Apportionment and districting by Sum of Ranking Differences.
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 is...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2020-01-01
|
| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0229209 |
| _version_ | 1818404467084623872 |
|---|---|
| author | Balázs R Sziklai Károly Héberger |
| author_facet | Balázs R Sziklai Károly Héberger |
| author_sort | Balázs R Sziklai |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T08:40:37Z |
| format | Article |
| id | doaj.art-db567f68eb8f4649ab21c088562c91fb |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-14T08:40:37Z |
| publishDate | 2020-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-db567f68eb8f4649ab21c088562c91fb2022-12-21T23:09:18ZengPublic Library of Science (PLoS)PLoS ONE1932-62032020-01-01153e022920910.1371/journal.pone.0229209Apportionment and districting by Sum of Ranking Differences.Balázs R SziklaiKároly HébergerSum 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.https://doi.org/10.1371/journal.pone.0229209 |
| spellingShingle | Balázs R Sziklai Károly Héberger Apportionment and districting by Sum of Ranking Differences. PLoS ONE |
| title | Apportionment and districting by Sum of Ranking Differences. |
| title_full | Apportionment and districting by Sum of Ranking Differences. |
| title_fullStr | Apportionment and districting by Sum of Ranking Differences. |
| title_full_unstemmed | Apportionment and districting by Sum of Ranking Differences. |
| title_short | Apportionment and districting by Sum of Ranking Differences. |
| title_sort | apportionment and districting by sum of ranking differences |
| url | https://doi.org/10.1371/journal.pone.0229209 |
| work_keys_str_mv | AT balazsrsziklai apportionmentanddistrictingbysumofrankingdifferences AT karolyheberger apportionmentanddistrictingbysumofrankingdifferences |