Strategy-proof voting schemes with continuous preferences

We prove that all nondictatorial voting schemes whose range has more than two alternatives will be manipulable, when their domain is restricted to the set of all continuous preferences over alternatives. Our result neither implies nor is implied by the original Gibbard-Satterthwaite theorem, except if the number of alternatives is finite, when they coincide. A new, direct line of reasoning is used in the proof. It is presented in an introductory section, which may be useful in classroom situations.The work of S. Barberà is partially supported by Research Grant PB 86-0613, from the Dirección General de la Investigación Científica y Técnica, Spanish Ministry of Education.     

Strategy-proof Cardinal Decision Schemes

This paper analyses strategy-proof mechanisms or decision schemes which map profiles of cardinal utility functions to lotteries over a finite set of outcomes. We provide a new proof of Hylland’s theorem which shows that the only strategy-proof cardinal decision scheme satisfying a weak unanimity property is the random dictatorship. Our proof technique assumes a framework where individuals can discern utility differences only if the difference is at least some fixed number which we call the grid size. We also prove a limit random dictatorship result which shows that any sequence of strategy-proof and unanimous decision schemes defined on a sequence of decreasing grid sizes approaching zero must converge to a random dictatorship. We are most grateful to an Associate Editor and two referees for very helpful comments on an earlier version of the paper. An erratum to this article can be found at     

Strategy-proof allocation of indivisible goods

Strategy-proof allocation of a finite number of indivisible goods among a finite number of individuals is considered. The main result is that in a pure distributional case, a mechanism is strategy-proof, nonbossy and neutral if and only if it is serially dictatorial. If the indivisible goods are initially owned by the individuals, a mechanism is strategy-proof, individually rational and Pareto consistent if and only if it is the core mechanism. Received: 15 September 1997/Accepted: 12 May 1998     

Strategy-proof resolute social choice correspondences

We qualify a social choice correspondence as resolute when its set valued outcomes are interpreted as mutually compatible alternatives which are altogether chosen. We refer to such sets as “committees” and analyze the manipulability of resolute social choice correspondences which pick fixed size committees. When the domain of preferences over committees is unrestricted, the Gibbard–Satterthwaite theorem—naturally—applies. We show that in case we wish to “reasonably” relate preferences over committees to preferences over committee members, there is no domain restriction which allows escaping Gibbard–Satterthwaite type of impossibilities. We also consider a more general model where the range of the social choice rule is determined by imposing a lower and an upper bound on the cardinalities of the committees. The results are again of the Gibbard–Satterthwaite taste, though under more restrictive extension axioms.     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

Maximal Domain for Strategy-proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy in The economics of market disequilibrium, Academic, New York, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: there is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaueddomain.     

Strategy-proof,efficient, and nonbossy quota allocations

We consider the problem of designing a mechanism to allocate objects to agents when each agent has a quota that must be filled exactly. Agents are assumed to have responsive preferences over items. We show that the only strategy-proof, Pareto optimal, and nonbossy mechanisms are sequential dictatorships. We also show that the only strategy-proof, Pareto optimal, nonbossy, and neutral mechanisms are serial dictatorships. Since these negative results hold for responsive preferences, they hold for more general preferences as well. We are grateful to Atila Abdulkadiroğlu, Syed Nageeb Mustafa Ali, Douglas Bernheim, Navin Kartik, Jon Levin, Paul Milgrom, and Azeem Shaikh and two anonymous referees and an editor for helpful discussions. This research has been supported by the Burt and Deedee McMurtry Stanford Graduate Fellowship.     

Strategy-proof division with single-peaked preferences and individual endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality, strategy-proofness, reversibility, and an equal-treatment condition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his individual endowment. Received: 8 September 1995/Accepted: 30 October 1996     

Strategy-proof rules for two public goods: double median rules

We consider the problem of selecting the locations of two (identical) public goods on an interval. Each agent has preferences over pairs of locations, which are induced from single-peaked rankings over single locations: each agent compares pairs of locations by comparing the location he ranks higher in each pair. We introduce a class of “double median rules” and characterize it by means of continuity, anonymity, strategy-proofness, and users only. To each pair of parameter sets, each set in the pair consisting of $(n+1)$ parameters, is associated a rule in the class. It is the rule that selects, for each preference profile, the medians of the peaks and the parameters belonging to each set in the pair. We identify the subclasses of the double median rules satisfying group strategy-proofness, weak efficiency, and double unanimity (or efficiency), respectively. We also discuss the classes of “multiple median rules” and “non-anonymous double median rules”.     

Strategy-proof allocation mechanisms for economies with an indivisible good

We consider economies with a single indivisible good and money. We characterize the set of mechanisms that satisfy strategy-proofness, individual rationality, equal compensation, and demand monotonicity. There are three types of mechanisms which have the following properties: (i) they determine the allocation of monetary compensation depending on who receives the indivisible good; (ii) they allocate the indivisible good to one of the pre-specified (one or two) agent(s); and (iii) they disregard preferences of agents other than the pre-specified agent(s). This result implies that the presence of an indivisible good induces serious asymmetry in mechanisms. Received: 26 March 1996 / Accepted: 23 September 1997     

More on Harsanyi's utilitarian cardinal welfare theorem

If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.I wish to thank Stephen Selinger for pointing out Resnick's argument to me and W. A. J. Luxemburg for a useful discussion which simplified the argument     

Strategy-proof and anonymous rule in queueing problems: a relationship between equity and efficiency

We consider a relationship between equity and efficiency in queueing problems. We show that under strategy-proofness, anonymity in welfare implies queue-efficiency. Furthermore, by combining the result of Kayı and Ramaekers (Games Econ Behav 68:220–232, 2010) with ours, we also give a characterization of the class of rules that satisfy strategy-proofness, anonymity in welfare, and budget-balance.     

Reference functions and possibility theorems for cardinal social choice problems

 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. Received: 8 August 1994/Accepted: 12 February 1996     

Neurobiological measurements of cardinal utility: Hedonimeters or learning algorithms?

A neurobiological argument has been used to defend the measurability and interpersonal comparability of cardinal utility. If true, a strong case could be made for the practical relevance of utility-based social welfare functions. In this paper I demonstrate that the current evidence does not corroborate the cardinal measurability and comparability of utility. Electrical stimulation of brain parts, or asymmetries in brain hemispherical activation, cannot be used to build a hedonimeter. The role of the neurotransmitter dopamine is that of a saliency detector or alternatively one validating adaptive learning models, but either way is not that of a general cardinal utility measure. Received: 3 March 2000/Accepted: 8 January 2001     

A case for cardinal utility and non-arbitrary choice of commodity units

With preference changes, cardinal utility is indispensable. For any necessity good, there exists an intermediate consumption level at which a change in preference intensity has no effect on utility, below/above which an increase in preference intensity decreases/increases utility. This is supported by an indicative empirical survey. At the intermediate consumption level, the utility from the relevant good is zero. For a Cobb-Douglas utility function, this intermediate consumption level equals one, making the choice of the unit of measurement non-arbitrary.We are grateful to a referee for some helpful comments     

Equitable insurance premium schemes

We analyze the equity properties of insurance premium schemes where agents are partitioned into groups with different average accident probabilities and each individual has to pay a premium according to the average probability of the group to which it belongs. In particular, we examine the question whether choosing finer partitions to define these groups generates more equitable situations than coarser groups. Though it turns out that partitioning the agents into finer groups can never be Lorenz dominated by the coarser partition, it cannot be guaranteed that finer partitions represent improvements over coarser ones except in very restrictive circumstances. Received: 27 March 2000/Accepted: 28 August 2000     

Fair cost allocation schemes

A class of allocation schemes is axiomatized for the allocation of variable costs to activities performed sequentially when their order of performance is not fixed in advance and costs depend on this order. An upper bound on the amount charged to each activity is assumed to be given. This bound is independent of the processing order and can be more or less than the cost the activity would incur if it were performed alone. Our axioms for fair allocation lead to a restricted (but nonunique) class of allocation schemes whose restrictions depend on whether the sum of the bounds is less than or more than the sum of the costs incurred when each activity is performed alone.     

Creating culturally sustainable agri-environmental schemes

Evidence is emerging from across Europe that contemporary agri-environmental schemes are having only limited, if any, influence on farmers’ long-term attitudes towards the environment. In this theoretical paper we argue that these approaches are not ‘culturally sustainable’, i.e. the actions are not becoming embedded within farming cultures as part of conventional ‘good farming’ practice. We propose (following Bourdieu) that, in order to culturally embed the environmental values, beliefs and knowledges that underlie such schemes, policy-makers need to devise approaches that allow the creation of cultural and social capital within farming communities - rather than simply compensating for economic capital lost. We outline the theoretical basis of our position and discuss how the contemporary agri-environmental approach of paying for specified environmental management services restricts the ability of such schemes to generate cultural and, thereby, social capital. Finally, we outline two possible ways of accounting for cultural capital in scheme creation: either through the development of measures of cultural capital that enable its incorporation into contemporary economic models or through a major revision to the way we construct and apply agri-environmental schemes.