Computing an Approximately Optimal Agreeable Set of Items

We study the problem of finding a small subset of items that is \emph{agreeable} to all agents, meaning that all agents value the subset at least as much as its complement. Previous work has shown worst-case bounds, over all instances with a given number of agents and items, on the number of items that may need to be included in such a subset. Our goal in this paper is to efficiently compute an agreeable subset whose size approximates the size of the smallest agreeable subset for a given instance. We consider three well-known models for representing the preferences of the agents: ordinal preferences on single items, the value oracle model, and additive utilities. In each of these models, we establish virtually tight bounds on the approximation ratio that can be obtained by algorithms running in polynomial time.Comment: A preliminary version appeared in Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI), 201

Approximate Maximin Shares for Groups of Agents

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not necessarily exist, one that gives every agent at least $2/3$ of her share always does. In this paper, we consider the more general setting where we allocate the goods to groups of agents. The agents in each group share the same set of goods even though they may have conflicting preferences. For two groups, we characterize the cardinality of the groups for which a constant factor approximation of the maximin share is possible regardless of the number of goods. We also show settings where an approximation is possible or impossible when there are several groups.Comment: To appear in the 10th International Symposium on Algorithmic Game Theory (SAGT), 201

Democratic Fair Allocation of Indivisible Goods

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least $1/2$ of the agents in each group, and prove that the $1/2$ fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting.Comment: Appears in the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence (IJCAI-ECAI), 201

Budgetary subsidies and the fiscal deficit case of Maharashtra

Introduction: Srivastava and Sen (1997) have advanced a framework for the study of government subsidies in India. Their approach estimates subsidy as the un-recovered costs in the provision of goods and services by the government (see the next section for various definitions of subsidy). Specifically, for the state of Maharashtra, the subsidy was estimated at Rupees 9607.41 Crores (Annexure 15, pg 151, NIPFP report) for the year 1993-94, while the Gross Fiscal Deficit (GFD) for the same year stood at Rupees 2265.3 Crores. As a proportion of Gross State Domestic Product (GSDP), these magnitudes were 8.5 and 2 per cent, respectively. The estimated subsidy constituted about 65 (73) per cent of the total (revenue) expenditure.5 Contrast this with the budgetary subsidies estimated between 2 and 2.35 per cent of GSDP by the Finance Department of the Government of Maharashtra (GoM) as shown in Table 1. Excluding the grants-in-aid, the estimate of subsidy varies between 0.8 to 1.05 percent of GSDP. Thus, estimates of subsidies vary widely between the official report (of GoM) and the NIPFP report. The present paper is not an attempt at comparing or reconciling these two estimates. Instead it focuses on the fundamental question of whether the governments budgetary subsidies, estimated as un-recovered costs, can exceed the GFD. The query came up specifically in the context of deciphering the sources of financing of the subsidies (both explicit and implicit) and thus ascertaining who bears the costs of the subsidies. Certain costs are borne by the society at large in terms of loss of productivity and efficiency. These maybe estimated as the social dead weight losses but they may or may not impinge upon the government budget. Subsidies that impact upon the budget must be a part of the expenditures (on goods and services provision) of the government. So long as public expenditure (on goods and services) is financed by tax and non-tax revenues, subsidies represent inter-personal transfers and redistribution, with the government acting as facilitator. The inter-personal transfers are generally achieved through price discrimination across different sections of consumers. So long as such price variations are revenue neutral they have an impact on the resource allocation mechanism but do not influence the sustainability of the government expenditure program. Often government expenditure exceeds the sum of tax and non-tax revenue. The revenues then constitute the recovered costs of government expenditures, while the un-recovered costs have to be financed by borrowings. The total borrowing requirements of the government from all sources are known as the GFD. The GFD is, therefore, a measure of the extent to which the economy is living beyond its present means (income). In reality a substantial component of the GFD may actually represent investment with only a part of it subsidizing the present consumption plan. Even if all the borrowings were assumed to be financing the present consumption plan, this measure of subsidy should not exceed the GFD. A relevant objective here would be to minimize this component of GFD. In this paper we explore the reasons for the wide gaps in the measure of fiscal deficit and the estimate of aggregate subsidy and suggest an improvement in the methodology to estimate the latter. The plan of this paper is as follows. Section II discusses the meaning, scope and definition of subsidy to dispel some of the myths associated with the term. In section III a simple algebraic structure is presented to provide a theoretical ceiling on aggregate subsidy. Section IV elucidates the economic rationale for subsidies and the need to study their impact / incidence as a significant policy tool. Section V critically analyses the methodology followed by NIPFP and outlines the reasons for the errors in the estimates. An alternative formulation to estimate the un-recovered costs (net aggregate subsidy) is then advanced. Finally, section VI concludes by emphasizing the need for reconciliation between the fiscal deficit and aggregate subsidy estimation and the consequent need for broader macroeconomic consistency

Almost Envy-Freeness in Group Resource Allocation

We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully characterize the cardinalities of two groups of agents for which a fair allocation can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new model where the agents are not partitioned into groups in advance, but instead the partition can be chosen in conjunction with the allocation of the goods. In this model, we show that for agents with arbitrary monotonic valuations, there is always a partition of the agents into two groups of any given sizes along with an EF1 allocation of the goods. We also provide an extension of this result to any number of groups

Hardness Results for Consensus-Halving

We study the consensus-halving problem of dividing an object into two portions, such that each of $n$ agents has equal valuation for the two portions. The $\epsilon$-approximate consensus-halving problem allows each agent to have an $\epsilon$ discrepancy on the values of the portions. We prove that computing $\epsilon$-approximate consensus-halving solution using $n$ cuts is in PPA, and is PPAD-hard, where $\epsilon$ is some positive constant; the problem remains PPAD-hard when we allow a constant number of additional cuts. It is NP-hard to decide whether a solution with $n-1$ cuts exists for the problem. As a corollary of our results, we obtain that the approximate computational version of the Continuous Necklace Splitting Problem is PPAD-hard when the number of portions $t$ is two