Demonstrating the Detrimental Effects of Gerrymandering with Mathematical Programming

In the image on the left side, one can see a result with 7 party A and 3 party B representatives can be elected in an electoral district in which 10 representatives are elected. On the the other hand, the values can be changed from 7 to 3 for party A and 3 to 7 for party B by just arranging the electoral district boundaries as shown in the image on the right side.

Note that overall rates are almost equal to each other (51.41% and 48.59% for party A and party B respectively).

Redrawing electoral district boundaries has been studied since the 60's in several democratic countries, particularly the USA. The major concern in political redistricting is gerrymandering, the manipulation of a district's boundaries in favor of a political party or group. In order to prevent unfair political advantage and propose fair representation, the political districting literature has introduced several criteria such as population equality, contiguity, and compactness. This study develops two new mixed-integer mathematical programming formulations to quantitatively demonstrate the detrimental result of this practice on the political balance even when these constraints have been operationalized to inhibit gerrymandering. Single-member and mixed single- and multi-member district electoral systems are used in the formulations. The d'Hondt method is applied for proportionality representation in the mixed-member district formulation. To test our claim, we obtain computational results using the 2015 Istanbul general election and the 2017 constitutional referendum data. Considering our claim and the formulations to validate it, the study is the first of its kind to the best of our knowledge.

Each folder in this folder is for one of four territorial areas with different number of units which are 17, 33, 68, and 85. There are two excel files in each folder: Election and Referendum data sets.

Required inital solutions have been achived by using the algorithm written in R programming language. Election and referendum results, adjacency matrices are used as input of the algorithm. The used data sets are same with the ones in Required Data Set for CPLEX Folder, however, form of the data sets may be different.

The Excel files that cover zeros and ones are represented the initial solutions. A unit that has one value means that the unit is assigned to the district that has that one value in its column.

You may want to change the parameters depending on the which territorial area you wants to work on.

Single-member district electoral system without initialization JAVA/CPLEX implementations

Single-member district electoral system with initialization JAVA/CPLEX implementations

Multi-member district electoral system without initialization JAVA/CPLEX implementations

Multi-member district electoral system with initialization JAVA/CPLEX implementations