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Shigehiro Serizawa - One of the best experts on this subject based on the ideXlab platform.
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A Maximal Domain for strategy-proof and no-vetoer rules in the multi-object choice model
International Journal of Game Theory, 2013Co-Authors: Kentaro Hatsumi, Dolors Berga, Shigehiro SerizawaAbstract:Following Barbera, Sonnenschein, and Zhou (1991, Econometrica 59, 595-609), we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate Domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable preferences is a Maximal Domain for the existence of rules satisfying strategy-proofness and no-vetoer.
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Maximal Domain for Strategy-proof Rules in Allotment Economies
SSRN Electronic Journal, 2005Co-Authors: Hideyuki Mizobuchi, Shigehiro SerizawaAbstract: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, 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-plateaued Domain.
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Maximal Domains for strategy-proof rules in the candidates selection problem
2002Co-Authors: Dolors Berga, Shigehiro SerizawaAbstract:We consider the problem where a set of voters have to elect candidates among a set of two alternatives. This is the same framework as in Barbera, Sonnenschein, and Zhou (1991), where they obtain �voting by committees� as the characterization class of all onto and strategy-proof voting schemes on the Domain of separable preferences. Furthermore, separable preferences turn out to be the Maximal rich Domain where voting by committees are strategy-proof. In this paper we study Maximal Domains of preferences for strategy-proofness of any rule and not only voting by committees. We obtain that the set of separable preferences is a Maximal Domain for the existence of strategy-proof and onto social choice functions satisfying the additional requirement of no vetoerness. For more than two alternatives this result is still a conjecture. Barbera, Sonnenschein, and Zhou (1991) (henceforth, BSZ) considered the problem where a finite set of voters N must choose, from a finite set K, which objects will be adopted. These objects can be bills considered by a legislature, candidates to enter a club, or they can also be interpreted as public goods with two feasible levels 0, 1. This last interpretation was given in Barbera, Gul, and Sttacchetti (1993) (henceforth, BGS) where the more general setting of any number of feasible levels for public goods is considered. BSZ obtained two important results concerning strategy-proofness. On the one hand, they characterized voting by committees (which we also call: generalized median voter schemes) as the only onto social choice functions satisfying strategy-proofness when agents� preferences are separable. On the other hand, they obtain the set of separable preferences as a Maximal rich Domain for which voting by committees with neither veto nor dummy voters are strategy-proof. Recently, other results improving this necessary condition on preferences for which voting by committees are strategy-proof have been obtained. See Serizawa (1995) and Barbera, Masso, and Neme (1999) for discrete sets of alternatives, and Barbera, Masso, and Serizawa (1996) and Berga (2000) for the case where social alternatives are continuously measured. Although any strategy-proof rule on separable preferences must be voting by committees, a strategy-proof social choice function may not belong to this class when the rule is defined outside that Domain. Thus, this literature may exclude interesting rules. From their two results mentioned above, two natural questions arise. We initially concentrate in BSZ�s framework with two objects. The first one is related to the existence of other Domains of preferences preserving voting by committees as the unique class of strategy-proof social choice functions. By BSZ, we know that the subDomain of additive preferences preserves these results. In our paper, we consider �rich Domains� and we conjecture that �a social choice function on a rich Domain is strategy-proof if and only if it is a generalized median voter scheme�. The second question is how large the Domain of preferences can be and still preserve the existence of strategy-proof rules (not necessarily generalized median voter schemes)? We qualify this question in two different ways. First, we employ the no vetoer condition to rule out trivial rules such as dictators. Second, we require Domains to be rich; that is, to contain a minimal variety of preferences. Then, we conjecture that �the unique Maximal rich Domain for strategy-proofness and the no vetoer condition is the Domain of separable preferences�. Additionally, in this paper we also show how relevant is the rich Domain condition for our results. In Theorem 2 we state our main result (unique for the moment) which says that �the Domain of separable preferences is a Maximal Domain for strategy-proofness and the no vetoer condition�. We provide and example of an onto and strategy-proof social choice function satisfying the no vetoer condition which is not a generalized median voter scheme and which is defined on a non-rich Domain. Moreover, we think we can obtain (we conjecture) that a slightly variation of this Domain is Maximal for our properties. Thus, the Domain of separable preferences is not unique in Theorem 2. These two questions are in the same line as the ones already answered in Berga and Serizawa (2000) where the authors do not restrict a priori the class of rules to be considered and they study the problem of the provision of a single public good. There, they obtain the Domain of convex preferences as the unique Maximal Domain including a minimally rich one allowing for strategy-proof and onto rules satisfying the no vetoer condition. In this paper we restrict to the case of two public goods (or two objects), however, we believe that our result can be generalized to any number of goods. This is still part of current research
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Maximal and Supremal Domains for Strategy-Proofness
SSRN Electronic Journal, 2001Co-Authors: Stephen Ching, Shigehiro SerizawaAbstract:In this paper, we pose the following question in a private-good model. To what extent can the single-peaked Domain be enlarged while preserving the existence of rules satisfying strategy-proofness, symmetry and unanimity? This formulation is adopted for three reasons. First, it marks a clear distinction between the two existing approaches to the Maximal Domain question in the literature. Second, it restores the role of strategy-proofness, which is suppressed by efficiency in an earlier result (Ching and Serizawa, 1998). Third, a private-good model allows us to conduct a richer analysis of strategy-proof rules. We show that the weakly single-peaked Domain is the unique Maximal Domain for strategy-proofness, symmetry and unanimity. The weakly single-peaked Domain is marginally bigger than the single-peaked Domain. A diagnosis of the result reveals that Maximal Domain can be a stringent concept. A less stringent concept is proposed: supermal Domain. (Supremal Domain is analogous to the concept of supremum in an open interval.) All supermal Domains for strategy-proofness, symmetry and unanimity are shown to be strictly smaller than the convex Domain, which is slightly bigger than the weakly single-peaked Domain. These results indicate that the assumption of single-peakedness essentially cannot be dispensed with if one is interested in strategy-proofness.
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Maximal Domain for Strategy-Proof Rules with One Public Good
Journal of Economic Theory, 2000Co-Authors: Dolors Berga, Shigehiro SerizawaAbstract:In the context of the provision of one pure public good, we raise the following question : how large can a preference Domain be to allow for the existence fo strategy-proof rules satisfying the no vetoer condition? This question is qualified by the additional requirement that a Domain should include " a minimal rich Domain". We discuss that this requirement is weak since the conditions for minimal richness are satisfied by a variety of small Domains including the class of quadratic preferences.
Martin T. Wells - One of the best experts on this subject based on the ideXlab platform.
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on the Maximal Domain of attraction of tracy widom distribution for gaussian unitary ensembles
Statistics & Probability Letters, 2013Co-Authors: Rajendran Narayanan, Martin T. WellsAbstract:Abstract The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy–Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy–Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel Domain of attraction.
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On the Maximal Domain of attraction of Tracy–Widom distribution for Gaussian unitary ensembles
Statistics & Probability Letters, 2013Co-Authors: Rajendran Narayanan, Martin T. WellsAbstract:Abstract The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy–Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy–Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel Domain of attraction.
Alejandro Neme - One of the best experts on this subject based on the ideXlab platform.
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A Maximal Domain of preferences for strategy-proof, efficient, and simple rules in the division problem
Social Choice and Welfare, 2004Co-Authors: Jordi Massó, Alejandro NemeAbstract: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.
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a Maximal Domain of preferences for strategy proof efficient and simple rules in the division problem
Social Choice and Welfare, 2004Co-Authors: Jordi Massó, Alejandro NemeAbstract: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. Copyright Springer-Verlag 2004
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A Maximal Domain of Preferences for Strategy-proof, Efficient, and Simple Rules in the Division Problem ∗
Social Choice and Welfare, 2004Co-Authors: Jordi Massó, Alejandro NemeAbstract: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. Copyright Springer-Verlag 2004
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A Maximal Domain of Preferences for Tops-only Rules in the Division Problem
2002Co-Authors: Jordi Massó, Alejandro NemeAbstract: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, continuity, and "tops-onlyness". These Domains (called weakly 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.
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Maximal Domain of Preferences in the Division Problem
Games and Economic Behavior, 2001Co-Authors: Jordi Massó, Alejandro NemeAbstract: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.
Rajendran Narayanan - One of the best experts on this subject based on the ideXlab platform.
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on the Maximal Domain of attraction of tracy widom distribution for gaussian unitary ensembles
Statistics & Probability Letters, 2013Co-Authors: Rajendran Narayanan, Martin T. WellsAbstract:Abstract The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy–Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy–Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel Domain of attraction.
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On the Maximal Domain of attraction of Tracy–Widom distribution for Gaussian unitary ensembles
Statistics & Probability Letters, 2013Co-Authors: Rajendran Narayanan, Martin T. WellsAbstract:Abstract The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy–Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy–Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel Domain of attraction.
Bing Xie - One of the best experts on this subject based on the ideXlab platform.
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Classification of Non-symmetric Sturm-Liouville Systems and Operator Realizations
Acta Applicandae Mathematicae, 2012Co-Authors: Bing Xie, Xinwei GuoAbstract:The main objective of this paper is to give a classification of Sturm-Liouville differential equations with non-symmetric matrices coefficients in terms of the number of square integrable solutions of the system and its conjugate system. The conjugate system is innovatively introduced to get the classification. Furthermore, the asymptotic behavior of elements in the Maximal Domain is studied. As applications, the J-self-adjoint operator realizations are given for a special case in the classification.
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Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients
Abstract and Applied Analysis, 2011Co-Authors: Bing XieAbstract:This paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in the Maximal Domain. The results of the present paper generalize the corresponding results for formally symmetric Sturm-Liouville differential equations to non-self-adjoint cases.