A Short Survey

Different types of graphical representation for local preferences have been proposed in the literature. Graphs may be directed or not. Modeling may be quantitative or qualitative. Principles for extending local preferences to complete configurations may be based on different independence assumptions. Some extensions of such graphical representation settings to multiple agent preferences have been proposed, with different ways of handling agents: they may be viewed just as a set of individual agents, or described in terms of attribute values inducing a partition of the set of agents in terms of subcategories, or they may be reduced to some anonymous statistical counting. The fact that preferences pertain to multiple agents raises the question of either working with a collective graphical representation or aggregating individual preferences, the preferences of each agent being then represented as a graph. Moreover the multiple agent nature of the representation enriches the types of preference queries that can be addressed. The purpose of this short note is to start with a brief survey of the main graphical preference models found in the literature, such as CP-nets, π-pref nets, GAI networks, and to discuss their multiple agent extensions in an organized way, with a view to understand how the different representation options could be combined when possible.