摘要翻译：
我们研究了Phragm\'en和Thiele在19世纪90年代提出的两个有影响力的投票规则，即选举一个由k名候选人组成的委员会或议会，该委员会或议会按比例代表选民。选民通过批准任意数量的候选人来提供他们的偏好。以前的工作已经提出了满足Thiele规则（现在称为比例批准投票，PAV)而不是Phragm\'en规则的比例公理。通过提出两个新的比例公理（层流比例公理和价格公理），我们证明了这两个规则实现了两种不同形式的比例表示。这两个公理都是Phragm\'en而不是Thiele所满足的。Phragm\'en的规则确保所有选民对委员会有同等数量的影响力，而Thiele的规则确保公平的效用分配。Thiele规则是一个福利主义投票规则（一个最大化选民效用函数的规则）。我们证明没有任何福利主义规则能满足我们的新公理，我们证明没有这样的规则能满足核心。相反，一些福利主义的公平属性不能由Phragm\'en类型的规则来保证。这正式确定了两种比例之间的区别。然后，我们引入了一个吸引委员会规则，该规则满足介于核心和扩展合理表示(EJR)之间的一个性质。它满足层流比例性、可价格性，并可在多项式时间内计算。我们证明了我们的新规则提供了对核的对数近似。另一方面，PAV提供了对核心的因子-2近似，这个因子对于在庇古-道尔顿原理意义上公平的规则是最优的。
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英文标题：
《Proportionality and the Limits of Welfarism》
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作者：
Dominik Peters and Piotr Skowron
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最新提交年份：
2019
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  We study two influential voting rules proposed in the 1890s by Phragm\'en and Thiele, which elect a committee or parliament of k candidates which proportionally represents the voters. Voters provide their preferences by approving an arbitrary number of candidates. Previous work has proposed proportionality axioms satisfied by Thiele's rule (now known as Proportional Approval Voting, PAV) but not by Phragm\'en's rule. By proposing two new proportionality axioms (laminar proportionality and priceability) satisfied by Phragm\'en but not Thiele, we show that the two rules achieve two distinct forms of proportional representation. Phragm\'en's rule ensures that all voters have a similar amount of influence on the committee, and Thiele's rule ensures a fair utility distribution.   Thiele's rule is a welfarist voting rule (one that maximizes a function of voter utilities). We show that no welfarist rule can satisfy our new axioms, and we prove that no such rule can satisfy the core. Conversely, some welfarist fairness properties cannot be guaranteed by Phragm\'en-type rules. This formalizes the difference between the two types of proportionality. We then introduce an attractive committee rule which satisfies a property intermediate between the core and extended justified representation (EJR). It satisfies laminar proportionality, priceability, and is computable in polynomial time. We show that our new rule provides a logarithmic approximation to the core. On the other hand, PAV provides a factor-2 approximation to the core, and this factor is optimal for rules that are fair in the sense of the Pigou--Dalton principle.
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PDF链接：
https://arxiv.org/pdf/1911.11747