Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality.     

A characterization of the uniform rule with several commodities and agents

We consider a problem of allocating infinitely divisible commodities among a group of agents. More specifically, there are several commodities to be allocated and agents have continuous, strictly convex, and separable preferences. We establish that a rule satisfies strategy-proofness, unanimity, weak symmetry, and nonbossiness if and only if it is the uniform rule. This result extends to the class of continuous, strictly convex, and multidimensional single-peaked preferences.     

Fair allocation of indivisible goods: the two-agent case

One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the subsets of goods, and a monotonicity property w.r.t. changes in preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, together with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods.     

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”.     

In quest of the banks set in spatial voting games

The Banks set (1(4):295–306, 1985) is one of the more important concepts in voting theory since it tells us about the sophisticated outcomes of standard amendment voting procedures commonly in use throughout the English speaking world (and elsewhere as well). While the properties of the Banks set for finite voting games have been extensively studied, little is known about how to find members of this set for majority rule spatial voting games involving possibly infinite agendas. We look at this question for two-dimensional games where voters have Euclidean preferences, and offer a variety of new results that delimit areas of the space that can be shown to lie within the Banks set, such as the Schattschneider set, the tri-median set, and the Banks line set—geometric constructs which we show to be nested within one another.     

‘The engine just started coughing!’ — Limits of physical performance,aging and career continuity in elite endurance sports

This research examines male endurance athletes' experience of aging and/or reaching the perceived limits of physical performance. More specifically, the current study aimed to explore how existential meanings attached to these experiences are connected with athletes' decision-making concerning career continuity and retirement. Life story interviews were conducted with 10 Finnish runners and/or orienteers aged between 25 and 62 and the data was analyzed with an existential-narrative framework. Four major storylines related to aging were identified: The end of an era, putting things in perspective, the attitude has to change and winning was never the only motive. Our results suggest that endurance athletes possess diverse ways of bringing meaning to the experience of aging, both confirming and resisting the dominant cultural narrative of decline. While three athletes' stories confirmed the normativity of retirement when unable to improve their results anymore, other athletes demonstrated career continuity and positive aspects in the late career years, such as lack of competitive anxiety, finding perspective and increased enjoyment in running. We suggest that through awareness of alternative narratives, sport psychology consultants may be able to help their clients to explore new meanings in the potentially challenging and beneficial experiences of aging and athletic retirement.     

A maximal domain of preferences for strategy-proof,efficient, and simple rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, tops-onlyness, and continuity. These domains (called partially single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.An earlier version of this paper circulated under the title A maximal domain of preferences for tops-only rules in the division problem. We are grateful to an associate editor of this journal for comments that helped to improve the presentation of the paper and to Matt Jackson for suggesting us the interest of identifying a maximal domain of preferences for tops-only rules. We are also grateful to Dolors Berga, Flip Klijn, Howard Petith, and a referee for helpful comments. The work of Alejandro Neme is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis. The work of Jordi Massó is partially supported by Research Grants BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and 2001SGR-00162 from the Generalitat de Catalunya, and by the Barcelona Economics Program of CREA from the Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB unde r a sabbatical fellowship from the Generalitat de Catalunya.     

Use of a Modified Chaining Procedure with Textual Prompts to Establish Intraverbal Storytelling

Echoic, tact, and textual transfer procedures have been proven successful in establishing simple intraverbals (Braam and Poling Applied Research in Mental Retardation, 4, 279–302, 1983; Luciano Applied Research in Mental Retardation, 102, 346–357, 1986; Watkins et al. The Analysis of Verbal Behavior, 7, 69–81, 1989). However, these strategies may be ineffective for some children due to the complexity of the targeted intraverbals. The current study investigated the use of a novel procedure which included a modified chaining procedure and textual prompts to establish intraverbal behavior in the form of telling short stories. Visual prompts and rule statements were used with some of the participants in order to produce the desired behavior change. Results indicated that the procedure was effective for teaching retelling of short stories in three children with autism.     

Auctioning or assigning an object: some remarkable VCG mechanisms

We construct a variant of the Vickrey auction of a single object where the surplus is split in exogenously fixed shares between the seller and the buyers, up to a margin of error vanishingly exponentially as the number of buyers grows. When the object is the common property of the participants, we can similarly construct VCG mechanisms with a vanishingly small cash transfer to the residual claimant. For any integer q, 3 ≤ q ≤ n, we find the mechanism guaranteeing to each participant a fair share of the qth highest valuation, while minimizing the worst possible ratio of the cash transfer to the efficient surplus. We perform a parallel analysis when the object is undesirable. We compare the cash lost to the largest spread between individual valuations, and obtain the same trade-offs between fairness and the relative loss of surplus.     

A Note on the Separability Principle in Economies with Single-Peaked Preferences

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and Ω-continuity. We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of Ω-continuity. Furthermore, we prove that the equal division lower bound and separability imply no-envy. Using this result, we strengthen one of Chun’s (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, the equal division lower bound, separability, and either Ω-continuity or duplication-invariance.     

On the manipulability of approval voting and related scoring rules

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable—has the smallest number of manipulable preference profiles—under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.     

Fair and efficient division through unanimity bargaining when claims are subjective

In a subjective claims problem several partners have conflicting perceptions on how a jointly produced surplus should be divided fairly amongst them. In a large-scale experiment, we compare the fairness and efficiency of three unanimity bargaining procedures used to reach a consensus in a three-partner subjective claims problem. Under each procedure partners move sequentially, making alternating proposals. The procedures differ in whether they ask for a complete division proposal (Offer and Exit rule) or only for a proposal regarding the partner’s own fair share (Demand rule); and in whether partners have to accept the entire division proposal (Offer and Demand rule) or only their own share (Exit rule). For the fairness assessment partial and impartial fairness views are used and we find that the Offer rule performs best in terms of allocative fairness and no worse in terms of efficiency.     

Maximal domain for strategy-proof probabilistic rules in economies with one public good

We consider the problem of choosing a level of a public good on an interval of the real line among a group of agents. A probabilistic rule chooses a probability distribution over the interval for each preference profile. We investigate strategy-proof probabilistic rules in the case where distributions are compared based on stochastic dominance relations. First, on a “minimally rich domain”, we characterize the so-called probabilistic generalized median rules (Ehlers et al., J Econ Theory 105:408–434, 2002) by means of stochastic-dominance (sd) strategy-proofness and ontoness. Next, we study how much we can enlarge a domain to allow for the existence of sd-strategy-proof probabilistic rules that satisfy ontoness and the no-vetoer condition. We establish that the domain of “convex” preferences is the unique maximal domain including a minimally rich domain for these properties.     

Strategy-proofness and the reluctance to make large lies: the case of weak orders

This article incorporates agents’ reluctance to make a large lie into an analysis. A social choice rule is D(k)-proof if the rule is nonmanipulable by false preferences within k distance from the sincere one, where k is a positive integer. If D(k)-proofness is not logically equivalent to strategy-proofness, then agents’ reluctance to make a large lie embodied in D(k)-proofness is effective to construct a nonmanipulable rule. This article considers weak orders as agents’ preferences. I prove that on the universal domain, D(k)-proofness is equivalent to strategy-proofness if and only if k ≥ m ? 1, where m is the number of alternatives. Moreover, I find a sufficient condition on a domain for the equivalence of D(1)-proofness and strategy-proofness.     

A characterization of the Walras rule

This paper has three purposes. First, we refine the characterization of the Walras rule proposed by Nagahisa (JET 1991) over a more natural and simple domain than the one he employed. We show that the Walras rule is the only social choice rule defined over the domain and satisfying Individual Rationality, Pareto Efficiency, and Local Independence. Second, assuming endowments to be collectively owned, we show that the Walras rule operated from equal division is the only social choice rule satisfying No Envy, Pareto Efficiency, and Local Independence. Third, we show that for every social choice rule satisfying Individual Rationality and Pareto Efficiency, Local Independence is equivalent to a condition of Nash implementation with a game form satisfying convexity.This article is a revised version of Toyama University Working Paper No. 141. We are grateful to Professors William Thomson, Shinsuke Nakamura, Tomoichi Shinotsuka and two anonymous referees for their detailed comments. Nagahisa is grateful for hospitality of the economics department of the University of Rochester.     

On representation of monotone preference orders in a sequence space

In this paper we investigate the relation between scalar continuity and representability of monotone preference orders in a sequence space. Scalar continuity is shown to be sufficient for representability of a monotone preference order and easy to verify in concrete examples. Generalizing this result, we show that a condition, which restricts the extent of scalar discontinuity of a monotone preference order, ensures representability. We relate this condition to the well-known order dense property, which is both necessary and sufficient for representability.     

Classification theorem for smooth social choice on a manifold

A classification theorem for voting rules on a smooth choice space W of dimension w is presented. It is shown that, for any non-collegial voting rule, σ, there exist integers v ^*(σ), w ^*(σ) (with v ^*(σ)<w ^*(σ)) such that

1. structurally stable σ-voting cycles may always be constructed when w ? v ^*(σ) + 1
2. a structurally stable σ-core (or voting equilibrium) may be constructed when w ? v ^*(σ) ? 1

Finally, it is shown that for an anonymous q-rule, a structurally stable core exists in dimension \(\frac{{n - 2}}{{n - q}}\) , where n is the cardinality of the society.     

Revealing consumers' willingness-to-pay: A comparison of the BDM mechanism and the Vickrey auction

We compare the capability of the Becker–DeGroot–Marschak (BDM) mechanism and the Vickrey auction to reveal willingness-to-pay information for a sample of French consumers. We measure the bias and dispersion of bids relative to valuations. We find that the Vickrey auction, for the particular training procedure we employ, is more effective as a willingness-to-pay elicitation device than the BDM process. We conjecture that differences in the shape of the payoff function account for some of the differences.     

Can strategic uncertainty help deter tax evasion? An experiment on auditing rules

This paper adds to the economic-psychological research on tax compliance by experimentally testing a simple auditing rule that induces strategic uncertainty among taxpayers. Under this rule, termed the bounded rule, taxpayers are informed of the maximum number of audits by a tax authority, so that the audit probability depends on the joint decisions among the taxpayers. We compare the bounded rule to the widely studied flat-rate rule, where taxpayers are informed that they will be audited with a constant probability. The experimental evidence shows that, as theoretically predicted, the bounded rule induces the same level of compliance as the flat-rate rule when strategic uncertainty is low, and a higher level of compliance when strategic uncertainty is high. The bounded rule also induces distinctive tax evasion dynamics compared to the flat-rate rule. The results suggest that increasing the level of strategic uncertainty among taxpayers could be an effective device to deter tax evasion.     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.