mCP Nets: Representing and Reasoning with Preferences of Multiple Agents

We introduce mCP nets, an extension of the CP net formalism to model and handle the qualitative and conditional preferences of multiple agents. We give a number of different semantics for reasoning with mCP nets. The semantics are all based on the idea of individual agents voting. We describe how to test optimality and preference ordering within a mCP net, and we give complexity results for such tasks. We also discuss whether the voting schemes fairly combine together the preferences of the individual agents. Introduction and Motivation In many situations, we need to represent and reason about the simultaneous preferences of several agents, and to aggregate such preferences (see for example (Yager 2001)). As a motivating example, suppose you invite three friends round for dinner. Alice prefers fish to beef. Bob, on the other hand, prefers beef to fish. Finally, Carol is like Alice and prefers fish to beef. What do you cook? Both choices are Pareto optimal. If you cook fish then changing to beef will be more preferred by Bob, but less preferred by Carol and Alice. Similarly, changing from beef to fish will be more preferred by Alice and Carol, but less preferred by Bob. However, fish is perhaps the “best” choice according to a majority ordering as it is the preferred choice for both Alice and Carol, whilst beef is the preferred choice for only Bob. Which wine do you serve with the main course? Alice, Bob and Carol are fortunately more consistent here. If it is fish then they all prefer white wine to red. However, if it is beef, then they all prefer red wine to white. Finally, do you serve cheese or dessert? Even though you are happy to serve everyone their own choice of cheese or dessert, you must still determine and reason about your friends’ preferences. For example, if his girlfriend Alice has cheese, Bob prefers cheese to dessert. However, if his girlfriend Alice has dessert, he will not be able to resist so he prefers dessert to cheese. This example demonstrates that multiple agents may have some features in common but not all (e.g. the main dish is common to all but the choice of cheese or dessert is not), that there may no longer be a single optimal solution, that there Copyright c © 2004, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. '&%$ !"# A