Option prioritization for unknown preference

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada.

Conflict of environmental sustainable development as a common phenomenon can be seen everywhere in life. To capture consensus problems of decision makers (DMs) in conflict, a consensus and non-consensus fuzzy preference relation (FPR) matrix is proposed to the framework of the Graph Model for Conflict Resolution (GMCR). Concentrating on the case of two DMs within GMCR paradigm, four standard fuzzy solution concepts are developed into eight fuzzy stability definitions which can fully represent DMs’ behavior characteristics of win-win and self-interested. To demonstrate how the novel GMCR methodology proposed in this paper can be conveniently utilized in practice, it is then applied to an environmental sustainable development conflict with two DMs. The results show that the general fuzzy equilibrium solutions are the intersection of consensus fuzzy equilibrium and non-consensus fuzzy equilibrium. Therefore, the GMCR technique considering DMs’ consensus can effectively predict the various possible solutions of conflict development under different DMs’ behavior preferences and provide new insights for analysts into a conflict.

Conflict is an inevitable social phenomenon and the analysis of it can effectively resolve disputes, improve the position of decision makers (DMs), forecast compromise solutions as well. At present, the Graph Model for Conflict Resolution (GMCR), a completely non-quantitative decision support system (DSS) based on DM’s ordinal preference information, is constructed to combat conflict analysis complicated by multiple participant or multiple criteria or both. The purpose of the study is to introduce an overview of GMCR in conflict analyzing through bibliometrics. In order to achieve this goal, a systematic review of articles in leading journals of Web of Science Core Collection (WoSCC) during 1987–2019 is posed, referring to the distribution of countries, institutions, authors, subjects and journals, research topics and hotspots exploration as well as frontiers prediction, by utilizing VOSviewer and CiteSpace. The contributions of this study are not only providing a handy method to grasp generalized scientific research situation, but also demonstrating status quo and emerging trends of GMCR for researchers and everyone who interested in.

Many solution concepts have been proposed within the Graph Model for Conflict Resolution to represent many behaviors that decision makers (DMs) can have in strategic settings. Among these solution concepts, the limited move stability stands out because it allows analyzing the conflict a variable number of steps forward, taking into account the preferences of all DMs involved in the conflict. However, for conflicts involving more than two DMs, there are two definitions of limited move stability that we argue to have undesired properties. For that reason, we present two alternative definitions for limited move stability for conflicts with multiple DMs, called: Alternative Limited-Move stability with Cooperative Coalition ( $$L_h^{CC}$$ ) and Alternative Limited-Move stability with Individualistic Coalition ( $$L_h^{CI}$$ ). Moreover, we obtained results relating these concepts to classical GMCR stability concepts. Furthermore, we provide results that establish the equivalence among the stability notions $$L_h^{CC}$$ , $$L_h^{CI}$$ and $$\text {Maximin}_h$$ , for conflicts in which the DMs belonging to the opposing coalition have equal and completely opposite preferences to those of the focal DM. An application to the Elmira conflict illustrates the usefulness of the proposed concepts in a real conflict situation.

A new analysis technique, appropriate to situations of high preference uncertainty, is added to the graph model for conflict resolution methodology. Interval fuzzy stabilities are now formulated, based on decision makers’ (DMs’) interval fuzzy preferences over feasible scenarios or states in a conflict. Interval fuzzy stability notions enhance the applicability of the graph model, and generalize its crisp and fuzzy preference-based stability ideas. A graph model is both a formal representation and an analysis procedure for multiple participant-multiple objective decisions that employs stability concepts representing various forms of human behavior under conflict. Defined based on a type-2 fuzzy logic, an interval fuzzy preference for one state over another is represented by a subinterval of [0, 1] indicating an interval-valued preference degree for the first state over the second. The interval fuzzy stabilities put forward in this research are interval fuzzy Nash stability, interval fuzzy general metarational stability, interval fuzzy symmetric metarational stability, and interval fuzzy sequential stability. A state is interval fuzzy stable for a DM if moving to any other state is not adequately desirable to the DM; where adequacy is measured by the interval fuzzy satisficing threshold of the DM and farsightedness, involving possible moves and countermoves by DMs, is determined by the interval fuzzy stability notion selected. Note that infinitely many degrees in an interval-valued preference are preserved in characterizing the desirability of a move. A state from which no DM can move to any sufficiently desirable scenario is an interval fuzzy equilibrium, and is interpreted as a possible resolution of the strategic conflict under study. The new stability concept is illustrated through its application to an environmental conflict that took place in Elmira, Ontario, Canada. Insightful results are identified and discussed.

We present a generalization of the graph model for conflict resolution, introducing the possibility of decision makers (DMs) expressing their preferences among the possible scenarios through probabilistic preferences. In this new scenario, four stability definitions (solution concepts) are proposed: 1) α-Nash stability; 2) (α, β)-metarationality; 3) (α, β)-symmetric metarationality; and 4) (α, β, γ)-sequential stability. We deal with conflicts that involve two or more DMs. Relationships between these definitions are demonstrated, as well as an analysis of how the values of the parameters α, β, and y influence the set of stable states is made. Applications of the proposed model to conflicts involving two and three DMs are presented. The analysis of these applications highlights the advantages gained by allowing individuals to express their preferences probabilistically.

This paper proposes a new algebraic definition that facilities calculating of Stackelberg stability in a graph model for conflict resolution with two decision makers. Most stability definitions used in the graph model methodology place decision makers at the same level, in the sense that their roles are symmetric. In practice, however, one decision maker may join by forcing the other to respond to his or her decision. So, to be applied, a model must specify the leader and the follower. Stackelberg stability can be defined logically, but an algorithm to implement it has not been developed until now, due to its complicated recursive formula. To permit Stackelberg stability to be calculated efficiently and encoded conveniently, within a decision support system, an algebraic test for the stability is developed. This algebraic representation of Stackelberg stability is easy to implement and interpret. A superpower military confrontation is used to illustrate how Stackelberg stability can be employed to a real-world application using the new approach.KeywordsConflict analysisDecision makerAlgebraic expressionsStackelberg stabilityGraph modelOrdinal preferences

For hundreds of years, conflicts in water sharing have existed all around the globe. Cauvery River, in the southern part of India, has been in the midst of such conflict for the last 130 years. Historically, the conflict has been about the right to use water and the states/provinces in conflict have used the water from the river for agricultural purposes. Due to industrialization in the late 1980s and increasing population, water availability in the region has become stressed. Climate change has exacerbated the region’s water availability issues. Faltering rainfall has caused unrest in the region, and the traditional methods of water sharing are dwindling under political pressure. Without a climate change strategy, the governments of these states will never be able to solve this complex issue at hand. The Graph Model for Conflict Resolution (GMCR) is applied to understand the nuances of this conflict. It models the preferences of the decision-makers (the states of Tamil Nadu and Karnataka) and the common option (goal) they can reach to potentially solve the conflict. Fuzzy preferences along with option prioritization is also applied to this conflict in order to account for the uncertainties in the decision-makers’ preferences. The purpose of this paper is to nudge decision-makers in a productive direction to overcome the long-impending political standoff, while introducing a new methodology of looking into this old conflict.

In this paper, status quo analysis is addressed by using both logical and matrix representations in the graph model with strength of preference. The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. The graph model has entertained diverse preference structures to characterize decision-makers' (DMs) preference over feasible states, including simple preference, preference uncertainty, and strength of preference. The ¿simple preference¿ structure consists of a strict preference relation and an indifference relation to represent a DM's preference for one state relative to another. Another ¿strength of preference¿ framework allows a DM to express its strong or mild preference for one state over another, as well as the indifference relation. When a graph model is established for a strategic conflict, the standard practice is to carry out a stability analysis first, and then, followed by a post-stability analysis such as coalition analysis and status quo analysis. Status quo analysis complements stability analysis and aims at assessing whether predicted equilibria are attainable from the status quo. So far, status quo analysis has been examined for the graph model with simple preference and both logical and matrix representations of status quo analysis have been developed. This article extends these results to handle status quo analysis for the graph model with strength of preference. The algebraic method is illustrated using a conflict over proposed bulk water exports from Lake Gisborne in Newfoundland.

On some properties of limited move stability, generalized metarationality, and policy equilibrium in bilateral conflicts

The graph model for conflict resolution (GMCR), along with its associated decision support system GMCR II, is employed for systematically studying the strategic aspects of a conflict existing in Per Aru basin. National Water Supply & Drainage Board has planned to build a reservoir on the Per Aru for the sole purpose of supplying drinking water to the urban areas of Vavuniya district. People who will be affected due to the inundation of their lands have shown resistance to the construction of the reservoir. Moreover, government organizations such as Forest Department and Wildlife Department also have expressed their concerns over the construction of a reservoir since that will have diverse impacts on forest lands and wildlife in the area that will be inundated by the proposed reservoir. The above three stakeholders, viz., National Water Supply & Drainage Board, affected people and government organizations suggest a few options to solve the conflict.The options are specific actions that can actually occur in a conflict. The decision support system, GMCR II, was used to investigate and resolve this conflict. The paper presents all the steps involved in the modeling of the conflict using GMCR II and analysis of the results obtained from the model. The National Water Supply & Drainage Board accepting to reduce the inundation area and agreeing to release sufficient environmental flow was resulted as the best possible solution acceptable for all the three parties.The solution includes affected people and Government Organizations agreeing for the construction of the reservoir at the original location. ENGINEER, Vol. 47, No. 03, pp. 61-70, 2014

Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia to Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers' interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker's choice, thereby influencing the evolution of the conflict.

Correction to: Investigating Limited-Move Stabilities in the Graph Model for Conflict Resolution with Unknown Preference

Conflict Analysis is a set of techniques to model and analyze a strategic conflict, or policy problem, using models of the purposive behavior of actors. After a review of these methods, the Graph Model for Conflict Resolution, which stands out for the flexibility of its models and the breadth of its analysis, is described in detail. After an historical overview, its development is compared to other Conflict Analysis techniques, including Drama Theory (See the chapter by Bryant, this volume), and to the Non-cooperative Game Theory (Chatterjee, in this volume) that inspired them. The graph model system is prescriptive, aiming to provide a specific decision-maker with relevant and insightful strategic advice. The capacity of the graph model to generate useful advice is emphasized throughout, and illustrated using a real-life groundwater contamination dispute. The description of the graph model includes the basic modeling and analysis components of the methodology and the decision support system GMCR II that has been used to apply it, including both basic (stability) analysis and follow-up analysis. New developments ensure that the next generation of decision support based on the graph model will be much more comprehensive and powerful.

A formal methodology for analyzing the importance of weighing a decision maker℉s attitudes in a conflict is introduced and applied to the problem of negotiating a fair transfer of a brownfield property. A decision maker℉s attitudes are expressed in his consideration of his own preferences, as well as those of his opponents. Dominating attitudes are used to suggest that in a circumstance in which a decision maker takes into account multiple perspectives due to his attitudes, he may favor one perspective more heavily. The analysis of a brownfield acquisition conflict illustrates the types of insights that this methodology reveals.