Network-Based Vertex Dissolution

Bevern, René van; Bredereck, Robert; Froese, Vincent; Niedermeier, Rolf; Woeginger, Gerhard J.

doi:10.1137/140978880

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…Naturally, however, it has been mainly explored in the political science arena [Erikson, 1972], primarily based on analysis of past elections [Grofman et al, 1997;Tangian, 2010;Felsenthal and Miller, 2015] -trying to figure out if it occurred, and trying to calculate some measure of its effects. In the past few years the computational social choice community has also taken interest in this topic, on issues such as worst case analysis of how districts effect voting rules [Bachrach et al, 2016], and the computational complexity of gerrymandering [Lewenberg et al, 2017;van Bevern et al, 2015]. Recently, [Pegden et al, 2017] suggested a "cut and choose"like mechanism to divide districts in practice.…”

Section: Related Workmentioning

confidence: 99%

Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering

Borodin

Lev

Shah

et al. 2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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Gerrymandering is the process by which parties manipulate boundaries of electoral districts in order to maximize the number of districts they can win. Demographic trends show an increasingly strong correlation between residence and party affiliation; some party’s supporters congregate in cities, while others stay in more rural areas. We investigate both theoretically and empirically the effect of this trend on a party's ability to gerrymander in a two-party model ("urban party" and "rural party"). Along the way, we propose a definition of the gerrymandering power of a party, and an algorithmic approach for near-optimal gerrymandering in large instances. Our 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. As partisan separation grows, the gerrymandering power of both parties converge so that each party can gerrymander to get only slightly more than what its voting share warrants, bringing about, ultimately, a more representative outcome. Moreover, there seems to be an asymmetry between the gerrymandering power of the parties, with the rural party being more capable of gerrymandering.

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Section: Related Workmentioning

confidence: 99%

Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering

Borodin

Lev

Shah

et al. 2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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“…Notably, the study of Gerrymandering over graphs, which is pretty much analogous to our setting, very recently gained significantly increased interest by various research groups [4,11,18,21]. A similar model for graph-based redistribution scenarios and political districting has been studied under the name "network-based vertex dissolution" [5].…”

Section: Related Workmentioning

confidence: 99%

A Refined Complexity Analysis of Fair Districting over Graphs

Boehmer¹,

Koana²,

Niedermeier³

2021

Preprint

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We study the NP-hard Fair Connected Districting problem: Partition a vertex-colored graph into k connected components (subsequently referred to as districts) so that in each district the most frequent color occurs at most a given number of times more often than the second most frequent color. Fair Connected Districting is motivated by various realworld scenarios where agents of different types, which are one-to-one represented by nodes in a network, have to be partitioned into disjoint districts. Herein, one strives for "fair districts" without any type being in a dominating majority in any of the districts. This is to e.g. prevent segregation or political domination of some political party.Our work builds on a model recently proposed by Stoica et al. [AAMAS 2020], thereby also strengthening and extending computational hardness results from there. More specifically, with Fair Connected Districting we identify a natural, already hard special case of their Fair Connected Regrouping problem. We conduct a fine-grained analysis of the (parameterized) computational complexity of Fair Connected Districting, proving that it is polynomial-time solvable on paths, cycles, stars, caterpillars, and cliques, but already becomes NP-hard on trees. Motivated by the latter negative result, we perform a parameterized complexity analysis with respect to various graph parameters, including treewidth, and problem-specific parameters, including the numbers of colors and districts. We obtain a rich and diverse, close to complete picture of the corresponding parameterized complexity landscape (that is, a classification along the complexity classes FPT, XP, W[1]-hardness, and para-NP-hardness). Doing so, we draw a fine line between tractability and intractability and identify structural properties of the underlying graph that make Fair Connected Districting computationally hard. * This work was initiated at the research retreat of the Algorithmics and Computational Complexity group held in September 2020 in Zinnowitz, Germany.† Supported by the Deutsche Forschungsgemeinschaft (DFG), project MaMu, NI 369/19. ‡ Supported by the Deutsche Forschungsgemeinschaft (DFG), project FPTinP, NI 369/16.

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“…Borodin et al (2018) investigated how geographic spread affects gerrymandering ability, though those results are mostly empirical. Furthermore, there is a whole line of research on allowing agents to move between districts, a form of "reverse gerrymandering," that has also been investigated in the past few years (see, Bervoets and Merlin (2012); van Bevern et al (2015); Lev and Lewenberg (2019)).…”

Section: Related Workmentioning

confidence: 99%

Selecting Voting Locations for Fun and Profit

Fitzsimmons¹,

Lev²

2020

Preprint

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While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is gerrymandering, in which district borderlines are changed to increase a party's chance to win, but a different geographical manipulation involves influencing the election by selecting the location of polling places, as many people are not willing to go to any distance to vote. In this paper we initiate the study of this manipulation. We find that while it is easy to manipulate the selection of polling places on the line, it becomes difficult already on the plane or in the case of more than two candidates. Moreover, we show that for more than two candidates the problem is inapproximable. However, we find a few restricted cases on the plane where some algorithms perform well. Finally, we discuss how existing results for standard control actions hold in the geographic setting, consider additional control actions in the geographic setting, and suggest directions for future study.

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Network-Based Vertex Dissolution

Cited by 10 publications

References 23 publications

Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering

Big City vs. the Great Outdoors: Voter Distribution and How It Affects Gerrymandering

A Refined Complexity Analysis of Fair Districting over Graphs

Selecting Voting Locations for Fun and Profit

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