Representations of status quo analysis in the graph model for strength of preference

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.