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"Election districts Mathematical models."
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Statistical detection of systematic election irregularities
Democratic societies are built around the principle of free and fair elections, and that each citizen’s vote should count equally. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their preferences. The large number of samples implies statistical consequences for the polling results, which can be used to identify election irregularities. Using a suitable data representation, we find that vote distributions of elections with alleged fraud show a kurtosis substantially exceeding the kurtosis of normal elections, depending on the level of data aggregation. As an example, we show that reported irregularities in recent Russian elections are, indeed, well-explained by systematic ballot stuffing. We develop a parametric model quantifying the extent to which fraudulent mechanisms are present. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces robust outcomes with respect to the resolution of the data and therefore, allows for cross-country comparisons.
Journal Article
A Logical Model for Predicting Minority Representation: Application to Redistricting and Voting Rights Cases
Understanding when and why minority candidates emerge and win in particular districts entails critical implications for redistricting and the Voting Rights Act. I introduce a quantitatively predictive logical model of minority candidate emergence and electoral success—a mathematical formula based on deductive logic that can logically explain and accurately predict the exact probability at which minority candidates run for office and win in given districts. I show that the logical model can predict about 90% of minority candidate emergence and 95% of electoral success by leveraging unique data of mayoral elections in Louisiana from 1986 to 2016 and state legislative general elections in 36 states in 2012 and 2014. I demonstrate that the logical model can be used to answer many important questions about minority representation in redistricting and voting rights cases. All applications of the model can be easily implemented via an open-source software logical.
Journal Article
Mathematical political districting taking care of minority groups
Political districting (PD) is a wide studied topic in the literature since the 60s. It typically requires a multi-criteria approach, and mathematical programs are frequently suggested to model the many aspects of this difficult problem. This implies that exact models cannot be solved to optimality when the size of the territory is too large. In spite of this, an exact formulation can also be exploited in a heuristic framework to find at least a sub-optimal solution for large size problem instances. We study the design of electoral districts in Mexico, where the population is characterized by the presence of minority groups (“indigenous community”) who have a special right to be represented in the Parliament. For this, the Mexican electoral law prescribes that a fixed number of districts must be designed to support the representation of the indigenous community. We formulate mixed integer linear programs (MILP) following these two principles, but also including the basic PD criteria of contiguity and population balance. The district map is obtained in two stages: first we produce the fixed number of indigenous districts established by the Law; then we complete the district map by forming the non-indigenous districts. This two-phase approach has two advantages: a dedicated objective function can be formulated in Phase 1 to form indigenous districts at best; in the second phase the instance size is reduced (both in the number of territorial units and in the number of districts) so that the computational effort to solve the problem is reduced as well. We test our procedure on the territory of Chiapas in Mexico and on some fictitious problem instances in which the territory is represented by a grid graph. We also compare our district map with the Institutional one currently adopted in Chiapas.
Journal Article
A Computational Approach to Measuring Vote Elasticity and Competitiveness
The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states' reform efforts has been the inclusion of competitiveness metrics, or scores that evaluate a districting plan based on the extent to which district-level outcomes are in play or are likely to be closely contested.
In this article, we examine several classes of competitiveness metrics motivated by recent reform proposals and then evaluate their potential outcomes across large ensembles of districting plans at the Congressional and state Senate levels. This is part of a growing literature using MCMC techniques from applied statistics to situate plans and criteria in the context of valid redistricting alternatives. Our empirical analysis focuses on five states-Utah, Georgia, Wisconsin, Virginia, and Massachusetts-chosen to represent a range of partisan attributes. We highlight situation-specific difficulties in creating good competitiveness metrics and show that optimizing competitiveness can produce unintended consequences on other partisan metrics. These results demonstrate the importance of (1) avoiding writing detailed metric constraints into long-lasting constitutional reform and (2) carrying out careful mathematical modeling on real geo-electoral data in each redistricting cycle.
Journal Article
Social media popularity and election results: A study of the 2016 Taiwanese general election
This paper investigates the relationship between candidates' online popularity and election results, as a step towards creating a model to forecast the results of Taiwanese elections even in the absence of reliable opinion polls on a district-by-district level. 253 of 354 legislative candidates of single-member districts in Taiwan's 2016 general election had active public Facebook pages during the election period. Hypothesizing that the relative popularity of candidates' Facebook posts will be positively related to their election results, I calculated each candidate's Like Ratio (i.e. proportions of all likes on Facebook posts obtained by candidates in their district). In order to have a measure of online interest without the influence of subjective positivity, I similarly calculated the proportion of daily average page views for each candidate's Wikipedia page. I ran a regression analysis, incorporating data on results of previous elections and available opinion poll data. I found the models could describe the result of the election well and reject the null hypothesis. My models successfully predicted 80% of winners in single-member districts and were effective in districts without local opinion polls with a predictive power approaching that of traditional opinion polls. The models also showed good accuracy when run on data for the 2014 Taiwanese municipal mayors election.
Journal Article
Lattice Studies of Gerrymandering Strategies
A new theoretical method for examining gerrymandering is presented based on lattice models of voters, in which districts are constructed by partitioning the lattice. We propose three novel algorithms for constructing equal-population, connected districts which favor the gerrymanderer and incorporate the spatial distribution of voters. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo techniques can be applied to study the impact of gerrymandering. We use the method developed here to compare our different gerrymandering algorithms, show approaches which ignore spatial data lead to (legally prohibited) disconnected districts, and examine the effectiveness of isoperimetric quotient tests.
Journal Article
Goal programming approach for political districting in Santa Catarina State: Brazil
In the Brazilian judiciary, the Electoral Registry Offices (EROs) are responsible for managing the Brazilian electoral districts. Moreover, not only do they organize elections in their district, but they are also responsible for managing the registration of electors and supervising the political parties. Brazil has a multi-party system with more than 35 political parties competing over the 295 cities of Santa Catarina state, which had over 4.98 million voters in 2017. In this context, we present a mixed integer model, with the concepts of goal programming and contiguity graph, to propose a more equilibrated distribution of political districts to Santa Catarina state. The mathematical model considers the political districting criteria (population balance, spatial contiguity, and compactness), and also considers the particularities of the Brazilian electoral system (minimum number of voters in an electoral district, maximum electoral zones per city, and so forth). The objective of the problem is to determine the optimum set of districts for the most efficient use of public resources and best service to the population. Therefore, there must be a balance of workload among the (EROs), i.e., a steady number of electors and nominating petitions per district. The solution proposed succeeded in presenting a set of districts with a better workload distribution while respecting all the districting criteria and the Brazilian legislation. Compared to the current situation, the model shows a reduction in the standard deviation of the electorate distribution per district of 7520 voters. The solution obtained by the proposed model for the Brazilian electoral system in the state of Santa Catarina may be used by any other of the 26 Brazilian states. The proposed model is a particularization of the classic political districting problem since it inserts complementary constraints to this classic problem from the operational research literature.
Journal Article
The mathematicians who want to save democracy
Gerrymandering has a long and unpopular history in the US. It is the main reason that the country ranked 55th of 158 nations--last among Western democracies--in a 2017 index of voting fairness run by the Electoral Integrity Project. Although gerrymandering played no part in the tumultuous 2016 presidential election, it seems to have influenced who won seats in the US House of Representatives that year. Here, Arnold features mathematicians who created models and algorithms to evaluate the impact of gerrymandering on the country's electoral system.
Journal Article
Maths strikes a blow for democracy
Republican politicians caught unfairly altering electoral districts thanks to computer algorithm.
Journal Article