1、 1 中文 2000 字， 1300 英文单词， 6800 英文字符 附 录 英文文献 Allocation of Seats Mathematical Programming Model Abstract Several methods of allocation of seats are studied. Based on these methods six mathematical programming models of allocation of seats have been given and their solutions have been given also. Thes
2、e mathematical models attempt to minimize a number of different measures of the deviation between the actual percentage of votes received and the percentage of seats allocated to a certain party. These methods are compared with foregone methods through the example.The six mathematical programming mo
3、dels are generalized, and the other 12 mathematical programming models are put up. The unified forms and equivalent forms of mathematical programming models are also discussed. Keywords: Allocation of Seats; Mathematical Programming; Equivalent Forms 1. Introduction Proportional representation (PR)
4、systems are a family of voting systems used in multiple-winner elections. The principle behind PR elections is that every vote deserves its representation in government and each political party involved should be represented in the legislature in proportion to its strength in the electorate. Essenti
5、ally, this means that each party should receive the same percentage of representation as the percentage of votes received. All PR systems set out to achieve this objective. In typical PR systems there are multi-member districts. The challenge in PR systems is to translate the electoral votes into se
6、ats in the same proportion as the actual votes received. Seat allocations are integer numbers, whilst the number of votes may be considered as continuous quantities in comparison to the number of seats. Therefore, the translation of the number of votes into the number of seats nearly always involves adjustment methods. The objective from an operations research point of view is to minimize some measure of the deviation between the actual percentage of votes cast and the percentage of seats a
