Abstract
A public divisible resource is to be divided among
projects. We study rules that decide on a distribution
of the budget when voters have ordinal preference
rankings over projects. Examples of such portioning
problems are participatory budgeting, time shares,
and parliament elections. We introduce a family of
rules for portioning, inspired by positional scoring
rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive
value with each rank in a vote, and an aggregation
function such as leximin or the Nash product. Our
family contains well-studied rules, but most are new.
We discuss computational and normative properties
of our rules. We focus on fairness, and introduce the
SD-core, a group fairness notion. Our Nash rules
are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient