【全集】2007 MCM A 不公正的选区划分 特等奖论文 教程

huashi3483

PROBLEM A: Gerrymandering The United States Constitution provides that the House of Representatives shall be composed of some number (currently 435) of individuals who are elected from each state in proportion to the state’s population relative to that of the country as a whole. While this provides a way of determining how many representatives each state will have, it says nothing about how the district represented by a particular representative shall be determined geographically. This oversight has led to egregious (at least some people think so, usually not the incumbent) district shapes that look “unnatural” by some standards.
2 n% Z% }4 H2 N" m* g! W: `9 jHence the following question: Suppose you were given the opportunity to draw congressional districts for a state. How would you do so as a purely “baseline” exercise to create the “simplest” shapes for all the districts in a state? The rules include only that each district in the state must contain the same population. The definition of “simple” is up to you; but you need to make a convincing argument to voters in the state that your solution is fair. As an application of your method, draw geographically simple congressional districts for the state of New York.

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A题：不公正的选区划分
美国宪法规定众议院由一定数目的众议员(目前是 435人)组成，他们是由各州按照该州人口占全国总人口的百分比选出来的。尽管这种规定提供了确定每个州有多少众议员的方法，但是一点也没有说及有关一个特定的众议员所代表的选区应该怎样按地区决定的问题。这种疏忽已经导致了按某种标准看来是违反常情的很不好的(至少某些人认为通常是不必这样做的) 选区安排。
因此就向你们提出了以下的问题：假设你们有机会去制定一个州的众议院的选区。你们会怎样把它作为一种纯“基础性”的练习来创建一个州的所有选区的“最简单”的划分。这些划分规则中至少要包含一条：该州的每个选区必须有同样的人口。“简单”的定义要由你们来下；但是你们必须就你们的解决方法是公正的做出一个能够使该州选民信服的论证。作为你们的方法的应用，试创建纽约州的按地域来说是简单的选区划分。

huashi3483

本题共评出5份特等奖（Outstanding Winners）获得者：

1、美国华盛顿大学— MAA Prize Recipient
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• 参赛编号：Control No. 1034
• 论文题目：Applying Voronoi Diagrams to the Redistricting Problem
• 论文作者：Sam Burden, Aaron Dilley, and Lukas
• 指导老师：James Morrow

2007 A O Applying Voronoi Diagrams to the Redistricting Problem.pdf (1.05 MB, 下载次数: 4416)

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2、美国华盛顿大学
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• 参赛编号：Control No. 1036
• 论文题目：A Cluster-Theoretic Approach to Political Districting
• 论文作者：Nate Bottman, Wes Essig, and Sam Whittle
• 指导老师：Anne Greenbaum

2007 A O A Cluster-Theoretic Approach to Political Districting.pdf (1.18 MB, 下载次数: 2790)

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% b: k1 {7 p8 N& _3、美国哈佛大学— INFORMS Prize Recipient  （摘要\全文）
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• 参赛编号：Control No. 1421
• 论文题目： What to Feed a Gerrymander
• 论文作者： Ben Conlee、Abe Othman、Chris Yetter
• 指导老师：Clifford Taubes

2007 A O Z What to Feed a Gerrymander.pdf (39.22 KB, 下载次数: 1206)

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+ s' ]/ j8 F, F/ a3 x+ ^ 2007 A O What to Feed a Gerrymander.pdf (2.07 MB, 下载次数: 1876)

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4、美国麻省理工学院— SIAM Prize Recipient   （摘要、演讲稿、全文）
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• 参赛编号：Control No. 2043
• 论文题目： Electoral Redistricting with Moment of Inertia and Diminishing Halves Models
• 论文作者： Andrew Spann、Daniel Kane、Dan Gulotta
• 指导老师：Martin Bazant

1 m9 s  Q( w* C3 m6 n 2007 A O Z Electoral Redistricting with Moment of Inertia.pdf (52.17 KB, 下载次数: 974)

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2007 A O P Electoral Redistricting with Moment of Inertia.pdf (3.85 MB, 下载次数: 2547)

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5、美国杜克大学

• 参赛编号：Control No. 2051
• 论文题目：When Topologists Are Politicians ...
• 论文作者：Nikifor Bliznashki, Aaron Pollack, Russell Posner
• 指导老师：David Kraines

2007 A O When Topologists Are Politicians.pdf (1.31 MB, 下载次数: 2002)

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& Q) Y' E4 u  A& @: l9 f2 P2 eA Genetic Algorithm for Non-Partisan Legislative Districting
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• Kyotaro Hemmi, Peter Mannisto, and Ting-You Wang
• 美国华盛顿大学
• 2007 Honorable Mention
• 2007 A H Genetic Algorithm for Non-Partisan Legislative Districting.pdf (1.73 MB, 下载次数: 1499)
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caozhe1987

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caozhe1987

矩阵币是怎么回事？现在数学中国收费了吗？

caozhe1987

明白了……

caozhe1987

是这样……

caozhe1987

得多回复[code][/code]

caozhe1987

现在下东西变的很麻烦很麻烦啊

690547674

利用资源就要支持数学中国

crystal9

嗯，谢谢楼主分享，打印出来，好好看看~~