社会福利函数独裁的特征

在这篇短文中,给出了关于社会福利函数F的半严格正向响应的概念,并且证明了如果备选对象至少有三个,则弱帕累托性质与半严格正向响应性质是独裁的充分必要条件.作为应用,我们给出了社会选择函数防止策略性操纵的一个等价描述,并对社会福利函数引进了防止局部策略性操纵的概念,得到了一个类似于Gibbard—Satterthwaite定理的结论.     

微分方程f″+e^{az}f′+Q(z)f=F(z) 的复振荡

该文研究了线性微分方程f″+e^{az}f′+Q(z)f=F(z)的复振荡问题，其中Q(z)、F(z )( 0)是整函数，且σ(Q)=1,σ(F)<+∞,Q(z)=h(z)e^{bz},h(z)是多项式，b≠-1是复常数，那么上述线性微分方程的所有解f(z)满足~λ(f)=λ(f)=σ(f)=∞,~λ_2(f)=λ_2(f)=σ_2(f)=1.至多除去两个例外复数a及一个可能的有穷级例外解f_0(z)。     

时变参数动力系统的两种跟踪性质

在时变参数动力系统中引入链传递,伪轨跟踪以及渐进伪轨跟踪的概念,并通过这些概念讨论时变参数动力系统的伪轨跟踪和渐进伪轨跟踪的性质.证明了扩张的时变参数动力系统满足伪轨跟踪性质蕴含其满足渐近伪轨跟踪性质;论证了时变参数动力系统的积系统满足伪轨跟踪和渐进伪轨跟踪性质的充要条件是其每一个分系统也满足相应的性质.最后构造出了一个时变参数动力系统的例子:(∑∞X,F),证明了(∑∞X,F)是拓扑传递的,并且满足渐近伪轨跟踪性质.     

非满等距映射的线性延拓

主要研究实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题．得到：若等距映射V_0：S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V：E→F,这是我们首次在非满的情况下考虑Tingley问题．     

两个l∞-空间单位球面间非满等距算子的讨论及其应用

该文给出了单位球面间等距算子在非满情况下的一些性质, 以及在这种情况下算子值域空间的一些结构特征, 并由此得出从c₀(Gamma)到l^∞-空间单位球面之间非满等距算子能够延拓的充要条件.     

逆极限的点式集体正规性

论文的主要结果如下：设X是拓扑空间的逆向系{Xa,π^aβ,∧}的极限且每个投射πa：X→Xa是开的满映射．设x是|∧|一仿紧的且P表示下列四条性质中的任意一条：(i)点式集体正规性,(ii)σ-点式集体正规性;(iii)几乎可膨胀性;(iv)σ-几乎可膨胀性．若每个Xa具有性质P,则X具有性质P．同时还具有相应的遗传性质．     

L-拓扑空间的单点超F紧化

给出L-拓扑空间的单点超F紧化的一种具体作法,以及局部超F紧性的定义,并证明了:(1)局部超F紧性是L-好推广;(2)一个L-拓扑空间是局部超F紧T2空间当且仅当其单点超F紧化空间是超F紧T2空间;(3)单点超F紧化在同胚意义下是唯一的。     

平面内到两个定点的距离的和等于常数的点的轨迹一定是椭圆吗?

考察一道选择题.满足|z-1| |z 1|=1在复数Z在复平面内对应的点(A)轨迹是椭圆;(B)轨迹是双曲线;(C)轨迹是圆;(D)轨迹是一条线段;(E)轨迹不存在。 不少同学这样分析:根据复数的几何意义,方程|z-1| |z 1|表示动点到两个定点的距离之和等于常数。再根据椭圆的定义,该动点的轨迹是椭圆。故应选(A)。 其实,选(A)是错误的。 证明:(反证法)若(A)正确,那么椭圆的两焦点是F,     

带核实域上的正定函数

称谓“带核实域”(formally real field with core)出自文献[1],通常的形式实域和有序域可看成此种结构之特款。本文仿照[2],讨论带核实域上的正定函数和Hilbert性质,并获得相应的结果。另外我们给出一个例子(定理2.6后面的例子),藉以说明有序域具有一些性质,这些性质不能推广到带核实域上去。设F是一个域。若C是F的一个非空子集,且满足(ⅰ)0(?)C;(ⅱ)C对于F中的乘法运算构     

正规族与复合亚纯函数

本文研究了亚纯函数族涉及复合有理函数与分担亚纯函数的正规性. 证明了一个正规定则:设 α(z) 和 F 分别是区域 D 上的亚纯函数与亚纯函数族, R(z) 是一个次数不低于 3 的有理函数.如果对族 F 中函数 f(z) 和 g(z), R○f(z) 和 R○g(z) 分担 α(z) IM,并且下述 条件之一成立:
(1) 对任何 z₀ ∈ D, R(z)-α(z₀) 有至少三个不同的零点或极点;
(2) 存在 z₀ ∈ D 使得 R(z)-α(z₀):=(z-β₀)^pH(z) 至多有两个零点(或极点) β₀,同时 k ≠ l|p|,其中 l 和 k 分别是 f(z)-β₀ 和 α(z)-α(z₀) 在 z₀ 处的零点重数, H(z) 是满足 H(β₀) ≠ 0, ∞ 的有理函数, α(z) 非常数并满足 α(z₀) ∈ C ∪{∞}.
那么 F 在 D 内正规.特别地,这个结果是著名的 Montel 正规定则的一种推广.     

Range convexity,continuity, and strategy-proofness of voting schemes

A voting scheme assigns to each profile of alternatives reported byn individuals a compromise alternative. A voting scheme is strategy-proof if no individual is better off by lying, i.e., not reporting a best alternative. In this paper the main results concern the case where the set of alternatives is the Euclidean plane and the preferences are Euclidean. It is shown that for strategy-proof voting schemes continuity is equivalent to convexity of the range of the voting scheme. Using a result by Kim and Roush (1984), this leads to characterizations of surjective or unanimous, anonymous, strategy-proof voting schemes.Furthermore, the paper contains an extensive discussion of related results in the area.     

Coalitional power structure without the pareto principle

In this paper we have extended Arrow's analysis to a framework where for any given profile of individual preference orderings the decision procedure specifies a non-trivial probability distribution over possible social orderings. We have demonstrated that if the social decision procedure satisfies certain probabilistic versions of weak independence of irrelevant alternatives, then it is characterized by a ‘power’ structure for all possible coalitions of individuals without assuming either the Pareto Principle or its antecedents. A generalised version of Arrow's impossibility theorem follows as a special case of our result. We have weakened Arrow's independence condition, and have shown the existence of a hierarchy of dictators without imposing the Pareto criterion.     

The categorical approach to social choice theory

A number of different problems in social choice theory are given a common treatment in the framework of category theory. A social choice function is a map μ from a set Hom(A, PX) of profiles - in applications functions from a set A of agents to the set PX of linear orders on a set X of alternatives - to a set GPX the nature of which depends on the application. The main theorem established is applied to social welfare functions and strategy-proof voting schemes.     

Strategy-proof and efficient allocation of an indivisible good on finitely restricted preference domains

We consider allocation mechanisms in economies with a single indivisible good and money. First, we show that there is no strategy-proof and Pareto efficient mechanism on some preference domains which consist of a sufficiently large but finite number of quasi-linear preferences. Second, we show that there is no strategy-proof, Pareto efficient, and equally compensatory mechanism on arbitrary preference domains which consist of more than three quasi-linear preferences. Received: July 1999/Final version: April 2000     

Metric rationalization of social welfare functions

Metric rationalization of social decision rules has been intensively investigated when the social outcome is a nonempty subset of alternatives. The present paper proposes a similar framework for social welfare functions (SWFs)—that is when each social outcome is a ranking of alternatives. A metric rationalizable SWF reports as an approximation of the unanimity consensus the relative ranking of any pair of alternatives as in the closest profile where individuals all agree on those alternatives, the closeness being measured with respect to a metric on profiles. Two notions of unanimity are in consideration: top unanimity on an alternative holds when individuals all agree that it is top ranked while pairwise unanimity on a pair occurs when individuals all prefer an alternative to another. Without strong requirements on metrics, characterizations provided in both cases show that metric rationalizations of SWFs are essentially equivalent to the Pareto principle for SWFs. Furthermore, two interesting classes of metric rationalizable SWFs–multi-valued scoring SWFs and pairwise scoring SWFs–are each uniquely identified by means of some appropriate and appealing properties on metrics among which decomposability, neutrality and monotonicity are known.     

Restricted domains,arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives

An n-person social choice problem is considered in which the alternatives are n dimensional vectors, with the ith component of such a vector being the part of the alternatives affecting individual i alone. Assuming that individuals are selfish (individual i must be indifferent between any two alternatives with the same components), that they may be indifferent among alternatives and that each individual may choose his preferences out of a different set of permissible preferences, we prove that any set of restricted domains of preferences admits an n person non-dictatorial Arrow-type social welfare function if and only if it admits a two-person Arrow-type social welfare function: we characterize all the sets of restricted domains of preferences which admit two-person Arrow-type social welfare functions (and therefore also admit n-person Arrow-type social welfare functions) and then we prove that we also characterized all the sets of restricted domains of preferences which admit nondictatorial, nonmanipulable, noncorruptible and rational social choice correspondences.     

Pareto optimal matchings with lower quotas

We consider the problem of allocating applicants to courses, where each applicant has a capacity, possibly greater than 1, and a subset of acceptable courses that she ranks in a strict order of preference. Each course has a lower and an upper quota, indicating that if it is assigned some applicants then their number has to be between these two bounds. We further suppose that applicants extend their preferences over courses to preferences over bundles of courses lexicographically.In this setting we present several algorithmic results concerned with the computation of Pareto optimal matchings (POMs). Firstly, we extend the Serial Dictatorship with Project Closures mechanism to the case when an applicant can be assigned more than one course. We show that unlike in the one-to-many case no mechanism is strategy-proof against dropping manipulations and that this mechanism is strategy-proof against reordering strategies only for some picking sequences. We further show the intractability of the following problems: deciding about the Pareto optimality of a given matching, computation of a POM with maximum cardinality and computation of a POM in case of indifferences.     

Extended anonymity and Paretian relations on infinite utility streams

We examine the range of anonymity that is compatible with a Paretian social welfare relation (SWR) on infinite utility streams. Three alternative coherence properties of an SWR are considered, namely, acyclicity, quasi-transitivity, and Suzumura consistency. For each case, we show that a necessary and sufficient condition for a set of permutations to be the set of permissible permutations of some Paretian SWR is given by the cyclicity of permutations and a weakening of group structure. Further, for each case of coherence property, we show that the extended Pareto rule is the least element of the class of anonymous Paretian SWRs.     

New optimality principles for economic efficiency and equilibrium

This paper develops several optimization principles relating the fundamental concepts of Pareto efficiency and competitive equilibria. The beginning point for this development is the introduction of a new function describing individual preferences, closely related to willingness-to-pay, termed the benefit function. An important property of the benefit function is that it can be summed across individuals to obtain a meaningful measure of total benefit relative to a given set of utility levels; and the optimization principles presented in the paper are based on maximization of this total benefit.Specifically, it is shown that, under appropriate technical assumptions, a Pareto-efficient allocationX maximizes the total benefit relative to the utility levels it yields. Conversely, if an allocationX yields zero benefit and maximizes the total benefit function, then that allocation is Pareto efficient. The Lagrange multipliersp of the benefit maximization problem serve as prices; and the (X,p) pair satisfies a generalized saddle-point property termed a Lagrange equilibrium. This in turn is equivalent, under appropriate assumptions, to a competitive equilibrium.There are natural duals to all of the results stated above. The dual optimization principle is based on a surplus function which is a function of prices. The surplus is the total income generated at pricesp, minus the total income required to obtain given utility levels. The dual optimization principle states that prices that are dual (or indirect) Pareto efficient minimize total surplus and render it zero. Conversely, a set of prices that minimizes total surplus and renders it zero is a dual Pareto efficient set of prices.The results of the paper can be viewed as augmenting the first and second theorems of welfare economics (and their duals) to provide a family of results that relate the important economic concepts of Pareto efficiency, equilibrium, dual (or indirect) Pareto efficiency, total benefit, Lagrange equilibrium, and total surplus.The author wishes to thank Charles R. Bowman and Andrew J. Yates for several valuable suggestions and corrections.