based on the Viewpoint-based Value-Driven - Enterprise Knowledge Management (ViVD-EKM) conceptual modelling frame- work proposed by Al-Shawa (2006b), and include facilities: to capture and model the goals and constraints of the different involved agents, in the decision making situation, in complex graphs within viewpoint models; and to model the complex cause-effect interrelationships among theses goals and constraints. The framework provides a set of robust, extensible and formal Goal-to-Goal and Constraint-to Goal relationships, through which qualitative linguistic value labels about the goals’ op- erationalization, achievement and prevention propagate these relationships until they are finalized to reflect the state of the goals’ achievement at any single point of time during the situation. The framework provides also sufficient, but extensible, representation facilities to model the agents’ priorities, emotional valences and attitudes as value properties with qualitative linguistic value labels. All of these goals and constraints, and the value labels of their respective value properties (operationalization, achievement, prevention, importance, emotional valence, etc.) are used to evaluate the different alternatives (options, plans, products, product/design features, etc.) agents have, and generate cardinal and ordinal preferences for the agents over their respective alternatives. For analysts, and decision makers alike, these preferences can easily be verified, validates and traced back to how much each of these alternatives con- tribute to each agent’s strategic goals, given his constraints, priorities, emotions and attitudes. The Constrained Rationality framework offers a detailed process to model and analyze decision making situations, with special paths and steps to satisfy the spe- cific needs of: 1) single-agent decision making situations, or multi-agent situations in which agents act in an individualistic manner with no regard to others’ current or future options and decisions; 2) collaborative multi-agent decision making situ- ations, where agents disclose their goals and constraints, and choose from a set of shared alternatives one that best satisfy the collective goals of the group; and 3) adversarial competitive multi-agent decision making situations (called Games, in gamete theory literature, or Conflicts, in the broader management science litera- ture). The framework’s modelling and analysis process covers also three types of con- flicts/games: a) non-cooperative games, where agents can take unilateral moves among the game’s states; b) cooperative games, with no coalitions allowed, where agents still act individually (not as groups/coalitions) taking both unilateral moves and cooperative single-step moves when it benefit them; and c) cooperative games, with coalitions allowed, where the games include, in addition to individual agents, agents who are grouped in formal alliances/coalitions, giving themselves the ability to take multi-step group moves to advance their collective position in the game. ...