Mathematical Social Sciences最新文献

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Multi-winner rules analogous to the Plurality rule 多赢家规则类似于多数规则

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-03-22 DOI: 10.1016/j.mathsocsci.2025.102405

Clinton Gubong Gassi , Frank Steffen

The aim of this paper is to identify the multi-winner voting rules that can be considered as extensions of the Plurality rule when voters’ preferences are expressed as linear rankings over the candidates. Multi-winner voting addresses the problem of selecting a fixed-size subset of candidates, called a committee, from a larger set of available candidates based on the voters’ preferences. In the single-winner setting, where each voter provides a strict ranking of the candidates and the goal is to select a unique candidate, Yeh (2008) characterized the Plurality rule as the only voting rule satisfying five independent axioms: anonymity, neutrality, consistency, efficiency, and top-only. In this paper, we demonstrate that a natural extension of these axioms to the multi-winner framework allows us to identify a class of top-

k

counting rules as multi-winner analogous to the Plurality rule, that does not contain the classical

k

-Plurality rule.

本文的目的是确定多赢家投票规则，当选民的偏好被表示为对候选人的线性排名时，多赢家投票规则可以被视为多数原则的延伸。多赢家投票解决的问题是，根据选民的偏好，从更多的可用候选人中选择一个固定规模的候选人子集（称为委员会）。在单一赢家的情况下，每个选民对候选人进行严格的排名，目标是选择一个唯一的候选人，Yeh（2008）将多数规则描述为唯一满足五个独立公理的投票规则：匿名性、中立性、一致性、效率和top-only。在本文中，我们证明了这些公理的自然扩展到多赢家框架允许我们识别一类顶k计数规则作为多赢家类似于多数规则，它不包含经典的k-多数规则。

引用次数: 0

Bargaining theory and the copyright royalty board’s rate setting decisions for interactive streaming of music 讨价还价理论和版权版税委员会的费率设置决策的交互式流媒体音乐

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-02-11 DOI: 10.1016/j.mathsocsci.2025.01.005

Elliott Hughes , Richard Watt

In the USA, the remuneration for songwriters whose copyrighted material is broadcast using online interactive music services is subject to a compulsory license with a rate that is regulated by the Copyright Royalty Board. On the other hand, an essentially equally necessary input to the interactive music services, namely the sound recording copyright, is freely negotiated between the parties. This sets up an interesting bargaining problem that is of interest to the regulator. The present paper sets out this problem formally, and resolves the equilibrium outcomes. The model is calibrated with the actual rates that have been set recently.

在美国，使用在线互动音乐服务播放受版权保护的作品的词曲作者的报酬受到版权版税委员会规定的强制许可的约束。另一方面，对于交互式音乐服务来说，一个本质上同样必要的投入，即录音版权，是双方自由协商的。这就形成了一个有趣的讨价还价问题，监管机构对此很感兴趣。本文正式阐述了这一问题，并求解了均衡结果。该模型是根据最近设定的实际利率进行校准的。

引用次数: 0

A measurement of population ageing: From the perspective of thickness of the labor force 人口老龄化的测度：基于劳动力厚度的视角

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-31 DOI: 10.1016/j.mathsocsci.2025.01.004

Yoko Kawada , Yuta Nakamura , Noriaki Okamoto

We propose a new measure of population ageing, and introduce a new condition called the working-age principle, which is a sensitivity condition to the “thickness” of the working-age population. Then, we characterize our measure by working-age principle and the other standard axioms. We also applied our measure to compute the degree of ageing in China, Japan, Niue, and Singapore, highlighting its importance in capturing the thickness of the labor force.

我们提出了一种新的人口老龄化衡量标准，并引入了一个新的条件，称为工作年龄原则，这是一个对工作年龄人口“厚度”的敏感性条件。然后，我们用工作年龄原则和其他标准公理来描述我们的测量。我们还应用我们的方法计算了中国、日本、纽埃和新加坡的老龄化程度，强调了其在捕捉劳动力厚度方面的重要性。

引用次数: 0

Cooperative games with types, outside options, and the egalitarian value 具有类型、外部选择和平等价值的合作游戏

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-22 DOI: 10.1016/j.mathsocsci.2025.01.003

Florian Navarro

This article introduces a new axiom of sub-game order preservation for TU-games as well as a model of cooperative games with types. The axiom, alongside efficiency, characterizes the egalitarian value. The model addresses situations where players of different types are needed. Each player has a specific type and coalitions are feasible only if it contains at most one player of each type. We use the new characterization of the egalitarian value for TU-games to obtain the following result in our class of problems: the egalitarian value is the only sharing rule that ensures that each player of the most productive group is better off joining this most productive group. We characterize the egalitarian value without fairness requirement and show that, for this new class of problems, egalitarianism can provide some form of incentives towards optimal cooperation.

本文给出了一个新的u -对策子对策序保持公理，以及一类合作对策的模型。这条公理与效率一道，代表了平等主义的价值。该模型解决了需要不同类型玩家的情况。每个参与者都有一个特定的类型，联盟只有在每种类型中最多包含一个参与者时才是可行的。我们使用tu博弈的平均主义价值的新特征，在这类问题中得到以下结果：平均主义价值是唯一的共享规则，它确保最具生产力群体的每个参与者加入这个最具生产力的群体会更好。我们描述了没有公平要求的平均主义价值，并表明，对于这类新问题，平均主义可以提供某种形式的激励，以实现最优合作。

引用次数: 0

Upper semicontinuous utilities for all upper semicontinuous total preorders 所有上半连续总预订量的上半连续效用

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-15 DOI: 10.1016/j.mathsocsci.2025.01.002

Gianni Bosi, Gabriele Sbaiz

Let

X

be an arbitrary nonempty set. Then a topology

t

X

is said to be completely useful (or upper useful) if every upper semicontinuous total preorder

≾

on the topological space

(X, t)

can be represented by an upper semicontinuous real-valued order-preserving function (i.e., utility function). In this paper the structures of completely useful topologies on

X

will be deeply studied and clarified. In particular, completely useful topologies will be characterized through the new notions of super-short and strongly separable topologies. Further, the incorporation of the Souslin Hypothesis and the relevance of these characterizations in mathematical utility theory will be discussed. Finally, various interrelations between the concepts of complete usefulness and other topological concepts that are of interest not only in mathematical utility theory are analyzed.

设X是一个任意的非空集合。如果拓扑空间（X,t）上的每个上半连续全预序≾都可以用上半连续实值保序函数（即效用函数）表示，则X上的拓扑t是完全有用的（或上有用的）。本文将深入研究和阐明X上完全有用拓扑的结构。特别是，完全有用的拓扑将通过超短和强可分拓扑的新概念来表征。此外，将讨论苏斯林假设的结合以及这些特征在数学效用理论中的相关性。最后，分析了完全有用性概念与其他拓扑概念之间的各种相互关系，这些概念不仅在数学效用理论中感兴趣。

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引用次数: 0

Information-based discrimination 以信息为基础的歧视

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-08 DOI: 10.1016/j.mathsocsci.2025.01.001

Naomi M. Utgoff

The distribution of a single college’s incoming freshman cohort by high school of origin differs from the population distribution of high school seniors (Bernhard, 2013), a fact typically attributed to taste-based or statistical discrimination. This paper models a third explanation which I call information-based discrimination: information asymmetries between a college and high schools incentivize the formation of a relationship between the college and one ex ante randomly selected high school, resulting in de facto discriminatory admissions even in the absence of taste-based and statistical discrimination. I construct an admissions game between one college and

N

identical in expectation high schools. The game features a perfect Bayesian equilibrium in which the ex ante randomly chosen high school provides truthful information to the college in exchange for future favorable admission treatment. When agents are sufficiently patient, this relationship between the college and the initially randomly chosen high school is sustained in equilibrium. This equilibrium increases overall admissions efficiency relative to but does not Pareto improve on a dominant strategy implementable alternative: the welfare gains accrue entirely to the college and high school in the relationship while harming students from all other high schools.

一所大学新生按高中出身的分布不同于高中毕业生的人口分布（Bernhard, 2013），这一事实通常归因于品味或统计歧视。本文模拟了第三种解释，我称之为基于信息的歧视：大学和高中之间的信息不对称激励了大学和事先随机选择的高中之间的关系的形成，即使在没有基于品味和统计的歧视的情况下，也会导致事实上的歧视性录取。我在一所大学和N所期望高中之间构建了一个招生博弈。该博弈具有完美的贝叶斯均衡，即事先随机选择的高中向大学提供真实信息，以换取未来有利的录取待遇。当代理人有足够的耐心时，大学和最初随机选择的高中之间的这种关系维持在均衡状态。这种均衡提高了总体的招生效率，但并没有改善帕累托主导策略的可实施方案：福利收益完全归于大学和高中，而损害了所有其他高中的学生。

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引用次数: 0

Evolutionary implementation with partially effective institutions 部分有效制度下的渐进式实施

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-03 DOI: 10.1016/j.mathsocsci.2024.12.004

Ratul Lahkar

We consider large population models of a public goods game and a tragedy of the commons. A planner applies externality pricing in these models. However, institutions in society are only partially effective. Hence, the externality price does not compel agents to internalize externalities fully. The resulting externality-adjusted game with partially effective institutions is a potential game. Evolutionary dynamics converge to its Nash equilibrium. More effective institutions bring this Nash equilibrium closer to the original Pareto efficient state. We trace the effectiveness of institutions to a primeval Tullock contest over natural resources in society. The society’s institutional structure arises from the contest’s Nash equilibrium. The institutional structure is more inclusive if natural resources in the contest are less appropriable. Institutions are then also more effective in implementing externality pricing.

我们考虑公共物品博弈和公地悲剧的大人口模型。计划者在这些模型中应用外部性定价。然而，社会制度只是部分有效。因此，外部性价格并不能迫使代理人完全内部化外部性。由此产生的经外部性调整的、具有部分有效制度的博弈是一种潜在博弈。进化动力学趋于纳什均衡。更有效的制度使纳什均衡更接近最初的帕累托有效状态。我们把制度的有效性追溯到原始的图洛克（Tullock）对社会自然资源的争夺。社会的制度结构源于竞争的纳什均衡。如果竞争中的自然资源不那么适宜，制度结构就更具包容性。这样，机构在实施外部性定价方面也会更有效。

引用次数: 0

Optimal top-n policy 最优顶优先策略

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.12.001

Isa Hafalir , Siqi Pan , Kentaro Tomoeda

A widely adopted affirmative action policy in the university sector is the “top-

n

” policy, where the universities guarantee admission to students in the top

n

fraction of their class from every high school. The efficacy of the top-

n

policy in university integration has been questioned because students strategically relocate to low-achieving high schools. We show that when minorities are less likely to strategize than others, the policy can even segregate minorities from the target university, compared to the school-blind policy. A suitably chosen eligibility requirement, featuring the minimum time students must spend at a high school in order to be eligible for top-

n

admissions, can restore the efficacy of this policy. However, the most stringent requirement is not always optimal. The optimal requirement depends on the original distribution of students across high schools.

大学部门广泛采用的平权行动政策是“top-n”政策，即大学保证从每所高中录取班级前n名的学生。由于学生们战略性地转移到成绩较差的高中，大学整合政策的有效性受到了质疑。我们表明，当少数族裔比其他人更不可能制定策略时，与不考虑学校的政策相比，该政策甚至可以将少数族裔从目标大学隔离开来。一个适当选择的资格要求，包括学生必须在高中度过的最低时间，才能有资格进入顶级录取，可以恢复这一政策的效力。然而，最严格的要求并不总是最佳的。最优需求取决于高中学生的原始分布。

引用次数: 0

With a little help from my friends: Essentiality vs opportunity in group criticality 在我朋友的帮助下：在群体临界性中，必要性vs机会

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.11.004

M. Aleandri, M. Dall’Aglio

We define a notion of the criticality of a player for simple monotone games based on cooperation with other players, either to form a winning coalition or to break a winning one, with an essential role for all the players involved. We compare it with the notion of differential criticality given by Beisbart that measures power as the opportunity left by other players.

We prove that our proposal satisfies an extension of the strong monotonicity introduced by Young, assigns no power to null players, does not reward free riders, and can easily be computed from the minimal winning and blocking coalitions. An application to the Italian elections is presented.

Our analysis shows that the measures of group criticality defined so far cannot weigh essential players while only remaining an opportunity measure. We propose a group opportunity test to reconcile the two views.

对于基于与其他玩家合作的简单单调游戏，我们定义了玩家的重要性概念，无论是形成胜利联盟还是打破胜利联盟，所有参与者都扮演着重要角色。我们将其与Beisbart提出的差分临界性概念进行比较，该概念将权力衡量为其他参与者留下的机会。我们证明了我们的建议满足Young引入的强单调性的扩展，不给零参与者分配权力，不奖励搭便车者，并且可以很容易地从最小获胜和阻塞联盟中计算出来。提出了意大利选举的申请。我们的分析表明，到目前为止，定义的群体临界性的措施不能衡量重要的球员，而只是一个机会的衡量。我们提出一个群体机会测试来调和这两种观点。

引用次数: 0

Condorcet domains on at most seven alternatives 孔多塞域在最多七个备选项上

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.12.002

Dolica Akello-Egwel , Charles Leedham-Green , Alastair Litterick , Klas Markström , Søren Riis

A Condorcet domain is a collection of linear orders which avoid Condorcet’s paradox for majority voting. We have developed a new algorithm for complete enumeration of all maximal Condorcet domains and, using a supercomputer, obtained the first enumeration of all maximal Condorcet domains on

n \leq 7

alternatives.

We investigate properties of these domains and use this study to resolve several open questions regarding Condorcet domains, and propose several new conjectures. Following this we connect our results to other domain types used in voting theory, such a non-dictatorial and strategy-proof domains. All our data are made freely available on the web.

孔多塞域是避免孔多塞悖论的线性序列集合。本文提出了一种完全枚举所有极大孔多塞域的新算法，并利用超级计算机得到了n≤7个备选项上所有极大孔多塞域的第一个枚举。我们研究了这些域的性质，并利用这项研究解决了关于孔多塞域的几个悬而未决的问题，并提出了几个新的猜想。接下来，我们将我们的结果与投票理论中使用的其他域类型联系起来，例如非独裁和策略证明域。我们所有的数据都在网上免费提供。

引用次数: 0

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