Sur les aspects computationnels du vote par approbation. (Computational Aspects of Approval Voting)

The subject of this thesis is the study of computational aspects of approval voting. Mostof the works are theoretical results about computational issues raised by approval voting, in manydi erent settings. Indeed, I use algorithmic techniques like polynomial reductions to prove that manyproblems are di cult to solve in the context of approval voting. However, I also study some questionsthat are more related to classical choice theory, such as manipulability and axiomatic properties ofapproval voting. Moreover, some problems are investigated through experimental analysis.Firstly, I study approval voting in the context of committee elections and multiple referenda.A general family of rules is suggested, for which I show that the winner determination problem isdi cult. Next, I explore extensively the manipulability of these rules, providing general examples ofmanipulation that adapt to any number of voters or candidats. Finally, experimental analysis allowus to get some insights about the number of co-winning committees.Secondly, I focus on a more general setting, approval voting in combinatorial domains. New methodsare suggested for how to use approval voting in this context. First, I study the axiomatic propertiesand the manipulability of these methods.Finally, I study approval voting in the context of incomplete preferences. In the case of single winnerapproval voting, I study the possible and necessary winners problems, and show that they lead tosome questions that are easy to solve and some that are di cult. Then an experimental studyis conducted to evaluate the sensitivity of approval voting to the number of candidates that areapproved by the voters. To conclude, I show that the possible winner problem is di cult for all therules in the literature in the context of multi-winner approval voting.