This article illustrates how the relationship between political geography and the electoral bias of a districting plan, as measured by the efficiency gap, can be analyzed in a statistically rigorous manner using computer simulations of the legislative redistricting process. By generating a large number of different districting plans designed to optimize on traditional redistricting criteria, th...

The aim of districting problems is to get an optimized partition of a territory into smaller units, called districts or zones, subject to some side constraints such as balance, contiguity, and compactness. Logistics districting problems usuually involve additional optimization criteria and constraints. Districting problems are called continuous when the underlying space, both for facility sites...

This paper investigates the problem of optimal districting in the context of a simple model of legislative elections. In the model, districting matters because it determines the seat-vote curve, which describes the relationship between seats and votes. The paper rst characterizes the optimal seat-vote curve, and shows that, under a weak condition, there exist districtings that generate this ide...

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 the connections and the differences between the two approaches are highlighted.

The City of Philadelphia recently redesigned districts for its council members based upon the 2010 census. The districting process evinced considerable public interest and engagement because council districts from the prior census had significant shortcomings. During the 2010 redistricting process, several public interest groups came together to organize a districting contest. The organizers ho...

In the context of discrete districting problems with geographical constraints, we demonstrate that determining an (ex post) unbiased districting, which requires that the number of representatives of a party should be proportional to its share of votes, turns out to be a computationally intractable (NP-complete) problem. This raises doubts as to whether an independent jury will be able to come u...

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis the problem without constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies sharp contrast between proportionality competitiveness how might be overcome a properly formulated objective function. It...

The political districting problem has been studied since the 60’s and many different models and techniques have been proposed with the aim of preventing districts’ manipulation which may favor some specific political party (gerrymandering). A variety of political districting models and procedures was provided in the Operations Research literature, based on singleor multiple-objective optimizati...

Privatization of municipal solid waste (MSW) collection can improve service quality and reduce cost. To reduce the risk of an incapable company serving an entire collection area and to establish a competitive market, a large collection area should be divided into two or more subregions, with each subregion served by a different company. The MSW subregion districting is generally done manually, ...