Social choice theory without Pareto: The pivotal voter approach

This paper extends the pivotal voter approach pioneered by Barberá [Barberá, S., 1980. Pivotal voters: A new proof of Arrow’s Theorem. Economics Letters 6, 13–6; Barberá, S., 1983. Strategy-proofness and pivotal voters: A direct proof of the Gibbard-Satterthwaite Theorem. International Economic Review 24, 413–7] to all social welfare functions satisfying independence of irrelevant alternatives. Arrow’s Theorem, Wilson’s Theorem, and the Muller–Satterthwaite Theorem are all immediate corollaries of the main result. It is further shown that a vanishingly small fraction of pairs of alternatives can be affected in the group preference ordering by multiple individuals, which generalizes each of the above theorems.     

Axiomatic characterizations under players nullification

Many axiomatic characterizations of values for cooperative games invoke axioms which evaluate the consequences of removing an arbitrary player. Balanced contributions (Myerson, 1980) and balanced cycle contributions (Kamijo and Kongo, 2010) are two well-known examples of such axioms. We revisit these characterizations by nullifying a player instead of deleting her/him from a game. The nullification (Béal et al., 2014a) of a player is obtained by transforming a game into a new one in which this player is a null player, i.e. the worth of the coalitions containing this player is now identical to that of the same coalition without this player. The degree with which our results are close to the original results in the literature is connected to the fact that the targeted value satisfies the null player out axiom (Derks and Haller, 1999). We also revisit the potential approach (Hart and Mas-Colell, 1989) similarly.     

Production-inventory games and PMAS-games: Characterizations of the Owen point

Production-inventory games were introduced in [Guardiola, L.A., Meca, A., Puerto, J. (2008). Production-Inventory games: A new class of totally balanced combinatorial optimization games. Games Econom. Behav. doi:10.1016/j.geb.2007.02.003] as a new class of totally balanced combinatorial optimization games. From among all core-allocations, the Owen point was proposed as a specifically appealing solution. In this paper we study some relationships of the class of production-inventory games and other classes of new and known games. In addition, we propose three axiomatic characterizations of the Owen point. We use eight axioms for these characterizations, among those, inessentiality and additivity of players’ demands are used for the first time in this paper.     

Population solidarity, population fair-ranking, and the egalitarian value

We investigate the implications of two axioms specifying how a value should respond to changes in the set of players for TU games. Population solidarity requires that the arrival of new players should affect all the original players in the same direction: all gain together or all lose together. On the other hand, population fair-ranking requires that the arrival of new players should not affect the relative positions of the original players. As a result, we obtain characterizations of the egalitarian value, which assigns to each player an equal share over an individual utility level. It is the only value satisfying either one of the two axioms together with efficiency, symmetry and strategic equivalence.     

Wavelet Characterizations for Anisotropic Besov Spaces

The goal of this paper is to provide wavelet characterizations for anisotropic Besov spaces. Depending on the anisotropy, appropriate biorthogonal tensor product bases are introduced and Jackson and Bernstein estimates are proved for two-parameter families of finite-dimensional spaces. These estimates lead to characterizations for anisotropic Besov spaces by anisotropy-dependent linear approximation spaces and lead further on to interpolation and embedding results. Finally, wavelet characterizations for anisotropic Besov spaces with respect to L_p-spaces with 0<p<∞ are derived.     

Torsten Brodén's work on the foundations of Euclidean geometry

The Swedish mathematician Torsten Brodén (1857–1931) wrote two articles on the foundations of Euclidean geometry. The first was published in 1890, almost a decade before Hilbert's first attempt, and the second was published in 1912. Brodén's philosophical view of the nature of geometry is discussed and his thoughts on axiomatic systems are described. His axiomatic system for Euclidean geometry from 1890 is considered in detail and compared with his later work on the foundations of geometry. The two continuity axioms given are compared to and proved to imply Hilbert's two continuity axioms of 1903.     

The proportional solution for rights problems

Recently there have been several studies to provide axiomatic characterizations of solutions to rights problems. However, these studies do not give a satisfactory answer to the question why the proportional solution is the most widely used. This is the question addressed in this paper. To that purpose, we adopt the axiomatic approach; we suggest a set of axioms which a desirable solution should satisfy and we show that the proportional solution is the only solution to satisfy these axioms. Our main axioms are no advantageous reallocation and additivity. A solution satisfies no advantageous reallocation if no subgroup of claimants ever benefits by transferring parts of their claims between themselves. A solution satisfies additivity if it yields the same allocation whether the total estate is divided at once or in several steps.     

The reflection effect for constant risk averse agents

Assume a decision maker has a preference relation over monetary lotteries. The reflection effect, first observed by Kahneman and Tversky, states that the preference order for two lotteries is reversed once they are multiplied by −1. The decision maker is constant risk averse (CRA) if adding the same constant to two distributions, or multiplying them by the same positive constant, will not change the preference relation between them. We combine these two axioms with the betweenness axiom and continuity, and prove a representation theorem. A technical curiosity is that the functions we get satisfy the betweenness axiom, yet are not necessarily Gâteaux (nor Fréchet) differentiable.     

Critères d'induction et de coinduction pour certains anneaux d'opérateurs différentiels

Soit une algèbre de Lie opérant par dérivations sur un anneau local commutatif noethérien (R, ,K=R/ ), et soit V l'anneau des opérateurs différentiels construits à partir de R et . Posons ( )={d /d( ) } et ₀ = ( )/ : ₀ est une algèbre de Lie qui opère sur K par dérivations et l'on peut construire un anneau d'opérateurs différentiels sur K à l'aide de ₀, noté V₀. Grâce au (V₀ − V)-bimodule V/ V on définit l'induction (resp. la coinduction) de V₀ à V par Ind^V_v0=−_v0V/ V (resp. Coind^V_v0=Hom_v0(V/ V,−)) et on donne un critère pour qu'un V-module soit induit (resp. coinduit) à partir de V₀. Ces résultats sont des analogues de ceux, établis par Mackey pour les groupes de Lie et par Blattner pour les algèbres de Lie, analogues, basés sur la notion de système d'imprimitivité.Let be a Lie algebra acting by derivations on a commutative noetherian local ring (R, ,K=R/ ) and let V be the ring of differential operators built on R and . Defining ( )={d /d( ) } et ₀ = ( )/ : ₀ is a Lie algebra which acts on K by derivations, and we can construct a differential operators ring on K with ₀, denoted by V₀. With the help of the (V₀ − V)-bimodule V/ V we define the induction (resp. coinduction) from V₀ to V by Ind^V_v0=−_v0V/ V and we give a criterion for a V-module to be induced (resp. coinduced) from V₀. These results are similar to those established by Mackey for Lie groups and Blattner for Lie algebras, which are based on the notion of the system of imprimitivity.     

Necessary versus equal players in axiomatic studies

This note introduces three variants of existing axioms in which equal players are replaced by necessary players. We highlight that necessary players can replace equal players in many well-known axiomatic characterizations, but not in all. In addition, we provide new characterizations of the Shapley value, the class of positively weighted Shapley values, the Solidarity value and the Equal Division value. This sheds a new light on the real role of equal treatment of equals in the axiomatic literature.     

Proof-theoretic conservations of weak weak intuitionistic constructive set theories

The paper aims to provide precise proof theoretic characterizations of Myhill–Friedman-style “weak” constructive extensional set theories and Aczel–Rathjen analogous constructive set theories both enriched by Mostowski-style collapsing axioms and/or related anti-foundation axioms. The main results include full intuitionistic conservations over the corresponding purely arithmetical formalisms that are well known in the reverse mathematics – which strengthens analogous results obtained by the author in the 80s. The present research was inspired by the more recent Sato-style “weak weak” classical extensional set theories whose proof theoretic strengths are shown to strongly exceed the ones of the intuitionistic counterparts in the presence of the collapsing axioms.     

双F-拓扑中的分离性(Ⅰ)

介绍在双F-拓扑中的T0-,T1-,T2-,T3-,T4-,R0-,R1-,R2-分离性,给出了它们一些等价刻画,研究了它们之间的关系。     

Bjarni Jónsson’s contributions in algebra: an addendum

Normal categories are pointed categorical counterparts of 0-regular varieties, i.e., varieties where each congruence is uniquely determined by the equivalence class of a fixed constant 0. In this paper, we give a new axiomatic approach to normal categories, which uses self-dual axioms on a functor defined using subobjects of objects in the category. We also show that a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0.     

Le rapport di isou (Euclide V, définition 17): Définition, utilisation, transmission

Dans le livre V des Eléments d'Euclide, la définition 17, du di isou logos, se compose de deux énoncés juxtaposés, qui ne sont pas équivalents. Le premier étant une simple réfection du théorème V,22, il convient de regarder le second seul comme authentique, comme le suggérent aussi bien l'emploi de l'expression di isou en géométrie grecque, que l'analyse précise de la tradition indirecte. En conséquence, la définition 17 doit être débarrassée de sa première partie; la définition 18.1, celle de la proportion réglée, doit être restituée comme authentique; la définition 18.2, de la proportion déréglée, doit être réduite à son libellé original, analogue à celui de 18.1.In Euclid's Elements V, Definition 17 (di isou logos) consists of two statements, which are not equivalent. The first one being a remake of theorem V,22, the second is the only one to be taken as genuine. This can be proved by the use of the expression di isou in Greek geometry, and also by a close scrutiny of the various witnesses of this part of the text. Consequently, Definition 17 should be cleared of its first part; Definition 18.1, of the ordered proportion, should be restored as genuine; Definition 18.2, of the perturbed proportion, should be reduced to its original core, and made similar to 18.1.     

拓扑分子格的ST*分离性公理

由半开元、半拓扑概念出发在拓扑分子格中引入 ST* 分离性公理 ,给出它们的刻画 ,推广文 [2 ]中 T* 分离性公理 ,并得到 ST* 分离性与 T* 分离性之间的关系。     

Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context

We consider several aspects of the role and evaluation of the four-sexagesimal-place approximation to on the well-known Old Babylonian tablet YBC 7289. By referring to what is known about OB school texts, we show that this text is most probably a school exercise by a trainee scribe who got the approximation from a coefficient list. These coefficient lists are briefly described, with their use in geometrical problems. We consider other texts involving square roots and derive an algorithm for evaluating them, which complies with all known OB examples, from a simple geometrical construction of the type that seems to underlie many other OB procedures.Copyright 1998 Academic Press.Nous considérons plusieurs aspects du rôle et de l'évaluation de l'approximation à quatre places sexagésimales de sur cette tablette paléo-babylonienne. En nous référant à l'état des connaissances quant aux textes scolaires paléo-babyloniens, nous montrons comment ce texte est très probablement un exercice scolaire exécuté par un apprenti scribe qui a obtenu l'approximation à partir d'une liste de coéfficients. Nous décrivons en bref ces listes de coéfficients, ainsi que leur utilisation dans les problèmes de géométrie. Nous considérons d'autres textes traitant de racines carrées , et pour les évaluer nous dérivons un algorithme qui est en accord avec tous les exemples paléo-babyloniens connus; ceci à partir d'une construction géométrique simple du type qui semble être charactéristique de beaucoup d'autres procédures paléo-babyloniennes.Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A17; 11-03     

The Missing Problems of Gersonides—A Critical Edition, II

Gersonides' Maaseh Hoshev (The Art of Calculation) is a major work known for its early use of rigorous combinatorial proofs and mathematical induction. There is a large section of problems at the end of the book, with the theme of proportions, which until now remained unpublished. I present a critical edition of this material. I also uncover a previously unknown second edition of Maaseh Hoshev. The material is appropriate for creative pedagogy and provides economic details of the author's culture and environs. A previous article presented the first, 15 problems and this article presents the rest. Copyright 2000 Academic Press.Le Maase Hoshev (L'Art du Calcul) de Gersonide est un ouvrage majeur connu pour son usage précoce de preuves combinatoires rigoreuses et de l'induction mathématique. La fin de l'ouvrage comporte une section importante consacrée a une série de trente problèmes sur le thème des proportions qui était restée inédite jusqu'à ce jour et dont je présente pour la première fois une édition critique. Je révèle également l'éxistence d'une séconde édition de Maase Hoshev. Le matériau peut servir de base à des projets de pédagogie créative et offre des détails sur la culture et l'environnement de l'auteur. Cet article fait suite a une première étude qui présentait les quinze premiers problèmes de Maase Hoshev et en présente les quinze autres.     

格上点式一致结构的刻划与点式度量化定理

本文通过对格上远域映射,特别是△-映射和＊-映射的性质的研究,给出了格上点式一致结构的若干简明刻划,证明了几个重要的格上点式度量化定理,并提出了与格上点式度量理论相协调的若干分离性公理.     

On separation axioms in fuzzy topological spaces,fuzzy neighborhood spaces,and fuzzy uniform spaces

A certain number of separation axioms for fuzzy topological spaces are provided, all of which are good extensions of the topological (T₀), (T₁), or (T₂). All valid implications between the different axioms are studied and counterexamples are given for the nonvalid ones.     

Consistency and monotonicity in assignment problems

This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem we use six axioms including the consistency (CONS) and the weak pairwise-monotonicity (W.P.MON) which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problem coincides with the set of the competitive allocations of the economy, our characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, our main result gives a new normative implication of competitive equilibria.