The independence condition in the theory of social choice View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1973-09

AUTHORS

Bengt Hansson

ABSTRACT

Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided. A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition. The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds. Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets. The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character. In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed. More... »

PAGES

25-49

Journal

TITLE

Theory and Decision

ISSUE

1

VOLUME

4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00133397

DOI

http://dx.doi.org/10.1007/bf00133397

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001863541


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/2008/2203", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Philosophy", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/22", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Philosophy and Religious Studies", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Lund University", 
          "id": "https://www.grid.ac/institutes/grid.4514.4", 
          "name": [
            "Department of Philosophy, University of Lund, Sweden"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hansson", 
        "givenName": "Bengt", 
        "id": "sg:person.013245527166.50", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013245527166.50"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf00484979", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020279043", 
          "https://doi.org/10.1007/bf00484979"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00484979", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020279043", 
          "https://doi.org/10.1007/bf00484979"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00869933", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027186921", 
          "https://doi.org/10.1007/bf00869933"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00132454", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043572229", 
          "https://doi.org/10.1007/bf00132454"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00132454", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043572229", 
          "https://doi.org/10.1007/bf00132454"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00139349", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049676791", 
          "https://doi.org/10.1007/bf00139349"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00139349", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049676791", 
          "https://doi.org/10.1007/bf00139349"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/259614", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058573095"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/288241", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058598284"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1909204", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069638388"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1909703", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069638787"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1973-09", 
    "datePublishedReg": "1973-09-01", 
    "description": "Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided. A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition. The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds. Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets. The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character. In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf00133397", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1026738", 
        "issn": [
          "0040-5833", 
          "1573-7187"
        ], 
        "name": "Theory and Decision", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "4"
      }
    ], 
    "name": "The independence condition in the theory of social choice", 
    "pagination": "25-49", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "08e07c44fd05e4b55d3e733bce876517945cb8d1efe1054461e54627a78d0366"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00133397"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1001863541"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00133397", 
      "https://app.dimensions.ai/details/publication/pub.1001863541"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:58", 
    "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/v90/0000000371_0000000371/records_130823_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF00133397"
  }
]
 

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/bf00133397'

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/bf00133397'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00133397'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00133397'


 

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

89 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00133397 schema:about anzsrc-for:22
2 anzsrc-for:2203
3 schema:author N9a3f35b6a9c4417a86d7161f1d0f4a07
4 schema:citation sg:pub.10.1007/bf00132454
5 sg:pub.10.1007/bf00139349
6 sg:pub.10.1007/bf00484979
7 sg:pub.10.1007/bf00869933
8 https://doi.org/10.1086/259614
9 https://doi.org/10.1086/288241
10 https://doi.org/10.2307/1909204
11 https://doi.org/10.2307/1909703
12 schema:datePublished 1973-09
13 schema:datePublishedReg 1973-09-01
14 schema:description Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided. A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition. The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds. Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets. The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character. In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed.
15 schema:genre research_article
16 schema:inLanguage en
17 schema:isAccessibleForFree false
18 schema:isPartOf N3399cf6b724d4235bf3b61d2e75fda0e
19 Nc1b61fab2ca64fdab7c8481fba33cd47
20 sg:journal.1026738
21 schema:name The independence condition in the theory of social choice
22 schema:pagination 25-49
23 schema:productId N80e062164cbc45f48f36893d091b676f
24 Nd0b6e101b2a843488fbab2d20e481ca3
25 Nf85ba684a1214747bb9e1ca75fe5d818
26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001863541
27 https://doi.org/10.1007/bf00133397
28 schema:sdDatePublished 2019-04-11T13:58
29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
30 schema:sdPublisher N18f652c836f9454192dee2380ba43388
31 schema:url http://link.springer.com/10.1007/BF00133397
32 sgo:license sg:explorer/license/
33 sgo:sdDataset articles
34 rdf:type schema:ScholarlyArticle
35 N18f652c836f9454192dee2380ba43388 schema:name Springer Nature - SN SciGraph project
36 rdf:type schema:Organization
37 N3399cf6b724d4235bf3b61d2e75fda0e schema:volumeNumber 4
38 rdf:type schema:PublicationVolume
39 N80e062164cbc45f48f36893d091b676f schema:name dimensions_id
40 schema:value pub.1001863541
41 rdf:type schema:PropertyValue
42 N9a3f35b6a9c4417a86d7161f1d0f4a07 rdf:first sg:person.013245527166.50
43 rdf:rest rdf:nil
44 Nc1b61fab2ca64fdab7c8481fba33cd47 schema:issueNumber 1
45 rdf:type schema:PublicationIssue
46 Nd0b6e101b2a843488fbab2d20e481ca3 schema:name readcube_id
47 schema:value 08e07c44fd05e4b55d3e733bce876517945cb8d1efe1054461e54627a78d0366
48 rdf:type schema:PropertyValue
49 Nf85ba684a1214747bb9e1ca75fe5d818 schema:name doi
50 schema:value 10.1007/bf00133397
51 rdf:type schema:PropertyValue
52 anzsrc-for:22 schema:inDefinedTermSet anzsrc-for:
53 schema:name Philosophy and Religious Studies
54 rdf:type schema:DefinedTerm
55 anzsrc-for:2203 schema:inDefinedTermSet anzsrc-for:
56 schema:name Philosophy
57 rdf:type schema:DefinedTerm
58 sg:journal.1026738 schema:issn 0040-5833
59 1573-7187
60 schema:name Theory and Decision
61 rdf:type schema:Periodical
62 sg:person.013245527166.50 schema:affiliation https://www.grid.ac/institutes/grid.4514.4
63 schema:familyName Hansson
64 schema:givenName Bengt
65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013245527166.50
66 rdf:type schema:Person
67 sg:pub.10.1007/bf00132454 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043572229
68 https://doi.org/10.1007/bf00132454
69 rdf:type schema:CreativeWork
70 sg:pub.10.1007/bf00139349 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049676791
71 https://doi.org/10.1007/bf00139349
72 rdf:type schema:CreativeWork
73 sg:pub.10.1007/bf00484979 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020279043
74 https://doi.org/10.1007/bf00484979
75 rdf:type schema:CreativeWork
76 sg:pub.10.1007/bf00869933 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027186921
77 https://doi.org/10.1007/bf00869933
78 rdf:type schema:CreativeWork
79 https://doi.org/10.1086/259614 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058573095
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1086/288241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058598284
82 rdf:type schema:CreativeWork
83 https://doi.org/10.2307/1909204 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069638388
84 rdf:type schema:CreativeWork
85 https://doi.org/10.2307/1909703 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069638787
86 rdf:type schema:CreativeWork
87 https://www.grid.ac/institutes/grid.4514.4 schema:alternateName Lund University
88 schema:name Department of Philosophy, University of Lund, Sweden
89 rdf:type schema:Organization
 




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


...