Indivisible Participatory Budgeting under Weak Rankings

TL;DR

This paper introduces new rule classes for indivisible participatory budgeting with weak ordinal preferences, analyzing their algorithmic complexity and axiomatic properties to address fairness and practicality trade-offs.

Contribution

It proposes layered approval and need-based rule classes for weak rankings, along with algorithmic analysis and axiomatic generalizations including a new pro-affordability axiom.

Findings

Layered approval rules can effectively translate weak rankings into approval votes.

Complexity analysis reveals trade-offs between rule simplicity and computational feasibility.

Axiomatic analysis introduces the pro-affordability axiom, expanding fairness criteria.

Abstract

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.