摘要翻译：
直接民主是分类者集合的一个特例，每个人（分类者）都对每个问题投票。当平均选民能力（分类器精度）低于50%时，这将失败，这可能发生在选民只有有限信息的嘈杂设置中，或者当有多个主题且平均选民能力对某些主题可能不够高时。代议制民主，即选民选择代表投票，在这两种情况下都可以是长生不老药。代议制民主是改进分类器集成的一种具体方式。我们引入了一个数学模型来研究代议制民主，特别是理解一个给予最大决策能力的代议制民主的参数。我们的主要结果表明，在一般和自然条件下，1。代议制民主可以同时对多个有争议的问题做出正确的决策。2.在投票成本固定的情况下，最优的代议制民主要求代表从规模不变的群体中选出：代表人数应与选民人数成线性关系。3.当投票的成本和收益都是多项式时，最优群体规模与投票人数接近线性。这项工作为研究代议制民主类型集合中的质量-数量权衡（较少的高资格代表与较多的低资格代表）奠定了数学基础。
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英文标题：
《A Mathematical Model for Optimal Decisions in a Representative Democracy》
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作者：
Malik Magdon-Ismail, Lirong Xia
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最新提交年份：
2018
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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：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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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：
  Direct democracy is a special case of an ensemble of classifiers, where every person (classifier) votes on every issue. This fails when the average voter competence (classifier accuracy) falls below 50%, which can happen in noisy settings where voters have only limited information, or when there are multiple topics and the average voter competence may not be high enough for some topics. Representative democracy, where voters choose representatives to vote, can be an elixir in both these situations. Representative democracy is a specific way to improve the ensemble of classifiers. We introduce a mathematical model for studying representative democracy, in particular understanding the parameters of a representative democracy that gives maximum decision making capability. Our main result states that under general and natural conditions,   1. Representative democracy can make the correct decisions simultaneously for multiple noisy issues.   2. When the cost of voting is fixed, the optimal representative democracy requires that representatives are elected from constant sized groups: the number of representatives should be linear in the number of voters.   3. When the cost and benefit of voting are both polynomial, the optimal group size is close to linear in the number of voters. This work sets the mathematical foundation for studying the quality-quantity tradeoff in a representative democracy-type ensemble (fewer highly qualified representatives versus more less qualified representatives).
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PDF链接：
https://arxiv.org/pdf/1807.06157