Positional Social Decision Schemes: Fair and Efficient Portioning

We introduce a new family of social decision schemes, which can be viewed as a probabilistic counterpart of positional scoring rules. A rule in this family is defined by a scoring vector associating a positive value with each rank in a vote, and an aggregation function. We focus on two types of aggregation functions: those corresponding to egalitarianism (min, and leximin) and the Nash product. We examine the computation of the rules and their normative properties. We argue that some of these rules are particularly useful for time-sharing in an efficient and fair manner, or more generally for portioning.