Objective
A wide research program on preference aggregation and modelling will be undertaken.
It will involve advances in:
- the normative theory of preference aggregation;
- the theory of rationality of choice functions;
- the cooperative game theory;
- the representative consumer theory;
- the theory of manipulability of social choice correspondences;
- implementation theory;
- the theory of rights;
- applications to particular decision problems. The professional scientific level and the complementary nature of the involved teams along with the research cooperation should enable the following results to be obtained:
- Axiomatic characterization of some preference aggregation rules that do not satisfy Independence of Irrelevant Alternatives.
- Determination of the Condorcet type properties of the approval voting with respect to a probabilistic measure. Determination of the geometrical properties of the Kemeny rule.
- Assessment in some economic contexts of the democratic electoral competition as defining an acceptable social choice correspondence (SCC).
- Determination of the properties of tournament solutions translated to the cases of weak and/or incomplete tournaments.
- New asymptotic results on the transitivity of social preferences derived from cardinal and ordinal individual preferences. Construction and axiomatization of new social choice functions for the class of social choice problems with a fixed alternative and for different scales of individual utility measurement. Application of the results to finding and axiomatization of new cooperative game solutions. Sufficient conditions that validate the (very common) use of single-individual models in the representative consumer problem.
- Clarification of the meaning of continuity assumptions in the fuzzy preference aggregation problem. Mathematical tools for representation of set comparisons in terms of qualitative measurements, with applications to opportunity sets and voting.
- Characterization of rationality of choice function w.r.t. the undominated and the strong maximals of a binary relation. Methods for the coordination of ordinal scales on the basis of combinatorial models.
- Characterizations of multistage aggregation rules based on uncoordinated preference information. Advances in the construction of quadratic objective functions.
- Evaluation of various SCC's ject to different indices of manipulability.This opens a way of using those SCC's for practical purposes knowing in advance their strategic properties. Development of new concepts in the implementation theory. Characterization of learning procedures in the jury problem. Innovations in the theory of rights.
Topic(s)
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14032 Caen
France