Study on the Theory and the Application of Apportionment Methods

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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.