Study on the Theory and the Application of Apportionment Methods

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。

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.