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

On 2-adic orders of some binomial sums

We prove that for any nonnegative integers $n$ and $r$ the binomial sum $$\sum_{k=-n}^n\binom{2n}{n-k}k^{2r}$$ is divisible by $2^{2n-\min\{\alpha(n),\alpha(r)\}}$, where $\alpha(n)$ denotes the number of 1's in the binary expansion of $n$. This confirms a recent conjecture of Guo and Zeng.Comment: 6 page

Party System Compactness: Measurement and Consequences

An important property of any party system is the set of choices it presents to the electorate. In this paper we analyze the distribution of parties relative to voters in the multidimensional issue space and introduce two measures of the dispersion of the parties in the issue space relative to the voters, which we call measures of the compactness of the parties in the issue space. We show how compactness is easily computed using standard survey items found on national election surveys. Because we study the spacing of the parties relative to the distribution of the voters, we produce metric-free measures of compactness of the party system. The measures can be used to compare party systems across issues, over time within countries, and across countries. Comparing the compactness of party systems across countries allows us to determine the relative amount of issue choice afforded voters in different polities. We examine the compactness of the issue space and test the impact it has on voter choice in four countries: the United States, the Netherlands, Canada, and Great Britain. We demonstrate that the more compact the distribution of the parties in the issue space on any given issue, the less voters weight that issue in their vote decision. Thus we provide evidence supporting theories suggesting that the greater the choice offered by the parties in an election, the more likely it is that issue voting will play a major role in that election

Is Investment in Agricultural Research a Good Substitute for Price Support in U.S. Cotton?

This article examines the effects of R&D on cotton yield and relationship between R&D and commodity support programs. The results indicate that yield elasticities with respect to cotton R&D is around 0.2-0.5 based on different regions. It further indicates that R&D increases government expenditures when both commodity programs and R&D funding exist. However, if the future WTO Doha negotiations rules out the possibility of price support programs, increasing R&D funding may provide one of the solutions for farmers to recover their income with 5-6 years lag.cotton, R&D, commodity support programs, Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies,

Strain amplitude response and the microstructure of PA/clay nanocomposites

Polyamide 6/clay nanocomposites (PAn, where n is the mass fraction of clay) with various clay loading were prepared by melt compounding in a twin screw extruder. Exfoliation of clay in a PA matrix was confirmed by X-ray diffraction. Strain amplitude response of PAn in both melt and solution states has been investigated. In the melt state, critical strain amplitude of PAn is sensitive to strain amplitude response and decrease logarithmically with increasing clay loading. The elastic moduli (G′) of PAn are reversible under frequency loop sweeps. Comparisons of strain amplitude response in both melt and solution states have been conducted. Two different responses have been observed: strain thinning in the melt state and weak strain overshoot in the solution state. FTIR studies show that amide II band of PAn shifts toward high wavenumbers, but amide I band and N–H stretching vibration are independent of clay loading. We suggest that two types of strain amplitude response of PAn can be explained: strain thinning which is dominant in PAn caused by physical adsorption and entanglement of PA chains on nanoclays and weak strain overshoot caused by weak bonds between PA chains and nanoclays