席位的公平分配.doc

目录 TOC \o 1-3 \h \z \u 摘 要 1 ABSTRACT 2 绪论 3 1.席位分配问题 3 2.各种分配方法 3 2.1 最大分数法 3 2.2 最大分数法的优缺点 5 2.3 不公平度指标 5 2.3.1定义不公平度 5 2.3.2 定义不公平程度 5 2.3.3 定义相对不公平度 6 2.4 Q值法 6 2.5 用Q值法解决问题 8 2.6 分析Q值法的优缺点 9 2.7 D’Hondt法 9 3.比较分配方法 9 参考文献 12 致 谢 13 附 录 14 贵州师范学院毕业论文（设计） PAGE PAGE 15 摘 要 约两个世纪以来，出于美国和欧洲诸如会议席位分配等社会政治活动的需要，一些人包括数学家们先后提出了许多分配方法，这些方法对同一个问题常常给出了不同的答案，还会违背人们意愿甚至违背常识现象，这更引起数学家们的深入研究的兴趣。本文从最简单的最大剩余法开始研究，一步步的优化方案。我主要根据了各系人数因素对席位获得的影响，首先定义了不公平指标及相对不公平度的定义，采用了最大剩余法，Q值法和D’Hondt法对模型进行比较，制定出更合理的方案。开始，我采用了最大剩余法对问题进行研究.然后，我对相关资料进行了查阅，则定义了不公平度指标和相对不公平度用来检查方案的公平性程度。确定了衡量公平的数量指标后，再优化模型采用Q值法进行分配，最后采用了D’Hondt法对模型进行了分析，几种方法的比较得出结论。 关键字：席位分配;Q值法;D’Hondt法 ABSTRACT About two of a century, the need for American and Europe such as meeting seat allocation of social political activities, including some mathematicians have put forward many distribution methods, these methods to the same problem often give different answers, but also goes against the crowd even contrary to common sense, this caused more in-depth research mathematicians the interest. This paper studies the maximum residual method is the most simple, optimization step by step. I mainly according to the number of seats available on line, first defines unfair index and relative unfair degree, adopt the maximum residual method, Q method and D Hondt method to compare the model, to develop a more reasonable scheme. To start, I adopt the maximum residual method to research the problem. Then, I carried out the inspection of the relevant information, define the unfair degree index and relative unfair degree used to check the program fairness degree. To determine the quantitative index to measure the fair, then optimization model with a Q value method is used, the D Hondt method for model analysis, compare several methods of conclusion. Keywords: seat allocation; Q value method; d’hondt method 绪论 起初，对于出现在社会政治领域中的席位分配，人们认为是一个简单的数学问题，用初等的办法解决，但是在应用中这样的办法