‘Hydraulic’ rationing

The theory of social choice is concerned with the problem of aggregating the preferences of several persons into a single preference order. The problem has the same structure as that of aggregating the preference orders of a single person with regard to several aspects of alternatives into a single preference order on the set of alternatives. For this reason, the theory of social choice comes logically not under the topic of collective action (as one might suppose) but rather under the topic of multi-objective decisions. This is so because the several participants in a situation defined as a problem of social choice do not really select courses of action among several available ones when they present their preference orders on a set of alternatives. Therefore they are not ‘actors’, as actors are defined in the theory of decision. To be sure, there are situations where voters do choose strategies, that is, choose among different preference orders to present, which may or may not represent their true preferences but which they believe will be more likely to lead to a more desirable aggregated order. These situations can be considered as n-person decision problems, and we will examine them in the context of non-cooperative n-person games (see Chapter 14. At this time, however, we will suppose that each voter acts ‘sincerely’, that is, presents his ‘actual’ preference order. The decision is now up to some agency, which must combine all these submitted preference orders into a ‘social’ preference order.KeywordsSocial ChoicePreference OrderPareto OptimalitySocial Welfare FunctionSimple MajorityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter provides a unifying survey of the literature devoted to cost-and revenue-allocation problems arising in a variety of optimization models. In general, the need to allocate the cost of operating or constructing a public facility among its users gives rise to a variety of cost-allocation issues. Such issues were considered, for example, by the Tennessee Valley Authority in the 1930s, when the cost of constructing a huge series of multipurpose reservoirs for integrated management of the Tennessee River had to be allocated to three different purposes: navigation, flood control, and power (Straffin and Heaney [66]). Additional examples include the allocation of an airport runway’s construction cost among the different aircraft using it (Littlechild and Thompson [49]), allocating library cost among its users (Bres, Charnes, et al. [4]), cost allocation in cablevision networks (D. Granot and Huberman [33]), and cost allocation in electric power development (Gately [25]). Revenue allocation problems arise whenever the benefits of joint investments have to be fairly allocated among the participants, or in certain bankruptcy problems where an estate has to be divided among the creditors (see, for example, Aumann and Mashler [1]).

In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions.

Social choice problems with fixed sets of alternatives

Problems of allocating joint costs in a reasonable way arise in many practical situations where people decide to work together to save costs. Cost allocation methods based on game theoretical concepts take into account the strategic aspects of cost allocation situations. We give a survey of cost allocation methods based on the nucleolus and the Shapley value, and introduce also a new one, the so-called cost gap allocation method which is based on the τ-value. It is shown that for some large subclasses of cost allocation problems this new cost allocation method coincides with old separable cost methods proposed in the thirties by the Tennessee Valley Authority and also with the separable costs-remaining benefits (SCRB) method. Properties of this cost gap allocation method are also treated.

A division rule for claims problems, also known as bankruptcy or rationing problems, based on the pseudo-average solution is studied (for 2-person problems). This solution was introduced in Moulin (Jpn Econ Rev 46:303–332, 1995) for discrete cost allocation problems. Using the asymptotic approach, we obtain a division rule for claims problems. We characterize the division rule axiomatically and show that it coincides with the rule associated to the equal area bargaining solution (this is not true for n = 3). Moreover, following Moulin and Shenker (J Econ Theor 64:178–201, 1994), we show that its associated solution for continuous homogeneous goods is precisely the continuous pseudo-average solution.

The assignment problem, a well-known variant of which is the problem of optimal staff distribution, has formerly been treated as a problem of linear optimization starting with numerical evaluations of the assignments. In this paper the assignment problem is regarded as a problem of social choice, where preference orders are used as the sole initial information. A formal definition of an assignment function is given and various conditions for such functions are suggested. Some conditions are found to be incompatible. Several reasonable assignment functions are examined with respect to which conditions they fulfil. Finally, some problems, related to the assignment problem, are informally discussed.

Collective decision making is the process of mapping the individual views of several individual agents into a joint decision. The need for collective decision making mechanisms is abundant, not just in the realm of politics, but also for a wide range of scientific and technological applications. These include, for instance, logistics, grid computing, and recommender systems. The alternatives to be decided upon often have a combinatorial structure: an alternative is characterised by a tuple of variables, each ranging over a finite domain. Classical approaches to collective decision making, developed in social choice theory, do not take the computational limitations induced by the combinatorial nature of the problem into account. For instance, if we are asked to elect a committee consisting of k representatives, choosing from a pool of n candidates, then we are in fact faced with a social choice problem with $(^n_k)$ alternatives. Asking each voter for their full preferences over these $(^n_k)$ alternatives may not be feasible in practice. Similarly, if we have to choose between accepting or rejecting each of n different propositions, then we are dealing with a social choice problem with 2 n possible outcomes. In this talk I will report on a number of recent developments in the area of collective decision making in combinatorial domains. This includes the study of languages for the compact representation of preferences [2,4], the design of voting rules for multi-issue elections [1], and the analysis of the computational complexity of decision problems arising in judgment aggregation [3].

We analyze some game-theoretic solution concepts associated with a cost allocation problem arising from the Capacitated Network Design (CND) problem. The problem is formulated as a cost cooperative game in characteristic function form to be referred to as the CND game. We provide an efficient representation of several game-theoretic solution concepts associated with the CND game. In particular, we efficiently characterize the core, and in some cases the nucleolus, the least weighted?-core and a certain "central" point in the least weighted?-core. Our model properly generalizes several previously studied cooperative games. We also employ our model to analyze cost allocation problems associated with several classes of network design problems, which were not previously studied in the literature. Specifically, we efficiently characterize the above cost allocation solutions for cost allocation problems associated with the Capacitated Concentrator Location problem, the Capacitated Minimum Spanning Tree problem, the Capacitated Fixed Cost Spanning Forest problem, and the Capacitated Steiner Tree problem.

Introduction Petroleum producers have been engaged for many years in supplying several different types of materials from the leases they operate. Some leases produce crude oil and casing-head gas, others produce gas-well gas and condensate, and still others produce all four of these materials. Therefore, the problem of allocating costs between these intermingled products is not a new one. While in some fields gas has been the dominant product, most producers have been interested principally in oil. Consequently, little has been done about the cost allocation problem by oil producing companies. For accounting purposes, these companies have generally considered gas a by-product, and whatever realization was obtained from it was accounted for as a reduction of producing costs, which were all considered to be applicable to crude oil. The inadequacy of this procedure under present day conditions, and the need for a more realistic approach to the problem of accounting for costs, can probably be illustrated best by a brief review of the growing importance of gas in the economic structure of the industry. Need for Allocation Known natural gas reserves in the United States approximately doubled during the 10 years ending with 1952, rising to a total of nearly 200 trillion cu ft at the beginning of 1953. In terms of heat value the 200 trillion cu ft of gas is approximately equal to the combined heat content of the 28 billion bbls of crude oil and the 5 billion bbls of condensate in reserve at the beginning of 1953. However, the heat units produced in the form of oil in 1952 were almost twice as great as those produced in the form of gas - a good indication that there is much more room for expansion in production of gas than for crude oil. The rapid growth in demand for gas since the end of World War II has brought about a substantial increase in the wellhead price, despite increasing reserves. In the Southwest, for instance, the price doubled in the period from 1943 to 1951, rising to an average of approximately 5.6 cents a thousand in the latter year. Marketed production of gas in the United States had increased to a rate of about 7.5 trillion cu ft in 1951 and over 8 trillion in 1952. The increase in demand thus indicated has been close to 12 per cent a year since 1946, more than twice as great as the rate of increase in demand for crude oil.

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations,....) and private facilities (such as distribution centers, switching stations, ....), we may want to find a 'fair' allocation of the total cost to the customers-this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them. We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem. In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained variant of the facility location problem. Moreover, we introduce a subtle variant of randomized rounding and derive new proofs for the existence of fair cost allocations for several classes of instances. We also show that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.

Cost and emission allocation for joint replenishment systems subject to carbon constraints

We explore the implications of “nosy” preferences—when individuals have rankings over the specific actions of others—using recent theoretical results in the behavioral economics literature. Our model jointly captures preference interdependence over utilities (benevolence) and actions (nosiness). We apply the model to two well‐known environments. The first is a classic social choice problem; the second is a model of relative consumption concerns. For the former we characterize the existence of the impossibility once the social choice problem has been modeled as a behavioral game. For the latter we characterize when the negative externality arising from relative consumption concerns can be overcome without a policy intervention.

Many practical scenarios involve solving a social choice problem: a group of self-interested agents have to agree on an outcome that best fits their combined preferences. We assume that each outcome presents a certain utility to an agent and that the best outcome is the one that maximizes the sum of these utilities. We call a mechanism for solving social choice problems incentive-compatible if for each agent, the behavior that maximizes its own utility is also the one that maximizes the group’s utility.One way to achieve incentive-compatibility is the Vickrey-Clarke-Groves (VCG) tax ([5]) mechanism. However, it produces a surplus of taxes that cannot be redistributed to the agents and can severely reduce agents’ utilities. Game theory has shown that it is not possible to have a general scheme that is incentive-compatible, budget-balanced and guarantees a Pareto-efficient solution.We present a scheme that sacrifices Pareto-efficiency to achieve budget balance while being both incentive-compatible and individually rational. On randomly generated social choice problems, the scheme results in significantly better overall agent utility than the VCG tax mechanism.KeywordsSocial ChoiceConstraint Satisfaction ProblemVickrey AuctionConstraint Optimization ProblemConsistent AssignmentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.