Allocation problems among sharing groups

We deal with allocation problems among sharing groups. There are n agents. The agents are divided into several sharing groups. A homogeneous good is allocated among sharing groups rather than among the agents. The good is a private good for sharing groups, and a public good for the members of each sharing group. That is, all of them in the same sharing group can consume it without rivalry. We introduce some allocation rules and axioms. The utilitarian allocation rule and the egalitarian allocation rule are characterized by some axioms.     

No-envy in queueing problems

We explore the implications of no-envy(Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiencyand no-envy. The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envytogether with an additional solidarity requirement how agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

The communication cost of selfishness

We consider how many bits need to be exchanged to implement a given decision rule when the mechanism must be ex post or Bayesian incentive compatible. For ex post incentive compatibility, the communication protocol must reveal enough information to calculate monetary transfers to the agents to motivate them to be truthful (agents' payoffs are assumed to be quasilinear in such transfers). For Bayesian incentive compatibility, the protocol may need to hide some information from the agents to prevent deviations contingent on the information. In both settings with selfish agents, the communication cost can be higher than in the case in which the agents are honest and can be relied upon to report truthfully. The increase is the “communication cost of selfishness.” We provide an exponential upper bound on the increase. We show that the bound is tight in the Bayesian setting, but we do not know this in the ex post setting. We describe some cases where the communication cost of selfishness proves to be very low.     

A NOTE ON SELECTION EFFECTS OF THE HAND RULE

The famous Hand rule weighs the burden of precaution against the reduction in expected harm. The burden may be type‐specific, implying different standards of care for different injurer types. We show that this fact may be exploited by principals in their search for minimized individual costs. Principals may hire agents with high cost of care‐taking although other agents are available. This is shown in a unilateral‐care setting either with perfect or with asymmetric information. We therefore highlight a neglected downside of the negligence rule.     

Prices in Mixed Cost Allocation Problems

We consider mixed cost allocation problems, i.e., joint cost problems that involve two types of heterogeneous outputs, divisible and indivisible. The Aumann–Shapley price mechanism is extended to this setting. We also present a set of properties which characterize this cost sharing rule. Journal of Economic Literature Classification numbers: D63, C79.     

Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Proposal power and majority rule in multilateral bargaining with costly recognition

This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.     

Decentralized decision-making in a large team with local information

We study a problem involving a team of agents each associated with a node in a chain. Each agent makes a decision that influences only his own cost and those of adjacent agents. Prior to making his decision, each agent observes only the cost structure associated with nodes that can be reached by traversing no more than r arcs. Decisions are selected without any coordination, with the common objective of minimizing average cost among agents. We consider such decisions decentralized since agents act based on different information. Cost incurred by an optimal centralized strategy, in which a single decision-maker has access to all information and dictates all decisions, is employed as a performance benchmark. We show that, to maintain a certain level of performance relative to optimal centralized strategies, decentralized deterministic strategies require r to be proportional to the number of agents. This means that the amount of information accessible to any agent should be proportional to the total number of agents. Stochastic strategies, on the other hand, decentralize more gracefully—the amount of information required by each agent is independent of the total number of agents.     

Consistent House Allocation

In practice we often face the problem of assigning indivisible objects (e.g., schools, housing, jobs, offices) to agents (e.g., students, homeless, workers, professors) when monetary compensations are not possible. We show that a rule that satisfies consistency, strategy-proofness, and efficiency must be an efficient generalized priority rule; i.e., it must adapt to an acyclic priority structure, except – maybe – for up to three agents in each object’s priority ordering. We are grateful to the Editor and an anonymous referee for helpful comments and suggestions. L. Ehlers acknowledges financial support from the SSHRC (Canada)     

Costing anaesthetic practice: reconciling perspectives and approaches

Summary

In a previously published article by Broadway and Jones, the anaesthesia-related cost of a hernia repair operation was estimated to be £74.40, of which 21% was accounted for by anaesthetic agents and adjunct drugs. This result contrasts with our estimate of the total procedure cost for an inpatient hernia repair operation of £1,037.39, of which anaesthetic agents and adjunct drugs comprised less than 1%. In order to explain this difference, in this paper we compare and contrast our methodology for and perspective on costing resource use in anaesthesia with those used by Broadway et al. We conclude that these two apparently divergent results, once reconciled in terms of cost coverage and perspectives taken, are broadly equivalent (a reconciled cost of £78.21 compared with the £74.40 of Broadway and Jones.), and that the cost of anaesthetic agents and adjunct drugs constitute a small proportion of total procedure costs.     

Decentralized pricing in minimum cost spanning trees

In the minimum cost spanning tree model we consider decentralized pricing rules, i.e., rules that cover at least the efficient cost while the price charged to each user only depends upon his own connection costs. We define a canonical pricing rule and provide two axiomatic characterizations. First, the canonical pricing rule is the smallest among those that improve upon the Stand Alone bound, and are either superadditive or piece-wise linear in connection costs. Our second, direct characterization relies on two simple properties highlighting the special role of the source cost.     

The Costs of Implementing the Majority Principle: The Golden Voting Rule

In a context of constitutional choice of a voting rule, this paper presents an economic analysis of scoring rules that identifies the golden voting rule under the impartial culture assumption. This golden rule depends on the weights β and (1−β) assigned to two types of costs: the cost of majority decisiveness (‘tyranny’) and the cost of the ‘erosion’ in the majority principle. Our first main result establishes that in voting contexts where the number of voters n is typically considerably larger than the number of candidates k, the golden voting rule is the inverse plurality rule for almost any positive β. Irrespective of n and k, the golden voting rule is the inverse plurality rule if β ≥ 1/2 .. This hitherto almost unnoticed rule outperforms any other scoring rule in eliminating majority decisiveness. The golden voting rule is, however, the plurality rule, the most widely used voting rule that does not allow even the slightest ‘erosion’ in the majority principle, when β=0. Our second main result establishes that for sufficiently “small size” voting bodies, the set of potential golden rules consists at most of just three rules: the plurality rule, the Borda rule and the inverse plurality rule. On the one hand, this finding provides a new rationalization to the central role the former two rules play in practice and in the voting theory literature. On the other hand, it provides further support to the inverse plurality rule; not only that it is the golden rule in voting contexts, it also belongs, together with the plurality rule and the Borda method of counts, to the “exclusive” set of potential golden voting rules in small committees. We are indebted to Jim Buchanan, Amichai Glazer, Noa Nitzan, Ken Shepsle, and an anonymous referee for their useful comments.     

Strategy-proof risk sharing

We consider risk sharing problems with a single good and a finite number of states. Agents have a common prior and their preferences are represented in the expected utility form and are risk averse. We study efficient and individually rational risk sharing rules satisfying strategy-proofness, the requirement that no one can ever benefit by misrepresenting his preference. When aggregate certainty holds, we show that “fixed price selections” from Walrasian correspondence are the only rules satisfying efficiency, individual rationality, and strategy-proofness. However, when aggregate uncertainty holds, we show that there exists no rule satisfying the three requirements. Moreover, in the two agents case, we show that dictatorial rules are the only efficient and strategy-proof rules. Dropping the common prior assumption in the model, we show that this assumption is necessary and sufficient for the existence of rules satisfying the three main requirements in the two agents and aggregate certainty case.     

General allocation problems with single-peaked preferences: path-independence and related topics

We face the problem of allocationg a fixed amount of a perfectly divisible good among a group of agents with single-peaked preferences. We survey the three different cases studied in the literature: the pure distribution case, the redistribution case, and the gerneral case. The so called general case provide with a natural framework to analyze the idea of path-independence. In this framework, we explore the existence of rules fulfilling this property. Our first result is negative: a strong version of this property cannot be fulfilled together with efficiency. Nonetheless, some restricted versions of the path-independence property are compatible with interesting properties, in particular no manipulability, and no envy. We then identify two solutions satisfying this sort of property: the equal distance rule, and a new extension of the uniform rule.     

Maximal Domain of Preferences in the Division Problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63.     

Allocating Tradable Permits on the Basis of Market Price to Achieve Cost Effectiveness

It is a well known result that distributional constraints can lead to an imperfectly competitive permit market where the emission target is no longer met at least cost. In this paper, we suggest an allocation rule for tradable permits which can handle this problem. If the permit allocation is dependent on the market price for permits, this allocation rule can achieve both cost effectiveness and meet specific requirements for cost distribution across agents.     

Diffusion in complex social networks

This paper studies how a behavior spreads in a population. We consider a network of interacting agents whose actions are determined by the actions of their neighbors, according to a simple diffusion rule. We find, using a mean-field approach, the threshold for the spreading rate above which the behavior spreads and becomes persistent in the population. This threshold crucially depends on the connectivity distribution of the social network and on specific features of the diffusion rule.     

Efficient priority rules

We study the assignment of indivisible objects with quotas (universities, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and reallocation-consistency. Such a rule respects an acyclic priority structure and the allocations are determined using the deferred acceptance algorithm.