Study on the Theory and the Application of Apportionment Methods

分配方法的理论及应用研究

• 批准号: 04832011
• 负责人: OYAMA Tatsuo
• 金额: $ 0.7万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04832011/
• 关键词: apportionment method; mathematical programming; discrete optimization; electoral system; 議員定数; 議員定数配分方法; 除数法; パラメトリック除数法

Research results in the fiscal year 1993 can be summarized as follows.(1).Reviewing the electoral system and apportionment methods in the USA,the UK,France, Germany, Italy and so on, we investigated historical changes and statistical aspects of apportionment methods.(2).Formulating the apportionment problem as a discrete optimization problem in the mathematical programming theory, we made a computer program of the solution method for the optimization problem. Solving these problems on the personal computer, we analyzed the characteristics of the optimal solution.(3).Making computer programs for representative apportionment methods, we calculated the allocation of seats in our Lower and Upper Houses based upon the Census data.(4).We examined the characteristics of the allocation of seats obtained from typical apportionment methods, making comparative study on the "bias" caused from the size of constituencies.(5).Interpreting the obtained allocation of seats from the viewpoint of global optimization problem, we examined the criterion of fairness. We added new insights of house property, stability and consistency into the allocated solution.(6).We investigated desirable apportionment methods we should apply to our contry judging from the aspects of fairness and equality.(7).We reviewed our single-member electoral voting system and proportional voting system from the mathematical viewpoints.

1.回顾了美国、英国、法国、德国、意大利等国的选举制度和分摊方法，考察了分摊方法的历史变迁和统计方面。(2)将分摊问题表述为数学规划理论中的离散优化问题，编制了求解该优化问题的计算机程序。在个人计算机上求解这些问题时，我们分析了最优解的特点。(3)编制了代表分配法的计算机程序，根据人口普查数据计算了我们下议院和上议院的席位分配。(4)考察了典型分配方法获得的席位分配的特点，比较研究了选区大小造成的“偏差”。(5)从全局优化问题的角度对获得的席位分配进行了解释，考察了公平的标准。我们在分配方案中加入了房产、稳定性和一致性的新见解。(6)从公平和平等的角度研究了适用于我国的合理分摊方法。(7)从数学的角度回顾了我国的单人选举投票制和比例投票制。

项目成果

T.Oyama: Saitekika Moderu Bunseki (Optimization Model Analysis), Chapter 3. Nikka-Giren Shuppan, 372 (1993)

T.Oyama：Saitekika Moderu Bunseki（优化模型分析），第 3 章。 Nikka-Giren Shuppan，372 (1993)

大山達雄: "選挙制度の数理-小選挙区制と比例代表制の問題点-" オペレーションズ・リサーチ. 39. 39-44 (1994)

小山达雄：“选举制度的数学 - 单一议员选区制度和比例代表制的问题 -”运筹学 39. 39-44 (1994)。

大山達雄: "最適化モデル分析(第3章)" 日科技連出版, 372 (1993)

Tatsuo Oyama：《最优化模型分析（第3章）》日本科学技术学会出版，372（1993）

T.Oyama: "Mathematics of electoral voting system --- problems for single-member and proportional voting systems ---" Communications of Operations Research Society of Japan. Vol.39, No.1. 39-44 (1994)

T.Oyama：“选举投票系统的数学——单一成员和比例投票系统的问题——”日本运筹学会通讯。

大山 達雄: "最適化モデル分析" 日科技連出版, 550 (1993)

Tatsuo Oyama：《优化模型分析》Nikkei Ren Shuppan，550 (1993)