The Complexity of Gerrymandering Over Graphs: Paths and Trees

@inproceedings{Bentert2021TheCO,
  title={The Complexity of Gerrymandering Over Graphs: Paths and Trees},
  author={Matthias Bentert and Tomohiro Koana and Rolf Niedermeier},
  booktitle={WG},
  year={2021}
}
Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view, addressing social network structures, the investigation of gerrymandering over graphs was recently initiated by Cohen-Zemach et al. [AAMAS 2018]. Settling three open questions of Ito et al. [AAMAS 2019], we classify the computational complexity of the NP-hard… 
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. In a representative democracy, elections involve partitioning geographical space into districts which each elect a single representative. Legislation is then determined by votes from these
Priced Gerrymandering
  • P. Dey
  • Economics, Computer Science
    AAMAS
  • 2022
TLDR
The results show that district based elections are quite resistant under this new kind of electoral attack by showing that two of the problems admit polynomial-time algorithms if the budget or the number of districts is a constant.
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A fine-grained analysis of the (parameterized) computational complexity of Fair Connected Districting is conducted, including its parameterized complexity with respect to various graph parameters, including treewidth, and problem-specific parameters, and its complexity on graphs from different classes (such as paths, stars, and trees).

References

SHOWING 1-10 OF 15 REFERENCES
Algorithms for Gerrymandering over Graphs
Manipulating Districts to Win Elections: Fine-Grained Complexity
TLDR
The rigorous study of the gerrymandering problem is initiated from the perspectives of parameterized and fine-grained complexity and asymptotically matching lower and upper bounds on its computational complexity are provided.
On theoretical and empirical algorithmic analysis of the efficiency gap measure in partisan gerrymandering
TLDR
This work provides a simple and fast algorithm that can “un-gerrymander” the district maps for the states of Texas, Virginia, Wisconsin and Pennsylvania by bring their efficiency gaps to acceptable levels from the current unacceptable levels.
Gerrymandering and computational redistricting
TLDR
Using US Census Bureau data, it is confirmed that the difference in compactness between the computed and actual districts would be greatest for states that are large and, therefore, difficult for humans to properly district given their limited capacities.
Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering
TLDR
The results suggest that beyond a fairly small concentration of urban party's voters, the gerrymandering power of a party depends almost entirely on the level of concentration, and not on the party's share of the population.
Divide and Conquer: Using Geographic Manipulation to Win District-Based Elections
TLDR
It is shown that many parties are potentially able to make themselves victorious using district manipulation, and that the relevant variables here go beyond share of the vote; the form of geographic dispersion also plays a crucial role.
Computers and Intractability: A Guide to the Theory of NP-Completeness
TLDR
The experiences, understandings, and beliefs that guide the professional practices of teacher educators are explored, and the book paints a picture of a profession that offers huge rewards, alongside challenges and frustrations.
The Political Districting Problem: A Survey
Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which
International Foundation for Autonomous Agents and MultiAgent Systems ( IFAAMAS )
  • Medicine, Economics
  • 2007
TLDR
It is suggested that authors submitting papers to IFAAMAS do so with the understanding that, if the article is accepted, the author has the right to reproduce, publish, disseminate electronically, and do all of the things it normally does with such an article or paper.
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