Ordinal power indices

What is the common point between the affectation of students to universities (in particular, in
France, the Parcoursup algorithm), the influence of someone in a social network (like Twitter), the
responsibility of a formula in the inconsistency of a belief base, the impact and synergy of some criteria
in a multi-criteria decision making situation? In all these situations we are confronting with a set of
objects/persons on which we have information on the results of some coalitions/groups, and where it is
interesting (if not decisive) to obtain information on individuals. An idealised version of this problem
has been studied for long in (cooperative) game theory, especially under the notion of power index.
But in real situations, like the ones given above, we are far from this idealised setting. In particular
we often lack of information, and in a lot of applications we only have ordinal information (what
coalition performs better, or is preferable, to another, etc.). In this project we want to provide a more
flexible theory of cooperative interaction situations and power indices based on the evidence that the nature of available information about the interaction of individuals and groups is mostly ordinal.

The objective of the internship will be to investigate theoretically and through computer simulations, one (or several) of the following issues :
- the impact of considering domain restrictions where we consider only a specific subset of the possible orders among the coalitions of agent.
- incomplete or adversarial preferences. In incomplete preferences, some of the coalitions are not ranked. In adversarial domains, agents can form coalition with agents of her type and we only have comparisons between adversarial coalitions.

The internship proposal is related to the ANR project Themis (involving LIP6, LAMSADE and CRIL). The student will participate to project meetings and seminar.

Encadrants : Aurélie Beynier(LIP6), Nicolas Maudet (LIP6), Meltem Oztürk (LAMSADE, Dauphine)

LIP6, Sorbonne Université
Beynier/ Maudet/ Oztürk
Référent Universitaire: 
2 022

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