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Exploring Welfare Maximization and Fairness in Participatory Budgeting

Series: Ph.D (Engg.)Thesis Defence -ONLINE

Speaker: Gogulapati Sreedurga Ph.D (Engg.) student Dept. of CSA

Date/Time: Dec 22 16:30:00

Location: Microsoft teams - Online

Faculty Advisor: Prof. Y. Narahari

Abstract:
Participatory budgeting (PB) is a voting paradigm for distributing a divisible resource, usually called a budget, among a set of projects by aggregating the preferences of individuals over these projects. It is implemented quite extensively for purposes such as government allocation of funds to public projects and funding agencies selecting research proposals to support. This dissertation aims to define welfare related and fairness related objectives for different PB models and proposes novel PB mechanisms that optimize these objectives. The thesis is divided into two main parts, focusing on dichotomous and ordinal preferences, respectively. Further, each part considers two cases: (i) the cost of each project is restricted to a single value and partial funding is disallowed and (ii) the cost of each project is flexible and can assume multiple values.

Part 1: Participatory Budgeting under Dichotomous Preferences

Welfare Maximization and Fairness under Restricted Costs

Egalitarianism holds significance in PB, serving as both a welfare and fairness objective. Our work introduces and studies a natural egalitarian rule, Maxmin Participatory Budgeting (MPB). The study consists of two parts: computational analysis and axiomatic analysis. In the computational part, we prove that MPB is weakly NP-hard and propose FPT algorithms and an approximation algorithm. We also establish an upper bound on the achievable approximation ratio for exhaustive strategy-proof PB algorithms. In the axiomatic part, we investigate MPB by generalizing existing axioms and introducing a new fairness axiom called maximal coverage, which MPB satisfies.

Welfare Maximization under Flexible Costs

In this work, we present a model where projects have a discrete set of permissible costs, reflecting different levels of project sophistication. Voters express their preferences by specifying upper and lower cost bounds for each project. The outcome of a PB rule involves selecting a subset of projects and determining their costs. We explore different utility concepts and welfare-maximizing rules. We demonstrate that positive findings from single-cost projects can be extended to our framework with multiple permissible costs and we further analyze the fixed parameter tractability of the problems. We also propose axioms rich on intuition and evaluate their compatibility with PB rules.


Part 2: Participatory Budgeting under Ordinal Preferences

Welfare Maximization and Fairness under Restricted Costs

This work focuses on incomplete weakly ordinal preferences and has two logical components. In the first component, we introduce dichotomous translation rules and the PB-CC rule which respectively expand on existing welfare-maximizing rules for dichotomous and strictly ordinal preferences. We show that our expansions largely maintain and even enhance the computational and axiomatic properties of these rules. We also propose a new relevant axiom, pro-affordability. The second component introduces the novel class of average rank-share guarantee rules to address fairness in participatory budgeting with ordinal preferences, overcoming limitations of existing fairness concepts in the literature.

Fairness under Flexible Costs

This work assumes that project costs have no restrictions, thereby making the model equivalent to random social choice. We investigate fairness in social choice under single-peaked preferences. Existing literature has extensively examined the construction and characterization of social choice rules in the single-peaked domain. We extend these findings by incorporating fairness considerations. To address group-fairness, we partition voters into logical groups based on attributes like gender or location. We introduce group-wise anonymity to capture fairness within each group and propose weak and strong notions of fairness to ensure fairness across groups. We characterize deterministic and random social choice rules that achieve group-fairness. We also explore the case without groups and provide more precise characterizations of rules achieving individual-fairness.


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