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Decision theory has a solid background in preference elicitation, modelling
and aggregation. However, the presence of huge amount of information as well as of combinatorial structures on the space of the alternatives to take into account imposes new constraints on the languages and models to be used. Typical examples include data fusion, combinatorial voting, consensus procedures, non conventional preference models. New structures have to be conceived, new axiomatic approaches have to be studied (specially conjoint measurement theory) and new efficient algorithms have to be designed. Specific subjects which are going to be considered include:
- Compact representation languages. Many applications require representation of and reasoning about preferences in combinatorial domains. For instance, in the context of resource allocation of indivisible goods each stake-holder will have to manage their preferences over a number of alternatives that is exponential in the number of goods. Computer scientists have developed techniques that can be applied successfully to such problems. An example are logic-based languages developed in Artificial Intelligence. Another example are the "bidding languages", designed specifically for the representation of preferences (bids) in the context of combinatorial auctions. These languages share a number of features, but to date there has been no systematic study of their respective advantages and drawbacks, in terms of expressive power, comparative succinctness, or computational complexity of associated decision and optimisation problems. The proposed project would gather a unique mix of expertises that will make such a study feasible.
- Positive and Negative Reasons in Preference Modelling. When decision makers express their preferences they often use both positive sentences (I like $X$) and negative sentences (I do not like $Y$). The problem which arises here is how to take into account positive reasons (supporting a preference statement) and negative reasons (against a preference statement) in the establishment of a preference model. Bi-polar structures, logic languages, argumentation theory are examples where such concerns have been studied and which are going to be extended in the particular case of preference modelling.
- Conjoint Measurement Theory. The existence of multi-attributed alternatives and the necessity to compute some ``utilities or preferences on such objects gave rise to this field of measurement theory which studies the necessary and sufficient conditions for the existence of ``measurable functions on sets of multi-attributed objects. It turns out that conjoint measurement theory can be used as a general framework for a very large set of preference models used in an extremely variety of cases (most of them quoted in this research project).