  Participatory budgeting (PB) has attracted much attention in recent times due
to its wide applicability in social choice settings. In this paper, we consider
indivisible PB which involves allocating an available, limited budget to a set
of indivisible projects, each having a certain cost, based on the preferences
of agents over projects. The specific, important, research gap that we address
in this paper is to propose classes of rules for indivisible PB with weak
rankings (i.e., weak ordinal preferences) and investigate their key algorithmic
and axiomatic issues. We propose two classes of rules having distinct
significance and motivation. The first is layered approval rules which enable
weak rankings to be studied by carefully translating them into approval votes.
The second is need-based rules which enable to capture fairness issues. Under
layered approval rules, we study two natural families of rules:
greedy-truncation rules and cost-worthy rules. The paper has two parts. In the
first part, we investigate algorithmic and complexity related issues for the
proposed rules. In the second part, we present a detailed axiomatic analysis of
these rules, for which, we examine and generalize axioms in the literature and
also introduce a new axiom, pro-affordability. The paper helps to highlight the
trade-offs among practical appeal, computational complexity, and axiomatic
compliance of these rules.
