席位公平分配的Q值法及其拓展模型  

The Q Value Method and Extended Model for Fair Apportionment Problem

作　　者：游咏琪 王若鹏[1] YOU Yongqi;WANG Ruopeng(Department of Mathematics,Beijing Institute of Petrochemical Technology,Beijing 102617,China)

机构地区：[1]北京石油化工学院数学教研中心,北京102617

出　　处：《北京石油化工学院学报》2023年第2期68-74,78,共8页Journal of Beijing Institute of Petrochemical Technology

基　　金：北京市大学生创新创业训练计划基金资助项目(2022J00121);北京市教委科技计划一般项目(KM20190017002)。

摘　　要：从χ2统计量的角度提出了席位公平分配问题相对公平性的统计学方法,从而奠定了从统计学角度建立公平分配模型的方法基础。基于χ2统计量提出了剩余部分与整体的多数相对公平性原则,建立了新的席位公平合理分配模型,给出了模型的求解步骤与计算方法。以最大熵、平均占比差及χ2统计值为公平性评价标准,通过仿真实验与多种分配方法进行比较,结果表明:该分配方法具有优越性和公平性,同时也显示了其合理性和可操作性。The classical Q-value method of the seat apportionment problem is reviewed and a relative fairness principle is established from the perspective ofχ2 statistics,which lay a foundation for establishing the fair apportionment model based onχ2 statistics.Further,a new fair and reasonable seat apportionment model is proposed with the relative fairness principle of the majority of the remainder and the whole.The solving steps and algorithm of the model are given.Taking the maximum entropy,average percentage difference andχ2 statistical value as the fairness evaluation criteria,the simulation results are compared with several typical methods to verify the effectiveness of the method。

关 键 词：公平分配 平均占比差 χ2统计量 相对公平性 

分 类 号：O221.2[理学—运筹学与控制论]