Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem

Optimal partisan districting on planar geographies

We show that optimal partisan districting and majority securing districting in the plane with geographical constraints are NP-complete problems. We provide a polynomial time algorithm for determining an optimal partisan districting for a simplified version of the problem. In addition, we give possible explanations for why finding an optimal partisan districting for real-life problems cannot be guaranteed

Measuring the circularity of congressional districts

Shape analysis has special importance in the detection of manipulated redistricting, which is called gerrymandering. In most of the US states, this process is made by non-independent actors and often causes debates about partisan manipulation. The somewhat ambiguous concept of compactness is a standard criterion for legislative districts. In the literature, circularity is widely used as a measure of compactness, since it is a natural requirement for a district to be as circular as possible. In this paper, we introduce a novel and parameter-free circularity measure that is based on Hu moment invariants. This new measure provides a powerful tool to detect districts with abnormal shapes. We examined some districts of Arkansas, Iowa, Kansas, and Utah over several consecutive periods and redistricting plans, and also compared the results with classical circularity indexes. We found that the fall of the average circularity value of the new measure indicates potential gerrymandering

Applications of Compter Vision: Skyline Extraction and Congressional Districting [védés előtt] = A gépi látás alkalmazásai: skyline-kiemelés és választókerület-szabdalás

This thesis discusses problems from the fields of computer vision and congressional districting. The connection between the two seemingly distant subjects is image processing, which can be applied for both skyline extraction and circularity measurement. Hiking applications have a serious problem with the sensor accuracy of mobile devices. With the help of the mountainous skyline and a 3D map, the precision of orientation can be significantly increased. Redistricting has to be carried out to resolve geographic malapportionment caused by the different district population growth rates and migration. This process can be manipulated for an electoral advantage of a party, but achieving optimal partisan districting is not easy at all. In most states of the USA, redistricting is made by non-independent actors and often causes debates about gerrymandering. The highest possible circularity is a natural requirement for a fair legislative district. Thus, shape analysis can be a powerful tool to detect potential manipulation. First, we present an algorithm for skyline extraction and orientation in mountainous terrain, and we also verify the method in a relevant environment. Then, we prove that optimal partisan districting and majority securing districting are NPcomplete problems, and demonstrate why finding optimal districting in real-life is challenging. Finally, we introduce a novel, parameter-free circularity measure that can be used to detect gerrymandering and apply it to congressional districts

Algorithmic Processes And Social Values

In this thesis, we study several problems at the interface of algorithmic decision-making and society, focusing on the tensions that arise between these processes and social values like fairness and privacy. In the first chapter, we examine the design of financial portfolios which adequately serve all segments of the population. In the second, we examine an allocation setting where the allocator wishes to distribute a scarce resource across many groups fairly, but does not know ahead of time which groups have a need for the resource. In the third, we study a game-theoretic model of information aggregation and the effects of individuals acting to preserve the privacy of their personal beliefs on the collective welfare of the population. Finally, we look at some of the issues that arise from the desire to apply automated techniques to problems in redistricting, including fundamental flaws in the definitions and frameworks typically used

Authoritative and Unbiased Responses to Geographic Queries

Trust in information systems stem from two key properties of responses to queries regarding the state of the system, viz., i) authoritativeness, and ii) unbiasedness. That the response is authoritative implies that i) the provider (source) of the response, and ii) the chain of delegations through which the provider obtained the authority to respond, can be verified. The property of unbiasedness implies that no system data relevant to the query is deliberately or accidentally suppressed. The need for guaranteeing these two important properties stem from the impracticality for the verifier to exhaustively verify the correctness of every system process, and the integrity of the platform on which system processes are executed. For instance, the integrity of a process may be jeopardized by i) bugs (attacks) in computing hardware like Random Access Memory (RAM), input/output channels (I/O), and Central Processing Unit( CPU), ii) exploitable defects in an operating system, iii) logical bugs in program implementation, and iv) a wide range of other embedded malfunctions, among others. A first step in ensuing AU properties of geographic queries is the need to ensure AU responses to a specific type of geographic query, viz., point-location. The focus of this dissertation is on strategies to leverage assured point-location, for i) ensuring authoritativeness and unbiasedness (AU) of responses to a wide range of geographic queries; and ii) useful applications like Secure Queryable Dynamic Maps (SQDM) and trustworthy redistricting protocol. The specific strategies used for guaranteeing AU properties of geographic services include i) use of novel Merkle-hash tree- based data structures, and ii) blockchain networks to guarantee the integrity of the processes