Preferences in an Open World Ulrich Junker uli.junker@free.fr Abstract. We consider constructive approaches to decision making which allow incomplete preference orders over multiple criteria. Whereas additional preferences may be acquired during the decision making pro- cess, the set of criteria is usually kept fixed. In this paper, we study the addition of new criteria and examine how this may refine or even reverse the existing preferences. We identify essential changes in the preference order and show that these changes provide a compact representation of preference relations in an open world. 1 Introduction We consider constructive approaches to decision making which allow incomplete preference orders over multiple criteria. Whereas additional preferences may be acquired during the decision making process, the set of criteria is usually kept fixed. We believe that this assumption is not realistic and that the discovery of new dimensions or the merging of different viewpoints may lead to the discov- ery of new preferences that could not be formulated within the more restricted viewpoints. In this paper, we propose a more realistic preference acquisition model. The key notion is that of enlarging given viewpoints. The notion of a viewpoint is used by [2] to describe an independent way of analyzing, evaluating, and comparing alternative actions. In collaborative decision making, different agents want to make a common decision by comparing the outcomes of the actions. As different agents may prefer different outcomes, each agent has a particular viewpoint and these viewpoints have different preference relations. In multi-criteria decision making, multiple outcomes of the actions may be compared independently of each other. Each of these outcomes constitutes a criterion for evaluating and comparing the actions. For example, we may compare the available hotels for a night stop by criteria such as their price and their distance to the airport. Each of these criteria can constitute an independent viewpoint. In this case, any trade-off between the two criteria price and distance is as good as the other those trade-offs. However, multiple criteria can also be combined into a single viewpoint. If the decision maker has preferences between different price- and distance-combinations, then we encounter a viewpoint which maps the different actions to a combinatorial outcome space defined by price and distance. In the same way as preferences may be acquired or discovered incrementally, it may also happen that new criteria are discovered during such an incremen- tal decision making process. We thus enlarge an existing viewpoint to a new