Apportionment and districting by Sum of Ranking Differences

Abstract

Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two critical issues that emerge in relation to democratic elections. Theoreticians invented clever heuristics to measure malapportionment and the compactness of the shape of the constituencies, yet, there is no unique best method in either cases. Using data from Norway and the US we rank the standard methods both for the apportionment and for the districting problem. In case of apportionment, we find that all the classical methods perform reasonably well, with subtle but significant differences. By a small margin the Leximin method emerges as a winner, but-somewhat unexpectedly-the non-regular Imperiali method ties for first place. In districting, the Lee-Sallee index and a novel parametric method the so-called Moment Invariant performs the best, although the latter is sensitive to the function's chosen parameter.

Frequent Errors in Modeling by Machine Learning: A Prototype Case of Predicting the Timely Evolution of COVID-19 Pandemic

“…A link to a downloadable program can be found here [22]. Two validation options are available: randomization test [23] and crossvalidation [23] with the application of the Wilcoxon test [24]. Although SRD was primarily developed to solve model comparison problems, it realizes multicriteria optimization [25], as long as the input matrix is arranged as such: alternatives in the columns and features (criteria) in the rows.…”

Discrimination Ability of Assessors in Check-All-That-Apply Tests: Method and Product Development

“…The reason for this choice is that we cannot arbitrarily select the best similarity metric a priori. By contrast, the merit of consensus metrics/methodologies have been extensively demonstrated [ 16 , 17 , 18 ]. Briefly, using the average of the 44 similarity metrics is supported by the maximum likelihood principle, which “yields a choice of the estimator as the value for the parameter that makes the observed data most probable” [ 19 ].…”

Data quality control considerations in multivariate environmental monitoring: experience of the French coastal network SOMLIT

“…To classify the different participating laboratories according to their respective overall performance in trueness and repeatability, we performed a Sum of Ranking Difference (SRD, see the Supplementary Materials for file format) test, a non-parametric multivariate technique recommended when the number of participating laboratories is less than 13 (Heberger and Kollaŕ-Hunek, 2011). While SRD has multiple applications (e.g., Andrićand Heberger, 2015;Kalivas et al, 2015;Sziklai and Heberger, 2020), it allows us to analyze similarities between laboratories by ranking (columns of the input matrix relative to trueness and replicability targets, across the measurement of several environmental variables, and rows of the input matrix). The closer to zero the SRD value, the better the overall performance of the laboratory.…”