We study budget aggregation under $\ell_1$-utilities, a model for collective decision making in which agents with heterogeneous preferences must allocate a public budget across a set of alternatives. Each agent reports their preferred allocation, and a mechanism selects an allocation. Early work focused on social welfare maximization, which in this setting admits truthful mechanisms, but may underrepresent minority groups, motivating the study of proportional mechanisms. However, the dominant proportionality notion, single-minded proportionality, is weak, as it only constrains outcomes when agents hold extreme preferences. To better understand proportionality and its interaction with welfare and truthfulness, we address three questions. First, how much welfare must be sacrificed to achieve proportionality? We formalize this via the price of proportionality, the best worst-case welfare ratio between a proportional mechanism and Util, the welfare-maximizing mechanism. We introduce a new single-minded proportional and truthful mechanism, UtilProp, and show that it achieves the optimal worst-case ratio. Second, how do proportional mechanisms compare in terms of welfare? We define an instance-wise welfare dominance relation and use it to compare mechanisms from the literature. In particular, we show that UtilProp welfare-dominates all previously known single-minded proportional and truthful mechanisms. Third, can stronger notions of proportionality be achieved without compromising welfare guarantees? We answer this question in the affirmative by studying decomposability and proposing GreedyDecomp, a decomposable mechanism with optimal worst-case welfare ratio. We further show that computing the welfare-dominant decomposable mechanism, UtilDecomp, is NP-hard, and that GreedyDecomp provides a 2-approximation to UtilDecomp in terms of welfare.
We study a participatory budgeting problem of aggregating the preferences of agents and dividing a budget over the projects. A budget division solution is a probability distribution over the projects. The main purpose of our study concerns the comparison between the system optimum solution and a fair solution. We are interested in assessing the quality of fair solutions, i.e., in measuring the system efficiency loss under a fair allocation compared to the one that maximizes (egalitarian) social welfare. This indicator is called the price of fairness. We are also interested in the performance o…
Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of members of the community. Different rules have been used to aggregate participants' votes. Past research has studied the trade-off between notions of social welfare and fairness in the multi-winner setting (a special case of participatory budgeting with identical project costs) by Lackner and Skowron (2020). But there is little understanding of this trade-off in the more general PB setting. This paper provides a theoretical and empirical study of the worst-case guarantees of several comm…
Participatory budgeting is a method used by city governments to select public projects to fund based on residents' votes. Many cities use participatory budgeting at a district level. Typically, a budget is divided among districts proportionally to their population, and each district holds an election over local projects and then uses its budget to fund the projects most preferred by its voters. However, district-level participatory budgeting can yield poor social welfare because it does not necessarily fund projects supported across multiple districts. On the other hand, decision making that o…
The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016 and TEAC 2019) that an allocation maximizing the NSW is envy-free up to one good (EF1). In this paper, we are interested in the fairness of the NSW in a budget-feasible allocation problem, in which each item has a cost that will be incurred to the agent it is allocated to, and each agent has a budget constraint on the total cost of items she receives. We sh…
We study the efficiency guarantees in the simple auction environment where the auctioneer has one unit of divisible good to be distributed among a number of budget constrained agents. With budget constraints, the social welfare cannot be approximated by a better factor than the number of agents by any truthful mechanism. Thus, we follow a recent work by Dobzinski and Leme (ICALP 2014) to approximate the liquid welfare, which is the welfare of the agents each capped by her/his own budget. We design a new truthful auction with an approximation ratio of $\frac{\sqrt{5}+1}{2} \approx 1.618$, impro…
We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service of the agents. These environments include position auctions where slots with decreasing click-through rates are auctioned to advertisers. We generalize and characterize the envy-free benchmark from Hartline and Yan (2011) to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue. We give prior-free mech…
International Institute of Information Technology (IIIT), Hyderabad（海得拉巴国际信息技术学院）
Civic Crowdfunding (CC) uses the ``power of the crowd'' to garner contributions towards public projects. As these projects are non-excludable, agents may prefer to ``free-ride,'' resulting in the project not being funded. For single project CC, researchers propose to provide refunds to incentivize agents to contribute, thereby guaranteeing the project's funding. These funding guarantees are applicable only when agents have an unlimited budget. This work focuses on a combinatorial setting, where multiple projects are available for CC and agents have a limited budget. We study certain specific c…
This paper aims to investigate how a central authority (e.g. a government) can increase social welfare in a network of markets and firms. In these networks, modeled using a bipartite graph, firms compete with each other \textit{à la} Cournot. Each firm can supply homogeneous goods in markets which it has access to. The central authority may take different policies for its aim. In this paper, we assume that the government has a budget by which it can supply some goods and inject them into various markets. We discuss how the central authority can best allocate its budget for the distribution of …
In settings where players have a limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor then the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one incentive-compatible auction that always outputs a Pareto-efficient solution, or that no truthful mechanism can…
We study the efficiency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis [Mathematics of Operations Research, 2004], a long list of papers studied the price of anarchy (in terms of the social welfare --- the total users' va…
We study incentive compatible mechanisms for Combinatorial Auctions where the bidders have submodular (or XOS) valuations and are budget-constrained. Our objective is to maximize the \emph{liquid welfare}, a notion of efficiency for budget-constrained bidders introduced by Dobzinski and Paes Leme (2014). We show that some of the known truthful mechanisms that best-approximate the social welfare for Combinatorial Auctions with submodular bidders through demand query oracles can be adapted, so that they retain truthfulness and achieve asymptotically the same approximation guarantees for the liqu…
Welfare, Improvability, and Variance: A Principal-Agent Approach to Optimal Benchmark Item Aggregation
Department of Economics & Computer Science（经济与计算机科学系）；Institute for Computational and Mathematical Engineering（计算与数学工程研究所）；Department of Computer Science（计算机科学系）；Department of Aeronautics & Astronautics（航空与航天系）
According to the proportional allocation mechanism from the network optimization literature, users compete for a divisible resource -- such as bandwidth -- by submitting bids. The mechanism allocates to each user a fraction of the resource that is proportional to her bid and collects an amount equal to her bid as payment. Since users act as utility-maximizers, this naturally defines a proportional allocation game. Recently, Syrgkanis and Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with respect to the social welfare and presented a lower bound of 26.8% on the price…
We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. Th…
Incorporating budget constraints into the analysis of auctions has become increasingly important, as they model practical settings more accurately. The social welfare function, which is the standard measure of efficiency in auctions, is inadequate for settings with budgets, since there may be a large disconnect between the value a bidder derives from obtaining an item and what can be liquidated from her. The Liquid Welfare objective function has been suggested as a natural alternative for settings with budgets. Simple auctions, like simultaneous item auctions, are evaluated by their performanc…
We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under $\ell_1$ preferences -- for which a voter's disutility is given by the $\ell_1$ distance between the aggregate division and the division he or she most prefers -- the social welfare-maximizing mechanism, which minimizes the average $\ell_1$ distance between the outcome and each voter's pro…
We consider dominant strategy implementation in private values settings, when agents have multi-dimensional types, the set of alternatives is finite, monetary transfers are allowed, and agents have quasi-linear utilities. We show that any implementable and neutral social choice function must be a weighted welfare maximizer if the type space of every agent is an $m$-dimensional open interval, where $m$ is the number of alternatives. When the type space of every agent is unrestricted, Roberts' theorem with neutrality \cite{Roberts79} becomes a corollary to our result. Our proof technique uses a …
This paper considers prior-independent mechanism design, namely identifying a single mechanism that has near optimal performance on every prior distribution. We show that mechanisms with truthtelling equilibria, a.k.a., revelation mechanisms, do not always give optimal prior-independent mechanisms and we define the revelation gap to quantify the non-optimality of revelation mechanisms. This study suggests that it is important to develop a theory for the design of non-revelation mechanisms. Our analysis focuses on welfare maximization in single-item auctions for agents with budgets and a natura…
We study a participatory budgeting problem, where a set of strategic agents wish to split a divisible budget among different projects, by aggregating their proposals on a single division. Unfortunately, the straight-forward rule that divides the budget proportionally is susceptible to manipulation. In a recent work, Freeman et al. [arXiv:1905.00457] proposed a class of truthful mechanisms, called moving phantom mechanisms. Among others, they propose a proportional mechanism, in the sense that in the extreme case where all agents prefer a single project to receive the whole amount, the budget i…
We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey-Clarke-Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using the liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria.
We design novel mechanisms for welfare-maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, budget-balance constraints and give constant-factor approximations to the optimal social welfare. We improve previous results in several settings: Our main focus is on mat…
We study the Nash Social Welfare problem: Given $n$ agents with valuation functions $v_i:2^{[m]} \rightarrow {\mathbb R}$, partition $[m]$ into $S_1,\ldots,S_n$ so as to maximize $(\prod_{i=1}^{n} v_i(S_i))^{1/n}$. The problem has been shown to admit a constant-factor approximation for additive, budget-additive, and piecewise linear concave separable valuations; the case of submodular valuations is open. We provide a $\frac{1}{e} (1-\frac{1}{e})^2$-approximation of the {\em optimal value} for several classes of submodular valuations: coverage, sums of matroid rank functions, and certain matchi…
We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical "unconstrained" mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budget-constrained Bayesian MD to unconstrained Bayesia…
We study online auction settings in which agents arrive and depart dynamically in a random (secretary) order, and each agent's private type consists of the agent's arrival and departure times, value and budget. We consider multi-unit auctions with additive agents for the allocation of both divisible and indivisible items. For both settings, we devise truthful mechanisms that give a constant approximation with respect to the auctioneer's revenue, under a large market assumption. For divisible items, we devise in addition a truthful mechanism that gives a constant approximation with respect to t…
Who Bears the Burden? Learning Responsibility for Shared Constraints in Multi-Agent Reinforcement Learning
Massachusetts Institute of Technology（麻省理工学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Stanford University（斯坦福大学）；University of California, Berkeley（加州大学伯克利分校）
We investigate computational and mechanism design aspects of scarce resource allocation, where the primary rationing mechanism is through waiting times. Specifically we consider allocating medical treatments to a population of patients. Each patient needs exactly one treatment, and can choose from $k$ hospitals. Hospitals have different costs, which are fully paid by a third party ---the "payer". The payer has a fixed budget $B$, and each hospital will have its own waiting time. At equilibrium, each patient will choose his most preferred hospital given his intrinsic preferences and the waiting…
Nanyang Technological University（南洋理工大学）；Technical University of Munich（慕尼黑工业大学）；LAMSADE, Université Paris Dauphine - PSL（LAMSADE，巴黎第九大学-PSL）；Shanghai University of Finance and Economics（上海财经大学）；Ariel University（阿里埃勒大学）；National University of Singapore（新加坡国立大学）
We study the efficiency of simple combinatorial auctions for the allocation of a set of items to a set of agents, with private subadditive valuation functions and budget constraints. The class we consider includes all auctions that allocate each item independently to the agent that submits the highest bid for it, and requests a payment that depends on the bids of all agents only for this item. Two well-known examples of this class are the simultaneous first and second price auctions. We focus on the pure equilibria of the induced strategic games, and using the liquid welfare as our efficiency …
Participatory Budgeting (PB) is a process in which voters decide how to allocate a common budget; most commonly it is done by ordinary people -- in particular, residents of some municipality -- to decide on a fraction of the municipal budget. From a social choice perspective, existing research on PB focuses almost exclusively on designing computationally-efficient aggregation methods that satisfy certain axiomatic properties deemed "desirable" by the research community. Our work complements this line of research through a user study (N = 215) involving several experiments aimed at identifying …
