The study of a new gerrymandering methodology

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different standards of the "simple" shape. The first standard is that the final shape of the congressional districts should be of a simplest figure and we apply a modified "shortest split line algorithm" where the factor of the same population is considered only. The second standard is that the gerrymandering should ensure the integrity of the current administrative area as the convenience for management. Thus we combine the factor of the administrative area with the first standard, and generate an improved model resulting in the new diagram in which the perimeters of the districts are along the boundaries of some current counties. Moreover, the gerrymandering should consider the geographic features.The third standard is introduced to describe this situation. Finally, it can be proved that the difference between the supporting ratio of a certain party in each district and the average supporting ratio of that particular party in the whole state obeys the Chi-square distribution approximately. Consequently, we can obtain an archetypal formula to check whether the gerrymandering we propose is fair.Comment: 23 pages,15 figures, 2007 American mathematical modeling contest "Meritorious Winner

The study of a new gerrymandering methodology ∗

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different standards of the ”simple ” shape. The first standard is that the final shape of the congressional districts should be of a simplest figure and we apply a modified ”shortest split line algorithm ” where the factor of the same population is considered only. The second standard is that the gerrymandering should ensure the integrity of the current administrative area as the convenience for management. Thus we combine the factor of the administrative area with the first standard, and generate an improved model resulting in the new diagram in which the perimeters of the districts are along the boundaries of some current counties. Moreover, the gerrymandering should consider the geographic features.The third standard is introduced to describe this situation. Finally, it can be proved that the difference between the supportin