ADT 2009 in Venice has been an amazing event, both personally and scientifically. Although unintended, it became the summit of my scientific career and allowed me to present new perspectives on preference modeling to eminent scientists. Thanks to the organizers and a great audience, things excelled!
Preferences guide decision making and guarantee that choice behavior is consistent in recurrent situations with varying options. Decision scientists use preference models to explain, predict, and improve human and organizational decision making. Those preference models include quantitative (cardinal) preferences such as numeric utilities as well as qualitative (ordinal) preferences such as complete preorders.
My own research on preference modeling was driven by the wish to have qualitative models that not only permit reasoning with preferences, but also reasoning about preferences. In this respect I followed the footsteps of Jon Doyle who has laid out this program in great detail. This endeavor can be characterized as applying the methodology of knowledge representation to preferences. Preferences can be represented as any other knowledge in a logical or graphical formalism. This preference representation provides the basis for reasoning with and about preferences, for acquiring and learning preferences, for revising preferences, and for generating explanations of optimality in terms of preferences.
A preference model is based on basic principles (axioms). An example is the transitivity of the preference order: if you prefer speaking to writing and you prefer writing to remaining silent, then you should also prefer speaking to remaining silent. Another important principle is the ceteris-paribus principle, which applies to preferences that are expressed over multiple attributes (multiple criteria) such as the main dish and the drink of a menu. If you prefer meat to fish, all else equal, then you will prefer meat with beer to fish with beer and you will prefer meat with wine to fish with wine. The ceteris-paribus principle supposes that a preference over an attribute or a group of attribute is valid independent of the values of the other attributes as long as those values are equal for the compared options.
The ceteris-paribus principle appears to be quite natural and not very restrictive. Combined with transitivity, the ceteris-paribus principle can nevertheless lead to strong results. If you additionally prefer beer to wine, all else equal, then you will prefer meat with beer to meat with wine and you will prefer fish with beer to fish with wine. By transitivity, you will then prefer meat with beer to fish with wine. Hence, if a preference relation rigorously respects given axioms, then it is possible to deduce new preferences from existing preferences.
But what if you don’t agree to those conclusions? Perhaps you prefer meat to fish and beer to wine in general, but you prefer the combination of fish and wine to the combination of meat and beer? Is there a way to relax the ceteris-paribus principle in certain circumstances and to model the reversal of its conclusions? Indeed, it turns out that quantitative models allow such reversals. Why can’t those qualitative effects of quantitive models be directly captured in a qualitative way?
I first came across those questions about the ceteris-paribus preferences in the concluding remarks of my PhD thesis Relationships between Assumptions . They constituted the starting point for a long-term study of preferences and they drove my research agenda forward. I started to learn more about the rich literature of preference modeling and to construct and explore new preference models and representations. Not all those tentatives were meaningful and I got valuable feed-back from eminent colleagues. Their advice helped me to finally come up with a meaningful qualitative preference model that allows the reversal of preferences.
When stating a ceteris-paribus preference between two values of an attribute, then this means that an option for the first value is preferred to an option for the second value if all other attributes have the same value for those options (all else equal). But how many attributes may be among those other attributes? If the world is closed and all attributes are known in advance, then it is possible to describe the semantics of the ceteris-paribus preference in terms of a preference relation over complete vectors of attribute values. However, what happens in an open world where new attributes may be added and others may be discarded? Will then the ceteris-paribus preference still hold under all possible value combinations for all kinds of unknown attributes?
The paper Preferences in an Open World published in the Proceedings of ADT 2009 provides a first answer to this question. It studies the effects of discovering new criteria when constructing a preference relation and the effects of combining preference relations over different subsets of attributes. The ceteris-paribus principle is applied by default, but its conclusions may be overridden by more specific preference statements. If two persons are choosing a common menu, then one of them may prefer meat to fish while ignoring all other attributes and the other one may prefer beer to wine while ignoring all other attributes. If nothing else is stated, the ceteris-paribus principle will be applied by default, meaning that the couple will prefer meat with beer to fish with wine. However, if this couple explicitly states a preference of fish with wine to meat with beer, then this specific preference will override the conclusions obtained by applying the ceteris-paribus principle to the general preferences. This reverses the preference of meat with beer to fish with wine.
This open-world model of preferences adds flexibility to preference modeling, while preserving the advantages of the existing approaches. Preference statements have a limited scope and are valid if all else attributes in this scope are equal. The scope can be extended in certain circumstances, but not in others. You can thus state preferences even if you don’t know all factors that may influence the validity of those statements. ◉
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