Sur la fusion de croyances égalitaire

There are two main sub-families of IC merging operators : majority operators and arbitration ones. While many majority belief merging operators have been defined so far, only few arbitration belief merging operators have been identified. In this paper, we study the more general notion of egalitarian belief merging. We translate to the belief merging framework two egalitarian conditions coming from social choice theory : Sen-Hammond equity, and Pigou-Dalton property. We show that the distance-based merging operators satisfying Sen-Hammond equity are mainly those for which leximax is used as the aggregation function. We also introduce two new families of belief merging operators, based respectively on the median and on an aggregated sum (Lorenz curves). We identify the rationality properties satisfied by these operators and study in particular their egalitarian behaviour.