Choix social et partage équitable : Une analyse mathématique a posteriori des élections législatives et présidentielles de 2006 et 2011 en RDC

The purpose of this master thesis is to have in a simple and detailed way the significant results of social choice theory and to study the resource sharing (goods or responsibilities) between petitioning agents in a proof of election. While analyzing social choice functions more insight, we present for each of them, with supporting examples, the difficulties and insufficiencies related to the aggregation of the individual preferences of each community member. We then have some theoretical results allowing the understanding of the nature and the magnitude of these difficulties. In addition, we study the situation of African societies in general, and that of the Democratic Republic of Congo in particular, therefore sort out social choice function which is the most appropriate to them. Meanwhile, we take into account the fair distribution of goods and work for the common benefit of society members, which is the guarantee of welfare for individuals, stability and social peace. These are social values seldom found in Africa. We finally study the properties of the recommended social choice function and possibly present its strength and weaknesses, its advantages and disadvantages when used as a mode of poll.