Assessing and Optimizing Redistricting Algorithms with a Bias-Variance Trade-Off and Real-World Voting Data
by Ivan Sinyavin and Owen Xu Li
Final Project for S&DS 431: Optimization and Computation (Fall 2024)
The above visualization shows the progression of our algorithm for Florida based on 2016 Election data. The figures below the map show the metrics we aim to optimize for. We aim to keep the population of the districts similar (first from left), favorability in the districts (second from left), which together, along with the compactness of the districts, make up the loss function (third from left). The last figure shows the estimated number of districts won based on regressions from different elections (2012,2016,2020), which goes up as our algorithm progresses.
Our project refits existing algorithmic redistricting methods to explicitly optimize for a specific party’s objectives. While current approaches lack explicit mechanisms and practical implementation toward the goal of optimizing toward one party or another, we develop an algorithm that explicitly optimizes towards a single party’s objectives, incorporating past election data to redistrict maps to create districts with equal population, a measure of compactness, and, most importantly, strategically distributed voters. We also fill a gap in optimizing long-term favorability of redistricting plans. Since the census and subsequent redistricting (on the congressional level) occurs every ten years, as time passes, the variance of voting result from the initial district plan often deviates. We capture the extent of this deviation from past historical data and propose ways to incorporate the variance of these temporal shifts into the redistricting algorithm. Therefore, our algorithm will be better equipped to predict party success in both the short term (1–2 years) and the long term (7–8 years).
We sourced election data from the 2012, 2016, and 2020 presidential elections. Our main modeling objective by using real-word data is to understand relationship between the percentage of voters supporting a particular party in one district and that party's electoral performance in subsequent elections. This relationship informs how a slight advantage, for example, translates into varying probabilities of victory and margins of success in the short and longer terms. We analyze district-level election data following the 2010 redistricting cycle, using 2012 as our baseline for exploring how initial percentages in 2010 influence shifts in voter outcomes over subsequent election cycles.
The logistic regression curves for 2012, 2016, and 2020 in above figure show the probability of a party's win as a function of voting share within that district, adjusted for the movement calculations/normalization based on U.S. election data. Over time, as evidenced by the progression of logistic regression curves, the predictive power of initial vote share on electoral outcomes diminishes. The sharpness of the 2012 curve reflects the immediate impact of redistricting decisions made in 2010. At that time, a small shift in voter share near the 50% threshold resulted in a significant change in the likelihood of a party's victory. As time progresses (2016 and 2020), the logistic curves flatten slightly, which suggests that initial vote share loses its predictive accuracy. As such, while redistricting efforts may optimize voter shares for the immediate future, the declining predictive power of voting shares may bias optimal redistricting efforts toward favoring solidly red/blue districts over narrower districts.
Estimated 18.5 Republican districts out of 27 districts, based on 2016 voting patters.
Estimated 4 Democrat districts out of 8 Districts.
Estimated 6 Republican districts out of 8 Districts.
- numpy
- geopandas
- pandas
- rasterio
- scipy
- IPython
- shapely
- skimage
- matplotlib
- PIL
elections_data/
Contains data from past elections used to estimate election outcomes as a function of time since redistricting.
state_examples/
Includes Jupyter notebooks implementing the redistricting optimization algorithm for Florida, Wisconsin, and Virginia.
party_favoribility.ipynb
Notebook that fits logistic curves to party favorability data based on historical voting patterns.
project_report.pdf
A comprehensive write-up of the full project, including methodology, implementation, and results.
project_slides.pdf
Summary slides presenting the key ideas and results from the project.
read_me_pics/
Contains supporting images (e.g., maps, diagrams) for the README or documentation.
gifs/
Contain final animated GIFs showing the redistricting algorithm outputs for Florida, Virginia, Wisconsin.
All the necessary functions are defined in the florida_opt.ipynb, wisconsin_opt.ipynb, virginia_opt.ipynb Jupyter notebooks in the state_examples folder.