Certificates of optimality: the third way to biproportional apportionment View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-02

AUTHORS

Paolo Serafini, Bruno Simeone

ABSTRACT

The biproportional apportionment problem (BAP) must be faced in many proportional electoral systems where seats must be allocated to parties within regions. BAP is a non-trivial optimization problem, and only sophisticated algorithms are currently available for solving it. The issue is: are they “writable” as an actual law? Citizens rightly demand simple, easy to understand, voting systems. The alternative, though, seems to have simple, but unsound electoral laws. We propose the following way out of this dilemma: leave to a mathematically sophisticated algorithm the task of producing an optimal apportionment, but attach to it a “certificate of optimality”, that is, describe a simple procedure whereby anybody can check, through some elementary operations, that the seat allocation output by the algorithm is indeed an optimal apportionment. We discuss one such certificate, based on the Max flow- min cut Theorem, relative to a parametric max flow method of ours for BAP. More... »

PAGES

247-268

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00355-010-0528-8

DOI

http://dx.doi.org/10.1007/s00355-010-0528-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1008592628


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Udine", 
          "id": "https://www.grid.ac/institutes/grid.5390.f", 
          "name": [
            "Department of Mathematics and Computer Science, University of Udine, Udine, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Serafini", 
        "givenName": "Paolo", 
        "id": "sg:person.012613244077.89", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012613244077.89"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Sapienza University of Rome", 
          "id": "https://www.grid.ac/institutes/grid.7841.a", 
          "name": [
            "Department of Statistics, University La Sapienza, Rome, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Simeone", 
        "givenName": "Bruno", 
        "id": "sg:person.012600006066.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012600006066.78"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01589103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003890771", 
          "https://doi.org/10.1007/bf01589103"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-35605-3_11", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014956826", 
          "https://doi.org/10.1007/3-540-35605-3_11"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/net.20434", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016455221"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mathsocsci.2008.01.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019178560"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0261-3794(97)00025-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020023481"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00186-007-0184-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031947199", 
          "https://doi.org/10.1007/s00186-007-0184-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00186-007-0184-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031947199", 
          "https://doi.org/10.1007/s00186-007-0184-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1287/moor.14.4.700", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064723413"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/pjm.1957.7.1073", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069062537"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2012-02", 
    "datePublishedReg": "2012-02-01", 
    "description": "The biproportional apportionment problem (BAP) must be faced in many proportional electoral systems where seats must be allocated to parties within regions. BAP is a non-trivial optimization problem, and only sophisticated algorithms are currently available for solving it. The issue is: are they \u201cwritable\u201d as an actual law? Citizens rightly demand simple, easy to understand, voting systems. The alternative, though, seems to have simple, but unsound electoral laws. We propose the following way out of this dilemma: leave to a mathematically sophisticated algorithm the task of producing an optimal apportionment, but attach to it a \u201ccertificate of optimality\u201d, that is, describe a simple procedure whereby anybody can check, through some elementary operations, that the seat allocation output by the algorithm is indeed an optimal apportionment. We discuss one such certificate, based on the Max flow- min cut Theorem, relative to a parametric max flow method of ours for BAP.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00355-010-0528-8", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1028302", 
        "issn": [
          "0176-1714", 
          "1432-217X"
        ], 
        "name": "Social Choice and Welfare", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "38"
      }
    ], 
    "name": "Certificates of optimality: the third way to biproportional apportionment", 
    "pagination": "247-268", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "28f000fc95018e139e7e2ad40cfd131549a95e9484819e6a8754ac59e737248b"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00355-010-0528-8"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1008592628"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00355-010-0528-8", 
      "https://app.dimensions.ai/details/publication/pub.1008592628"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T20:39", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8684_00000480.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/s00355-010-0528-8"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00355-010-0528-8'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00355-010-0528-8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00355-010-0528-8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00355-010-0528-8'


 

This table displays all metadata directly associated to this object as RDF triples.

98 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00355-010-0528-8 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N5e1b6505f5cc4a0aa99da1aa58ecbbf5
4 schema:citation sg:pub.10.1007/3-540-35605-3_11
5 sg:pub.10.1007/bf01589103
6 sg:pub.10.1007/s00186-007-0184-7
7 https://doi.org/10.1002/net.20434
8 https://doi.org/10.1016/j.mathsocsci.2008.01.004
9 https://doi.org/10.1016/s0261-3794(97)00025-5
10 https://doi.org/10.1287/moor.14.4.700
11 https://doi.org/10.2140/pjm.1957.7.1073
12 schema:datePublished 2012-02
13 schema:datePublishedReg 2012-02-01
14 schema:description The biproportional apportionment problem (BAP) must be faced in many proportional electoral systems where seats must be allocated to parties within regions. BAP is a non-trivial optimization problem, and only sophisticated algorithms are currently available for solving it. The issue is: are they “writable” as an actual law? Citizens rightly demand simple, easy to understand, voting systems. The alternative, though, seems to have simple, but unsound electoral laws. We propose the following way out of this dilemma: leave to a mathematically sophisticated algorithm the task of producing an optimal apportionment, but attach to it a “certificate of optimality”, that is, describe a simple procedure whereby anybody can check, through some elementary operations, that the seat allocation output by the algorithm is indeed an optimal apportionment. We discuss one such certificate, based on the Max flow- min cut Theorem, relative to a parametric max flow method of ours for BAP.
15 schema:genre research_article
16 schema:inLanguage en
17 schema:isAccessibleForFree true
18 schema:isPartOf Nd62ae70cf39c4c38bea3d5fcbb4782a2
19 Nebf9ef587baa43e293f01a792f3fa7f4
20 sg:journal.1028302
21 schema:name Certificates of optimality: the third way to biproportional apportionment
22 schema:pagination 247-268
23 schema:productId N0634cca8d26143458954dd1d4c75c36a
24 N1c9593673f89474bbce3a518f243f960
25 N4c34d18c69204b98977461bee1e58213
26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008592628
27 https://doi.org/10.1007/s00355-010-0528-8
28 schema:sdDatePublished 2019-04-10T20:39
29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
30 schema:sdPublisher N40a632fa92cd42a58b1efa7099f2ab8f
31 schema:url http://link.springer.com/10.1007/s00355-010-0528-8
32 sgo:license sg:explorer/license/
33 sgo:sdDataset articles
34 rdf:type schema:ScholarlyArticle
35 N0634cca8d26143458954dd1d4c75c36a schema:name dimensions_id
36 schema:value pub.1008592628
37 rdf:type schema:PropertyValue
38 N1c9593673f89474bbce3a518f243f960 schema:name readcube_id
39 schema:value 28f000fc95018e139e7e2ad40cfd131549a95e9484819e6a8754ac59e737248b
40 rdf:type schema:PropertyValue
41 N40a632fa92cd42a58b1efa7099f2ab8f schema:name Springer Nature - SN SciGraph project
42 rdf:type schema:Organization
43 N427d2e69605c49c9a7d48ac612eb2284 rdf:first sg:person.012600006066.78
44 rdf:rest rdf:nil
45 N4c34d18c69204b98977461bee1e58213 schema:name doi
46 schema:value 10.1007/s00355-010-0528-8
47 rdf:type schema:PropertyValue
48 N5e1b6505f5cc4a0aa99da1aa58ecbbf5 rdf:first sg:person.012613244077.89
49 rdf:rest N427d2e69605c49c9a7d48ac612eb2284
50 Nd62ae70cf39c4c38bea3d5fcbb4782a2 schema:issueNumber 2
51 rdf:type schema:PublicationIssue
52 Nebf9ef587baa43e293f01a792f3fa7f4 schema:volumeNumber 38
53 rdf:type schema:PublicationVolume
54 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
55 schema:name Mathematical Sciences
56 rdf:type schema:DefinedTerm
57 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
58 schema:name Numerical and Computational Mathematics
59 rdf:type schema:DefinedTerm
60 sg:journal.1028302 schema:issn 0176-1714
61 1432-217X
62 schema:name Social Choice and Welfare
63 rdf:type schema:Periodical
64 sg:person.012600006066.78 schema:affiliation https://www.grid.ac/institutes/grid.7841.a
65 schema:familyName Simeone
66 schema:givenName Bruno
67 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012600006066.78
68 rdf:type schema:Person
69 sg:person.012613244077.89 schema:affiliation https://www.grid.ac/institutes/grid.5390.f
70 schema:familyName Serafini
71 schema:givenName Paolo
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012613244077.89
73 rdf:type schema:Person
74 sg:pub.10.1007/3-540-35605-3_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014956826
75 https://doi.org/10.1007/3-540-35605-3_11
76 rdf:type schema:CreativeWork
77 sg:pub.10.1007/bf01589103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003890771
78 https://doi.org/10.1007/bf01589103
79 rdf:type schema:CreativeWork
80 sg:pub.10.1007/s00186-007-0184-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031947199
81 https://doi.org/10.1007/s00186-007-0184-7
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1002/net.20434 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016455221
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1016/j.mathsocsci.2008.01.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019178560
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/s0261-3794(97)00025-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020023481
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1287/moor.14.4.700 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064723413
90 rdf:type schema:CreativeWork
91 https://doi.org/10.2140/pjm.1957.7.1073 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069062537
92 rdf:type schema:CreativeWork
93 https://www.grid.ac/institutes/grid.5390.f schema:alternateName University of Udine
94 schema:name Department of Mathematics and Computer Science, University of Udine, Udine, Italy
95 rdf:type schema:Organization
96 https://www.grid.ac/institutes/grid.7841.a schema:alternateName Sapienza University of Rome
97 schema:name Department of Statistics, University La Sapienza, Rome, Italy
98 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...