Gerrymandering and Compactness: Implementation Flexibility and Abuse

The shape of an electoral district may suggest whether it was drawn with political motivations, or gerrymandered. For this reason, quantifying the shape of districts, in particular their compactness, is a key task in politics and civil rights. A growing body of literature suggests and analyzes compactness measures mathematically, but little consideration has been given to how these scores should be calculated in practice. Here, we consider the effects of a number of decisions that must be made in interpreting and implementing a set of popular compactness scores. We show that the choices made in quantifying compactness may themselves become political tools, with seemingly innocuous decisions leading to disparate scores. We show that when the full range of implementation flexibility is used, it can be abused to make clearly gerrymandered districts appear quantitatively reasonable. This complicates using compactness as a legislative or judicial standard to counteract unfair redistricting practices. This paper accompanies the release of packages in C++, Python, and R which correctly, efficiently, and reproducibly calculate a variety of compactness scores.Comment: 10 pages, 17 figures, 1 tabl

Introduction

Publication within the project “The V4 towards migration challenges in Europe. An analysis and recommendations” is financed by Visegrad Fund

Counting and Enumerating Crossing-free Geometric Graphs

We describe a framework for counting and enumerating various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, who used them to count triangulations in time $O(2^nn^2)$ where $n$ is the number of points. The main idea is to reduce the problem of counting geometric graphs to counting source-sink paths in a directed acyclic graph. The following new results will emerge. The number of all crossing-free geometric graphs can be computed in time $O(c^nn^4)$ for some $c < 2.83929$. The number of crossing-free convex partitions can be computed in time $O(2^nn^4)$. The number of crossing-free perfect matchings can be computed in time $O(2^nn^4)$. The number of convex subdivisions can be computed in time $O(2^nn^4)$. The number of crossing-free spanning trees can be computed in time $O(c^nn^4)$ for some $c < 7.04313$. The number of crossing-free spanning cycles can be computed in time $O(c^nn^4)$ for some $c < 5.61804$. With the same bounds on the running time we can construct data structures which allow fast enumeration of the respective classes. For example, after $O(2^nn^4)$ time of preprocessing we can enumerate the set of all crossing-free perfect matchings using polynomial time per enumerated object. For crossing-free perfect matchings and convex partitions we further obtain enumeration algorithms where the time delay for each (in particular, the first) output is bounded by a polynomial in $n$. All described algorithms are comparatively simple, both in terms of their analysis and implementation

Introduction: Commercial Diplomacy and International Business.

International business has always been intimately linked to the politics of the global economy. Expansion and investment strategies of business play a key role in de?ning the architecture of the global economy. The shifting dynamic of the global economy such as the emergence of fast growing economies in, for example, India, China, South Africa and Brazil can be partly explained by the emergence of new market players such as the India transnational car manufacturer Tata, as well as the adaptation of established international businesses in the West to the new market opportunities in the South and the East. Equally, the recent (and in places ongoing) economic crises of the West owes as much to the failures of international business — notably the banking and investment industry — as it does to the failures of government policy. At the same time the international political dimension to the global economy explains the regulatory forces which also determine the architecture of the global economy. The far reaching policy liberalization of international trade through international (namely the World Trade Organisation) and regional treaties and rule- making, and the global deregulation of the investment and ?nancial services sector of the global economy driven by the neoliberal policies of the World Bank and the International Monetary Fund have created economic risks and opportunities for international business by opening up and creating new markets. The strategies of nation states and international business determine the architecture of the global economy and create both economic crises and dynamic growth at one and the same time in the contemporary global economy. So it is that for much of the ?rst decade or so of the new century the West has endured an age of austerity brought on by sustained economic decline and high indebtedness. The once market dominant economies of the United States and West European economies are now struggling to reverse negative economic growth. By contrast large previously peripheral under- developed economies in Africa and Asia are enjoying remarkable and sustained growth rates and their exports and investments now fuel an overall growth in the global economy