Papers by Vladimir Danilov
Mathematical Social Sciences, 1987
In this paper we prove a structure theorem for the binary aggregation rule of dichotomic preferen... more In this paper we prove a structure theorem for the binary aggregation rule of dichotomic preferences. Each such rule is characterized by a qualitative measure on the set of individuals. In some interesting cases a qualitative measure can be represented by a quantitative measure.
Econometrica, 1992
This paper is concerned with a problem of implementation of a given social choice correspondence.... more This paper is concerned with a problem of implementation of a given social choice correspondence. The authors introduces an essential monotonicity condition and show that any implementable social choice correspondence satisfies this condition. Conversely, in a case of three or more participants, any essentially monotone social choice correspondence is implementable. In a case of two participants, the essential monotonicity condition
Mathematical Social Sciences, 2003
We call the three-sided system the following collection of data. There are three (disjoined) fini... more We call the three-sided system the following collection of data. There are three (disjoined) finite sets M, W and C (whose elements represent, somewhat obviously, men, women and children). A family is a triple (w, c, m) W×C×M. A matching is a bundle of monogamous ...
Dam, Nov 12, 2010
A Condorcet domain (CD) is a collection of linear orders on a set of candidates satisfying the fo... more A Condorcet domain (CD) is a collection of linear orders on a set of candidates satisfying the following property: for any choice of preferences of voters from this collection, a simple majority rule does not yield cycles. We propose a method of constructing "large" CDs by use of rhombus tiling diagrams and explain that this method unifies several constructions of CDs known earlier. Finally, we show that three conjectures on the maximal sizes of those CDs are, in fact, equivalent and provide a counterexample to them.
... No. 08-30 Equilibria with indivisible goods and package-utilities Vladimir I. Danilov∗ and Gl... more ... No. 08-30 Equilibria with indivisible goods and package-utilities Vladimir I. Danilov∗ and Gleb A. Koshevoy∗∗ and Christine Lang∗∗∗ December 2008 ... Page 2. Equilibria with indivisible goods and package-utilities Vladimir I., Danilov∗, Gleb A. Koshevoy, and Christine Lang ...
Secondly, using merely combinatorial means, we demonstrate a relationship between regular $B_n$-c... more Secondly, using merely combinatorial means, we demonstrate a relationship between regular $B_n$-crystals (resp. $C_n$-crystals) and regular symmetric $A_{2n-1}$-crystals (resp. $A_{2n}$-crystals).
Journal of the New Economic Association, 2012
Условие отбрасывания в теории выбора В работе даются две характеризации функций выбора, удовлетво... more Условие отбрасывания в теории выбора В работе даются две характеризации функций выбора, удовлетворяющих условию отбрасывания -порядковое и алгебраическое -в терминах некоторой операции на множестве стабильных меню. Изучаются следствия ассоциативности этой операции, а также другие усиления свойства отбрасывания. Ключевые слова: функция выбора, условие наследования, условие согласия, ассоциативность, независимость от пути. Класси фикация JEL: D71. 3 Данный результат был «переоткрыт» Ф. Брандтом и П. Харренштейном в (Brandt, Harrenstein, 2011) спустя 30 лет. Несмотря на то что работа (Айзерман, Малишевский, 1981) приведена в их списке литературы, создается впечатление, что они ее просто не читали. 4 «Порождающее гиперотношение для такой функции подбирается, вообще говоря, неоднозначно» (Айзерман, Малишевский, 1981). Это же отмечается и в (Brandt, Harrenstein, 2011).
It is well known, due to Lindstr\"om, that the minors of a (real or complex) matrix can be expres... more It is well known, due to Lindstr\"om, that the minors of a (real or complex) matrix can be expressed in terms of weights of flows in a planar directed graph. Another classical fact is that there are plenty of homogeneous quadratic relations involving flag minors, or Pl\"ucker coordinates of the corresponding flag manifold. Generalizing and unifying these facts and their tropical counterparts, we consider a wide class of functions on $2^{[n]}$ that are generated by flows in a planar graph and take values in an arbitrary commutative semiring, where $[n]=\{1,2,\ldots,n\}$. We show that the ``universal'' homogeneous quadratic relations fulfilled by such functions can be described in terms of certain matchings, and as a consequence, give combinatorial necessary and sufficient conditions on the collections of subsets of $[n]$ determining these relations.
Mpra Paper, 2011
We introduce a new approach to showing existence of equilibrium in models of economies with unbou... more We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange economies, all papers known to us stating conditions for existence of equilibrium with unbounded short sales place conditions on recession cones of agents' preferred sets or, more recently, require compactness of the utility possibilities set.. In contrast, in this paper, we place conditions on the preferred sets themselves. Roughly, our condition is that the sum of the weakly preferred sets is a closed set. We demonstrate that our condition implies existence of equilibrium. In addition to our main theorem, we present two theorems showing cases to which our main theorem can we applied. We also relate our condition to the classic condition of Hart (1974).
Journal of Mathematical Analysis and Applications, Jul 1, 2000
Let¨be a cooperative TU game and¨s¨y¨be a decomposition of¨as a 1 2 Ž . difference of two convex ... more Let¨be a cooperative TU game and¨s¨y¨be a decomposition of¨as a 1 2 Ž . difference of two convex games¨and¨. Then the core C¨of the game¨has a 1 2 Ž . Ž . Ž . similar decomposition C¨s C¨] C¨, where ] denotes the Minkowski 1 2
Journal of the New Economic Association, 2009
В работе предлагается подход, позволяющий на формальном уровне обсуждать некоммутирующие измерени... more В работе предлагается подход, позволяющий на формальном уровне обсуждать некоммутирующие измерения. Такие измерения «возмущают» измеряемую систему и меняют ее состояния. Центральной структурой, ответственной за описание таких измерений, оказывается структура ортопосета (булева в классическом случае коммутирующих измерений). Состояния системы реализуются как вероятностные меры на этом ортопосете. Приводится применение предложенного подхода к принятию решений в условиях «неклассической» неопределенности, а также моделированию «неклассических» предпочтений.
Journal of Algebraic Combinatorics, Jan 28, 2012
In this paper, generalizing those earlier results, we reveal wider classes of pure domains in $2^... more In this paper, generalizing those earlier results, we reveal wider classes of pure domains in $2^{[n]}$. This is obtained as a consequence of our study of a novel geometric--combinatorial model for weakly separated set-systems, so-called \emph{combined (polygonal) tilings} on a zonogon, which yields a new insight in the area.
Lecture Notes in Economics and Mathematical Systems, 1997
Algebra, 2013
-crystals are certain edge-colored directed graphs, which are related to representations of the q... more -crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra (sl +1 ). For such a crystal with colors 1, 2, . . . , , we consider its maximal connected subcrystals with colors 1, . . . , −1 and with colors 2, . . . , and characterize the interlacing structure for all pairs of these subcrystals. This enables us to give a recursive description of the combinatorial structure of via subcrystals and develop an efficient procedure of assembling .
Social Choice and Welfare, 2014
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Papers by Vladimir Danilov