Date of Award

December 2020

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Hamid K Seifoddini

Second Advisor

Wilkistar Otieno

Committee Members

Seyed Hosseni, Habib Tabatabai, Xiaohang Yue, Hamid K Seifoddini, Wilkistar Otieno


Efficiency Gap, Gerrymandering, Political Fairness, Redistricting


Political parties’ attempts to manipulate district boundaries in order to gain political advantages in the election system lead to huge inefficiency and unfair election results. Previously some studies have developed methods for forming political districts considering various factors such as population equality, compactness, and contiguity; but only a few recent studies have considered political fairness as an objective for redistricting political map.This study attempts to find a solution to draw political districts using political fairness as a factor in addition to integrity, population equality, contiguity, and compactness of the districts in order to prevent gerrymandering. In this research, we introduce two new metrics to measure political fairness that supplement efficiency gap which is the standard measure of political fairness. We then develop several mathematical models, that address various aspects of political redistricting to form state assembly, senate and congressional maps. Due to several drawbacks in these models, a heuristic methodology – in particular simulated annealing (SA) algorithm – is ultimately utilized to find a good solution for this problem. The algorithm is coded in C++ and then tested on three large scenarios. The first is a fictional rectangular state having 3000 wards. The second and third scenarios focus on combining nearly 7000 election wards to form U.S. Congressional and state legislative districts in Wisconsin respectively. The results for the Wisconsin scenarios are displayed as maps that are created using state-of-the-art ArcGIS software. A significant data collection and cleaning effort was undertaken before the Wisconsin scenarios were considered. Experimental results demonstrate the effectiveness of the proposed heuristic method, the efficiency of political redistricting problems in general, and the inevitable trade-off that are made between competing objectives in this highly challenging real-world problem.