集合对策中值的标准性与分配方案的单调性

本文介绍了合作对策中一种新的类型一集合对策，讨论了集合对策中三种分配方案的性质，证明了边缘贡献值和联盟力量值具有二人分配的标准性与分配方案的单调性，而共享边缘贡献值仅具有分配方案的单调性．     

May简单多数规则的描述

本文将Asan就两个备选对象定义的弱路径独立性和Woeginger就两个备选对象定义的亚社会可约性概念推广到任意备选对象集,在给定的有限参与人集及任意备选对象集的条件下,讨论了一社会福利函数是简单多数规则的充要条件,从而推广了Asan和Woeginger的工作.     

投票悖论概率计算的基本定理

多数偏好规则是求解群体最优化问题最重要和应用最广泛的规则之一.但是,在使用这一规则对给定的群体最优化问题寻求最优解中,有时会发生群体偏好循环排序的"投票悖论"现象,从而发生"投票悖论"现象的概率计算,便成为群体最优化中一个基本的研究课题.为此,引进群体在方案集上的"投票悖论排序剖面"和"投票悖论选型剖面"的概念.借助于这两个概念,建立了群体中每一个体对所有方案的偏好排序都可各具不同概率分布的一般情况下,群体对问题进行方案择优时,发生"投票悖论"概率计算的基本定理.于是,解决了求解群体最优化时发生"投票悖论"的概率计算研究中,长期未能得到彻底解决的基本问题.     

高考中导数应用的新变化——用导数探讨函数图象的交点问题

观察近几年高考试题,其中导数命题的方向基本没变,主要从五个方面(①与切线有关的问题;②函数的单调性和单调区间问题;③函数的极值和最值问题;④不等式证明问题;⑤与函数的单调性、极值、最值有关的参数问题)考查了学生对导数的掌握水平,但在方向基本没变的情况下,又有所创新,导数命题创新有两个方面:一是研究对象的多元化,由研究单一函数转向研究两个函数或多个函数;二是研究内容的多元化,由用导数研究函数的性质(单调性、最值、极值)转向运用导数进行函数的性质、函数图象的交点和方程根的分布等综合研究,实际上就是导数考查函数图象的交…     

函数单调性的应用

学过函数的性质后,觉得单调性是函数的所有性质中,最为一般的一种性质.因为几乎所有的函数都有单调性可言,并且在解决诸如确定函数的单调区间、求函数值域、最大(小)值等数学问题时,可大显身手.有些表面上与函数的单调性关联不大数学问题,一旦我们把它们与函数的单调性联系起来,似乎对问题的理解就会变得容易起来,解题过程就将变得快捷起来.下面,把一些心得写在下面,以供同学们参考.     

大型群体决策问题中的简单多数规则（3个评选对象场合）

一个群体决策问题取决于两个因素,一个是群体决策的规则,另一个是投票。当选定群体决策规则时,一个群体决策问题由投票完全决定,此时,群体决策问题与投票之间一一对应。简单多数规则是个简单且被广泛采用的群体决策规则,但它有缺陷,我们可举出些群体决策问题使用简单多数规则没法从投票得到最后群体决策的结果。这里我们将给出一个简单多数规则的有趣性质,即在3个评选对象场合,使用简单多数规则没法从投票得到最后群体决策结果的n个评选人的群体决策问题的个数与所有n个评选人的群体决策问题的个数之比当评选人个数n趋向无穷时趋于零,这说明3个评选对象的大型群体决策场合,简单多数规则的缺陷不严重。     

非凸映射的非线性本征值问题的正解

<正> 最近在[5]中 Amann H.和 Leatsch T.对凸映射的非线性本征值问题的正解进行了详细地讨论,这种解的大范围性质,依赖于半序 Banach 空间中凸映射的性质、单调映射的性质、正算子的性质,特別要借助于拓扑方法.本文将[5]中结果推广到一类非凸映射情形,在更一般的条件下讨论了非线性本征值问题的大范围性质,这些结果不仅包含了[5]     

聚焦指数函数单调性的应用

单调性是函数的重要性质之一,而指数函数的单调性更是尤为重要.对于指数函数y=a^x(a>0,a≠1),当a>1时,它在实数集R上单调递增;当a∈(0,1)时,它在实数集R上单调递减.由此可见,指数函数的单调性并不复杂,但它的应用却不简单,它可以用来比较大小、求函数的定义域、求函数的最值或值域、求参数的值或范围、解方程或证明不等式,还可以解决综合性问题.     

函数y=ax＋b／x的单调性及其应用

一、如何讨论函数y=ax+b/x(a>0,b>0)函数的单调性? 先从“图象”上来寻求函数性质,再作论证. 不妨先讨论具体的a、b值.例如:a=2、b=1,即研究函数y=2x+1/x的单调性. 1.用图象叠加法作出大致图象     

T-单调映射及其性质

T-单调映射在变分不等式及非线性互补问题中经常遇到.此映射对应的非线性问题的解具有一些非常好的性质.这些性质在解的存在性证明,数值算法的构造及其收敛性分析中占有重要地位.本文系统讨论T-单调映射的性质,建立T-单调映射与常见的一些映射,如单调映射和Z-映射之间的联系.     

An experimental study of voting rules and polls in three-candidate elections

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.     

Asymptotic vulnerability of positional voting rules to coalitional manipulation

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.     

Voting cycles,plurality rule and strategic manipulation

In this note, we investigate the connection between the existence of cycles and the opportunities of strategic manipulation under a specific social decision function, the plurality rule. Contrary to previous research in this field, voting cycles are considered as a possible cause rather than a consequence of strategic voting. The results we obtain allow us to evaluate the vulnerability of the plurality rule to strategic voting, and to study how the distribution of voters over preference orderings affects the risk of manipulation.Partial support has been obtained from the Swedish Council for Research in the Humanities and Social Sciences.     

Comparing influence theories in voting games under locally generated measures of dissatisfaction

The Isbell desirability relation (I), the Shapley?CShubik index (SS) and the Banzhaf?CColeman index (BC) are power theories that grasp the notion of individual influence in a yes?Cno voting rule. Also, a yes?Cno voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes?Cno voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters.     

Optimal bounds for the no-show paradox via SAT solving

One of the most important desirable properties in social choice theory is Condorcet-consistency, which requires that a voting rule should return an alternative that is preferred to any other alternative by some majority of voters. Another desirable property is participation, which requires that no voter should be worse off by joining an electorate. A seminal result by Moulin (1988) has shown that Condorcet-consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters. We leverage SAT solving to obtain an elegant human-readable proof of Moulin’s result that requires only 12 voters. Moreover, the SAT solver is able to construct a Condorcet-consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters, proving the optimality of the above bound. We also obtain tight results for set-valued and probabilistic voting rules, which complement and significantly improve existing theorems.     

A Bayesian approach to a sequential three‐decision problem: Voting and the uses of information in electoral choice*

This paper investigates a situation of decision‐making under risk in which an individual must select one of three actions. Substantively, an electoral example in which a citizen must decide how and whether to vote in a two‐candidate election is used to illustrate the argument. Only the value of the consequences of one action, which is to abstain from voting, is known. The expected values of voting for either candidate must be estimated based upon a sample of information. Specifically, we are interested in how one may decide when to stop gathering information and the behavioral consequences of that choice for the voting decision. The dependence of the voting decision on the original ambiguity and magnitude of the expected utilities and on the costs of information is also explored.     

Symplectic geometry of constrained optimization

In this paper, we discuss geometric structures related to the Lagrange multipliers rule. The practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows one to effectively do it even for very degenerate problems with complicated constraints. The main geometric and analytic tool is an appropriately rearranged Maslov index. We try to emphasize the geometric framework and omit analytic routine. Proofs are often replaced with informal explanations, but a well-trained mathematician will easily rewrite them in a conventional way. We believe that Vladimir Arnold would approve of such an attitude.     

Equilibrium and effectiveness of two-parameter scoring rules

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.     

An axiomatic characterization of some locations in trees

We describe axioms that uniquely characterize the absolute median and the squared median (the point that minimizes the sum of squared distances) of a tree. A common feature of these characterizations is a Consistency axiom of the type first used by H.P. Young to characterize a voting procedure called Borda's rule. These results make it possible to argue in favor of, or against, a particular location in terms of principles satisfied or violated.     

An approach to different voting rules from cooperative games with alternatives. Case study: the Catalonia Parliament

We apply simple games with alternatives to describe voting mechanisms used in parliamentary organizations. As a matter of example, we analyze the Catalonia Parliament. Special attention is paid to abstention, which is allowed in most voting rules but is not taken into account when a voting rule is modelled as a simple classical game. To measure the power of each voter in each game, the extended Shapley–Shubik index is considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)