Serial dictatorship and Pareto optimality

In a deterministic allocation problem in which each agent is entitled to receive exactly one object, an allocation is Pareto optimal if and only if it is the outcome of a serial dictatorship. We extend the definition of serial dictatorship to settings in which some agents may be entitled to receive more than one object, and study the efficiency and uniqueness properties of the equilibrium allocations. We prove that subgame perfect equilibrium allocations of serial dictatorship games are not necessarily Pareto optimal; and generally not all Pareto optima can be implemented as subgame perfect equilibrium allocations of serial dictatorship games, except in the 2-agent separable preference case. Moreover, serial dictatorship games do not necessarily have unique subgame perfect equilibrium allocations, except in the 2-agent case, hence their outcomes are indeterminate and manipulable.     

Strategy-proofness of the plurality rule over restricted domains

We give a complete characterization of preference domains over which the plurality rule is strategy-proof. In case strategy-proofness is required to hold under all tie-breaking rules, strategy-proof domains coincide with top-trivial ones where the range of the plurality rule admits at most two alternatives. This impossibility virtually prevails when strategy-proofness is weakened so as to hold under at least one tie-breaking rule: unless there are less than five voters, the top-triviality of a domain is equivalent to the (weak) non-manipulability of the plurality rule. We also characterize the cases with two, three or four voters. I am grateful to Attila Tasnadi for his thorough reading of the paper and pointing to an error in an earlier version. I thank Levent Kutlu, Clemens Puppe, Arunava Sen, an anonymous referee and an anonymous AE for their comments. This research is part of the project “Social Perception—A Social Choice Perspective” supported by Istanbul Bilgi University Research Fund. I also acknowledge the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).     

Non-manipulable domains for the Borda count

Summary. We characterize the preference domains on which the Borda count satisfies Arrows independence of irrelevant alternatives condition. Under a weak richness condition, these domains are obtained by fixing one preference ordering and including all its cyclic permutations (Condorcet cycles). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable on a broader class of domains when combined with appropriately chosen tie-breaking rules. On the other hand, we also prove that the rich domains on which the Borda count is non-manipulable for all possible tie-breaking rules are again the cyclic permutation domains.Received: 24 November 2003, Revised: 12 December 2004, JEL Classification Numbers: D71. Correspondence to: Clemens PuppeThe third author gratefully acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG), Graduiertenkolleg 629 at the University of Bonn and from the Hungarian Scientific Research Fund (OTKA F 043496).     

Dictatorial domains

Summary. In this paper, we introduce the notion of a linked domain and prove that a non-manipulable social choice function defined on such a domain must be dictatorial. This result not only generalizes the Gibbard-Satterthwaite Theorem but also demonstrates that the equivalence between dictatorship and non-manipulability is far more robust than suggested by that theorem. We provide an application of this result in a particular model of voting. We also provide a necessary condition for a domain to be dictatorial and use it to characterize dictatorial domains in the cases where the number of alternatives is three. Received: July 12, 2000; revised version: March 21, 2002 RID="*" ID="*" The authors would like to thank two anonymous referees for their detailed comments. Correspondence to: A. Sen     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains

Summary. We study the problem of allocating several units of homogeneous indivisible goods when monetary compensations are possible. First, we show that there is no strategy-proof, budget balanced, and egalitarian-equivalent mechanism even on extremely restricted preference domains. Next, we present two characterizations of strategy-proof and decision-efficient mechanisms that satisfy a stronger version of egalitarian-equivalence on preference domains bounded above. These characterizations tell us a trade-off between strategy-proofness and Pareto efficiency, and a relationship with strategy-proof and envy-free mechanisms. Finally, we prove that no egalitarian-equivalent mechanism is Nash implementable even on extremely restricted preference domains.Received: 22 April 2002, Revised: 17 February 2003, JEL Classification Numbers: C72, D63, D71, D82.I am very grateful to Naoki Yoshihara for useful discussions and suggestions that motivate me to study this subject. I would also like to thank Kotaro Suzumura, Koichi Tadenuma, Yoshikatsu Tatamitani, and the editor and two anonymous referees of this journal for helpful comments.     

Second price auctions on general preference domains: two characterizations

Auction theory usually assumes the quasi-linearity of individual preferences. We drop this assumption and define an extension of second price mechanisms that applies to general preferences. It turns out that the extended second price mechanisms are the only rules satisfying efficiency, strategy-proofness, and a mild non-imposition property. Their definition is simple just as much as the definition of usual second price mechanisms: everyone reports his maximum willingness to pay and the bidder whose reported value is highest buys the auctioned object for the price equal to the second highest reported value. The characterization is valid if efficiency is replaced by envy-freeness. I gratefully acknowledge an associate editor and two anonymous referees for their very helpful comments. Hiroki Saitoh and Shigehiro Serizawa independently obtain a result that is closely related to my main result (see, Remark in Sect. 1). I thank them for sending me the paper and communication, and Yuji Fujinaka for informing me about their work. I also thank the financial support by KAKENHI (19310031).     

Candidate stability and probabilistic voting procedures

Summary. We extend the analysis of Dutta, Jackson and Le Breton (Econometrica, 2001) on strategic candidacy to probabilistic environments. For each agenda and each profile of voters preferences over running candidates, a probabilistic voting procedure selects a lottery on the set of running candidates. Assuming that candidates cannot vote, we show that random dictatorships are the only unanimous probabilistic voting procedures that never provide unilateral incentives for the candidates to withdraw their candidacy at any set of potential candidates. More flexible probabilistic voting procedures can be devised if we restrict our attention to the stability of specific sets of potential candidates.Received: 4 February 2003, Revised: 14 September 2004, JEL Classification Numbers: D71, D72.This is a revised version of a chapter of my Ph.D. Dissertation submitted to the Universitat Autónoma de Barcelona. I am indebted to my supervisor Salvador Barberá for his advice and constant support. I am grateful to Dolors Berga and an anonymous referee for their detailed comments and suggestions. I thank José Alcalde, Walter Bossert, Bhaskar Dutta, Lars Ehlers, Jordi Massó, Diego Moreno, Clara Ponsatí, Yves Sprumont, and William Thomson for many helpful comments and discussions. I thank the hospitality of the C.R.D.E. at the Université de Montréal and the Department of Economics of the University of Warwick where parts of this research were conducted. Financial support through Research Grant 1998FI00022 from Comissionat per Universitats i Recerca, Generalitat de Catalunya, Research Project PB98-870 from the Ministerio de Ciencia y Tecnología, and Fundación Barrié de la Maza is gratefully acknowledged.     

Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

On the constancy of bribe-proof solutions

Summary. We consider the problem of choosing one point in a set of alternatives when monetary transfers are possible. In this context, Schummer (2000) shows that a social choice function must be a constant function if manipulation through bribes is ruled out. But he requires two kinds of domain-richness conditions. One is either smooth connectedness or the finiteness of the set of alternatives and the other is monotonical closedness. However, dispensing with the former condition, we alternatively prove the same result under a weaker condition than monotonical closedness. Received: April 11, 2000; revised version: February 25, 2002 RID="*" ID="*" This paper received the Osaka University Institute of Social and Economic Research Moriguchi Prize in January 2001. I am grateful to Prof. Ryoichi Nagahisa, Prof. Tatsuyoshi Saijo, Prof. Ken-ichi Shimomura, Prof. Ken Urai, and especially two anonymous referees for their useful and helpful comments and suggestions. I am a Research Fellow of the Japan Society for the Promotion of Science.     

Random shocks in a simple growth model

The variables in my earlier paper [4] oscillated around smooth paths and did not exhibit the irregular movements characteristic of economic time-series As illustrated in this note, irregularities make their appearance if a random term is introduced into the model, and the results provide another confirmation of Wicksell's conjecture that random shocks serve to maintain cycles which would otherwise die away.     

Strategy-proof contract auctions and the role of ties

A contract auction establishes a contract between a center and one of the bidders. As contracts may describe many terms, preferences over contracts typically display indifferences. The Qualitative Vickrey Auction (QVA) selects the best contract for the winner that is at least as good for the center as any of the contracts offered by the non-winning players. When each bidder can always offer a contract with higher utility for the center at an arbitrarily small loss of her own utility, the QVA is the only mechanism that is individually rational, strategy-proof, selects stable outcomes, and is Pareto efficient. For general continuous utility functions, a variant of the QVA involving fixed tie-breaking is strategy-proof and also selects stable outcomes. However, there is no mechanism in this setting that in addition also selects Pareto efficient outcomes.     

Should Reference Alternatives in Pivot Design SC Surveys be Treated Differently?

Analysts are increasingly making use of pivot style Stated Choice (SC) data in the estimation of choice models. These datasets often contain a reference alternative whose attributes remain invariant across replications for the same respondent. This paper presents evidence to suggest that respondents react differently to the attributes of these reference alternatives and those of purely hypothetical alternatives. While some such evidence has been reported in the existing literature, this paper goes further and details a number of different departures from a common treatment of the two types of alternatives, relating both to the observed part of utility and the error term.     

A general impossibility result on strategy-proof social choice hyperfunctions

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D^λ of lexicographic orderings which exhibits an impossibility of the Gibbard–Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D^λ. As most of the standard extension axioms induce superdomains of D^λ while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.     

Random dynamical systems: a review

Summary. This paper provides a review of some results on the stability of random dynamical systems and indicates a number of applications to stochastic growth models, linear and non-linear time series models, statistical estimation of invariant distributions, and random iterations of quadratic maps.Received: 16 August 2002, Revised: 9 January, 2003, JEL Classification Numbers: C1, C6, D8, D9. Correspondence to: Mukul MajumdarThanks are due to A. Goswami and B.V. Rao for their detailed comments on an earlier version.     

Integer programming on domains containing inseparable ordered pairs

Using the integer programming approach introduced by Sethuraman et al. (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions “without ties,” but also Arrovian social welfare functions “with ties,” since they satisfy the strictly decomposability condition introduced by Busetto et al. (2015). Moreover, we go further in the comparison between Kalai and Ritz (1978)’s inseparability and Arrow (1963)’s single-peak restrictions, showing that the former condition is more “respectable,” in the sense of Muller and Satterthwaite (1985).     

Understanding Heterogeneous Preferences in Random Utility Models: A Latent Class Approach

A finite mixture approach toconditional logit models is developed in whichlatent classes are used to promoteunderstanding of systematic heterogeneity. The model is applied to wilderness recreationin which a branded choice experiment involvingchoice of one park from a demand system wasadministered to a sample of recreationists. The basis of membership in the classes orsegments in the sample involved attitudinalmeasures of motivations for taking a trip, aswell as their stated preferences overwilderness park attributes. The econometricanalysis suggested that four classes of peopleexist in the sample. Using the model toexamine welfare measures of some hypotheticalpolicy changes identified markedly differentwelfare effects than the standard singlesegment model, and provided insight into thedifferential impact of alternative policies.     

Non-dictatorial extensive social choice

Summary. Different social planners may have different opinions on the well-being of individuals under different social options (Roberts, 1980). If utilities are translation- or ratio-scale measurable, or if the social ranking might be incomplete, or if interplanner comparability is allowed; then there exist non-dictatorial aggregation rules. We propose extensions, intersections, and mixtures of the Pareto, utilitarian, leximin, Kolm-Pollak, and iso-elastic rules.Received: 16 May 2001, Revised: 18 November 2003, JEL Classification Numbers: D63, D71. Correspondence to: Erwin OogheErwin Ooghe, Luc Lauwers: We are extremely grateful to the referee who was willing to review this paper many times. Her/his extensive and in-depth comments had a strong impact. Further thanks are due to Bart Capéau, Marc Fleurbaey, Maurice Salles, Erik Schokkaert, and Alain Trannoy. The first author gratefully acknowledges the financial support by the TMR network Living Standards, Inequality and Taxation (ERBFMRXCT 980248) of the European Communities.