On the Tractability Landscape of the Conditional Minisum Approval Voting Rule
This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational complexity of this rule, demonstrating that no approach can s...
Saved in:
| Published in: | Information processing letters Vol. 189; p. 106561 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.03.2025
|
| ISSN: | 0020-0190 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational complexity of this rule, demonstrating that no approach can significantly outperform the brute-force algorithm under common computational complexity assumptions and various natural input restrictions. In response, we propose two practical restrictions (the first in the literature) that make the problem computationally tractable and show that these restrictions are essentially tight. Overall, this work provides a clear picture of the tractability landscape of the problem, contributing to a comprehensive understanding of the complications introduced by conditional ballots and indicating that conditional approval voting can be applied in practice, albeit under specific conditions.
•Multiple strong intractability results for the Conditional Minisum Approval Voting Rule are demonstrated.•Tractability is established with constraints on voters' ballot types, specifically for group-dichotomous preferences.•Tractability is demonstrated when voters' dependencies can be illustrated by graphs with bounded vertex cover numbers. |
|---|---|
| AbstractList | This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational complexity of this rule, demonstrating that no approach can significantly outperform the brute-force algorithm under common computational complexity assumptions and various natural input restrictions. In response, we propose two practical restrictions (the first in the literature) that make the problem computationally tractable and show that these restrictions are essentially tight. Overall, this work provides a clear picture of the tractability landscape of the problem, contributing to a comprehensive understanding of the complications introduced by conditional ballots and indicating that conditional approval voting can be applied in practice, albeit under specific conditions.
•Multiple strong intractability results for the Conditional Minisum Approval Voting Rule are demonstrated.•Tractability is established with constraints on voters' ballot types, specifically for group-dichotomous preferences.•Tractability is demonstrated when voters' dependencies can be illustrated by graphs with bounded vertex cover numbers. |
| ArticleNumber | 106561 |
| Author | Papasotiropoulos, Georgios Amanatidis, Georgios Lampis, Michael Markakis, Evangelos |
| Author_xml | – sequence: 1 givenname: Georgios surname: Amanatidis fullname: Amanatidis, Georgios organization: Athens University of Economics and Business; Archimedes / Athena RC, Athens, Greece – sequence: 2 givenname: Michael surname: Lampis fullname: Lampis, Michael organization: LAMSADE, CNRS, Université Paris Dauphine – PSL, Paris, France – sequence: 3 givenname: Evangelos surname: Markakis fullname: Markakis, Evangelos organization: Athens University of Economics and Business; Archimedes / Athena RC, Athens, Greece – sequence: 4 givenname: Georgios orcidid: 0000-0003-4246-886X surname: Papasotiropoulos fullname: Papasotiropoulos, Georgios email: gpapasotiropoulos@gmail.com organization: University of Warsaw, Warsaw, Poland |
| BookMark | eNp9kE1rAjEQhnOwULX9Ab3tH1g7idno0pNIPwRFKLbXkI9JG1mTJVkF_33X2nNPw8zwvLw8IzIIMSAhDxQmFKh43E9820wYsKrfRSXogAwBGJRAa7glo5z3ACD4dDYkm20oum8sdkmZTmnf-O5crFWw2agWi-h-v8sYrO98DKopNj74fDwUi7ZN8dQfPmPnw1fxfmzwjtw41WS8_5tj8vHyvFu-levt62q5WJeG8borWa21EBy5AnBCzSlVnCJqoJWwltNKM9Cc6Vmla85QCTatUThjwXE1t246JvSaa1LMOaGTbfIHlc6Sgrw4kHvZO5AXB_LqoGeergz2xU4ek8zGYzBofULTSRv9P_QPkPZojA |
| Cites_doi | 10.1007/s00453-011-9554-x 10.1016/j.tcs.2010.10.043 10.1006/jcss.2000.1727 10.4086/toc.2010.v006a005 10.1007/s00224-009-9167-9 10.1137/S0097539799349948 10.1016/j.jcss.2006.04.007 10.1016/0196-6774(86)90023-4 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier B.V. |
| Copyright_xml | – notice: 2025 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ipl.2025.106561 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| ExternalDocumentID | 10_1016_j_ipl_2025_106561 S0020019025000055 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 29I 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AATTM AAXKI AAXUO AAYFN ABBOA ABDPE ABEFU ABFNM ABFSI ABJNI ABMAC ABTAH ABWVN ABXDB ACDAQ ACGFS ACNNM ACRLP ACRPL ACZNC ADBBV ADEZE ADJOM ADMUD ADNMO AEBSH AEIPS AEKER AENEX AFJKZ AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AKRWK ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU AOUOD ASPBG AVWKF AXJTR AZFZN BKOJK BKOMP BLXMC BNPGV CS3 DU5 E.L EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HMJ HVGLF HZ~ IHE J1W KOM LG9 M26 M41 MO0 MS~ O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SEW SME SPC SPCBC SSH SSV SSZ T5K TN5 UQL WH7 WUQ XPP ZMT ZY4 ~G- 9DU AAYWO AAYXX ACLOT ACVFH ADCNI AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP APXCP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c249t-29bb664e4a00f6a811a41eeb0156dd415b20b42b75b942ea6239e6fcd0f4a8df3 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001414372700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-0190 |
| IngestDate | Thu Nov 27 00:56:32 EST 2025 Sun Apr 06 06:52:57 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c249t-29bb664e4a00f6a811a41eeb0156dd415b20b42b75b942ea6239e6fcd0f4a8df3 |
| ORCID | 0000-0003-4246-886X |
| ParticipantIDs | crossref_primary_10_1016_j_ipl_2025_106561 elsevier_sciencedirect_doi_10_1016_j_ipl_2025_106561 |
| PublicationCentury | 2000 |
| PublicationDate | March 2025 2025-03-00 |
| PublicationDateYYYYMMDD | 2025-03-01 |
| PublicationDate_xml | – month: 03 year: 2025 text: March 2025 |
| PublicationDecade | 2020 |
| PublicationTitle | Information processing letters |
| PublicationYear | 2025 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Khanna, Sudan, Trevisan, Williamson (br0130) 2001; 30 Fellows, Lokshtanov, Misra, Rosamond, Saurabh (br0070) 2008 Brill, Markakis, Papasotiropoulos, Peters (br0020) 2023 Peters, Skowron (br0190) 2020 Khanna, Sudan (br0120) 1996 Karthik, Marx, Pilipczuk, Souza (br0110) 2024 Marx (br0160) 2010; 6 Markakis, Papasotiropoulos (br0170) 2020 Fiala, Golovach, Kratochvíl (br0060) 2011; 412 Markakis, Papasotiropoulos (br0180) 2021 Chen, Huang, Kanj, Xia (br0040) 2006; 72 Robertson, Seymour (br0200) 1986; 7 Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh (br0030) 2015 Thiele (br0210) 1895 Barrot, Lang (br0010) 2016 Janson (br0100) 2016 Eiben, Ganian, Ordyniak (br0050) 2018 Fellows, Lokshtanov, Misra, Mnich, Rosamond, Saurabh (br0080) 2009; 45 Lampis (br0140) 2012; 64 Lang, Xia (br0150) 2016 Impagliazzo, Paturi (br0090) 2001; 62 Chen (10.1016/j.ipl.2025.106561_br0040) 2006; 72 Lampis (10.1016/j.ipl.2025.106561_br0140) 2012; 64 Fiala (10.1016/j.ipl.2025.106561_br0060) 2011; 412 Khanna (10.1016/j.ipl.2025.106561_br0130) 2001; 30 Fellows (10.1016/j.ipl.2025.106561_br0070) 2008 Markakis (10.1016/j.ipl.2025.106561_br0170) 2020 Markakis (10.1016/j.ipl.2025.106561_br0180) 2021 Barrot (10.1016/j.ipl.2025.106561_br0010) 2016 Cygan (10.1016/j.ipl.2025.106561_br0030) 2015 Fellows (10.1016/j.ipl.2025.106561_br0080) 2009; 45 Eiben (10.1016/j.ipl.2025.106561_br0050) 2018 Karthik (10.1016/j.ipl.2025.106561_br0110) 2024 Thiele (10.1016/j.ipl.2025.106561_br0210) 1895 Brill (10.1016/j.ipl.2025.106561_br0020) 2023 Peters (10.1016/j.ipl.2025.106561_br0190) 2020 Impagliazzo (10.1016/j.ipl.2025.106561_br0090) 2001; 62 Lang (10.1016/j.ipl.2025.106561_br0150) 2016 Robertson (10.1016/j.ipl.2025.106561_br0200) 1986; 7 Khanna (10.1016/j.ipl.2025.106561_br0120) 1996 Janson (10.1016/j.ipl.2025.106561_br0100) Marx (10.1016/j.ipl.2025.106561_br0160) 2010; 6 |
| References_xml | – start-page: 197 year: 2016 end-page: 222 ident: br0150 article-title: Voting in combinatorial domains publication-title: Handbook of Computational Social Choice – volume: 30 start-page: 1863 year: 2001 end-page: 1920 ident: br0130 article-title: The approximability of constraint satisfaction problems publication-title: SIAM J. Comput. – start-page: 415 year: 1895 end-page: 441 ident: br0210 article-title: Om flerfoldsvalg publication-title: Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger – start-page: 88 year: 2016 end-page: 94 ident: br0010 article-title: Conditional and sequential approval voting on combinatorial domains publication-title: International Joint Conference on Artificial Intelligence – volume: 6 start-page: 85 year: 2010 end-page: 112 ident: br0160 article-title: Can you beat treewidth? publication-title: Theory Comput. – start-page: 793 year: 2020 end-page: 794 ident: br0190 article-title: Proportionality and the limits of welfarism publication-title: Proceedings of the 21st ACM Conference on Economics and Computation – volume: 7 start-page: 309 year: 1986 end-page: 322 ident: br0200 article-title: Graph minors. II. Algorithmic aspects of tree-width publication-title: J. Algorithms – year: 2016 ident: br0100 article-title: Phragmén's and Thiele's election methods – volume: 62 start-page: 367 year: 2001 end-page: 375 ident: br0090 article-title: On the complexity of k-SAT publication-title: J. Comput. Syst. Sci. – year: 1996 ident: br0120 article-title: The optimization complexity of constraint satisfaction problems publication-title: Electonic Colloquium on Computational Complexity – start-page: 2537 year: 2023 end-page: 2545 ident: br0020 article-title: Proportionality guarantees in elections with interdependent issues publication-title: International Joint Conference on Artificial Intelligence – year: 2015 ident: br0030 article-title: Parameterized Algorithms – start-page: 294 year: 2008 end-page: 305 ident: br0070 article-title: Graph layout problems parameterized by vertex cover publication-title: Algorithms and Computation: International Symposium – start-page: 383 year: 2024 end-page: 395 ident: br0110 article-title: Conditional lower bounds for sparse parameterized 2-CSP: a streamlined proof publication-title: Symposium on Simplicity in Algorithms – volume: 72 start-page: 1346 year: 2006 end-page: 1367 ident: br0040 article-title: Strong computational lower bounds via parameterized complexity publication-title: J. Comput. Syst. Sci. – volume: 64 start-page: 19 year: 2012 end-page: 37 ident: br0140 article-title: Algorithmic meta-theorems for restrictions of treewidth publication-title: Algorithmica – start-page: 304 year: 2020 end-page: 310 ident: br0170 article-title: Computational aspects of conditional minisum approval voting in elections with interdependent issues publication-title: International Joint Conference on Artificial Intelligence – start-page: 203 year: 2018 end-page: 209 ident: br0050 article-title: A structural approach to activity selection publication-title: International Joint Conference on Artificial Intelligence – volume: 412 start-page: 2513 year: 2011 end-page: 2523 ident: br0060 article-title: Parameterized complexity of coloring problems: treewidth versus vertex cover publication-title: Theor. Comput. Sci. – volume: 45 start-page: 822 year: 2009 end-page: 848 ident: br0080 article-title: The complexity ecology of parameters: an illustration using bounded max leaf number publication-title: Theory Comput. Syst. – start-page: 342 year: 2021 end-page: 348 ident: br0180 article-title: Winner determination and strategic control in conditional approval voting publication-title: International Joint Conference on Artificial Intelligence – volume: 64 start-page: 19 year: 2012 ident: 10.1016/j.ipl.2025.106561_br0140 article-title: Algorithmic meta-theorems for restrictions of treewidth publication-title: Algorithmica doi: 10.1007/s00453-011-9554-x – start-page: 197 year: 2016 ident: 10.1016/j.ipl.2025.106561_br0150 article-title: Voting in combinatorial domains – volume: 412 start-page: 2513 issue: 23 year: 2011 ident: 10.1016/j.ipl.2025.106561_br0060 article-title: Parameterized complexity of coloring problems: treewidth versus vertex cover publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2010.10.043 – start-page: 793 year: 2020 ident: 10.1016/j.ipl.2025.106561_br0190 article-title: Proportionality and the limits of welfarism – start-page: 203 year: 2018 ident: 10.1016/j.ipl.2025.106561_br0050 article-title: A structural approach to activity selection – volume: 62 start-page: 367 issue: 2 year: 2001 ident: 10.1016/j.ipl.2025.106561_br0090 article-title: On the complexity of k-SAT publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2000.1727 – volume: 6 start-page: 85 issue: 1 year: 2010 ident: 10.1016/j.ipl.2025.106561_br0160 article-title: Can you beat treewidth? publication-title: Theory Comput. doi: 10.4086/toc.2010.v006a005 – year: 1996 ident: 10.1016/j.ipl.2025.106561_br0120 article-title: The optimization complexity of constraint satisfaction problems – volume: 45 start-page: 822 year: 2009 ident: 10.1016/j.ipl.2025.106561_br0080 article-title: The complexity ecology of parameters: an illustration using bounded max leaf number publication-title: Theory Comput. Syst. doi: 10.1007/s00224-009-9167-9 – start-page: 415 year: 1895 ident: 10.1016/j.ipl.2025.106561_br0210 article-title: Om flerfoldsvalg – start-page: 2537 year: 2023 ident: 10.1016/j.ipl.2025.106561_br0020 article-title: Proportionality guarantees in elections with interdependent issues – volume: 30 start-page: 1863 issue: 6 year: 2001 ident: 10.1016/j.ipl.2025.106561_br0130 article-title: The approximability of constraint satisfaction problems publication-title: SIAM J. Comput. doi: 10.1137/S0097539799349948 – year: 2015 ident: 10.1016/j.ipl.2025.106561_br0030 – volume: 72 start-page: 1346 issue: 8 year: 2006 ident: 10.1016/j.ipl.2025.106561_br0040 article-title: Strong computational lower bounds via parameterized complexity publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2006.04.007 – start-page: 383 year: 2024 ident: 10.1016/j.ipl.2025.106561_br0110 article-title: Conditional lower bounds for sparse parameterized 2-CSP: a streamlined proof – ident: 10.1016/j.ipl.2025.106561_br0100 – volume: 7 start-page: 309 issue: 3 year: 1986 ident: 10.1016/j.ipl.2025.106561_br0200 article-title: Graph minors. II. Algorithmic aspects of tree-width publication-title: J. Algorithms doi: 10.1016/0196-6774(86)90023-4 – start-page: 342 year: 2021 ident: 10.1016/j.ipl.2025.106561_br0180 article-title: Winner determination and strategic control in conditional approval voting – start-page: 294 year: 2008 ident: 10.1016/j.ipl.2025.106561_br0070 article-title: Graph layout problems parameterized by vertex cover – start-page: 304 year: 2020 ident: 10.1016/j.ipl.2025.106561_br0170 article-title: Computational aspects of conditional minisum approval voting in elections with interdependent issues – start-page: 88 year: 2016 ident: 10.1016/j.ipl.2025.106561_br0010 article-title: Conditional and sequential approval voting on combinatorial domains |
| SSID | ssj0006437 |
| Score | 2.4028592 |
| Snippet | This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 106561 |
| Title | On the Tractability Landscape of the Conditional Minisum Approval Voting Rule |
| URI | https://dx.doi.org/10.1016/j.ipl.2025.106561 |
| Volume | 189 |
| WOSCitedRecordID | wos001414372700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0020-0190 databaseCode: AIEXJ dateStart: 19950113 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0006437 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LT9wwELa2wKEXoAUEhSIfeioKynqdOD6uVosK4qVqW-0tshNHCkTJCnZX9Cf0X3cmzgsoEhy4RKs4mbUyn8bj8TczhHwTLDZK-8rxeWwcHrjSURqMofZjNxAD1tdR2bXkXFxeBtOpvO71_ta5MMtM5Hnw8CBn76pquAfKxtTZN6i7EQo34DcoHa6gdri-SvFXlrg4wfQnW4T7z9E5JvQi1ammBIwKPKq2YcALrC6CcXosLw4zOfpdlFzon4vsEU-oylwqATOz-QX4WFYmBDWu-RD5sPM0TtuQe1o0o1jf0Y50-fq2nMEtOrOlbV5ixkPWvnUNK_o9TAo7Oiyy4rnkKmzBvJa31aQRICPO9gptTbHsGFPYrXq2UvszO29DDjfH6QyPj5h33D77uKb2k7WuYSDW5LabEESEKCK0Ij6QVSY8CQZydXg6np41yzqecFq-kJ13fURekgWfzOP_Tk7HcZlskvVqx0GHFimfSM_kn8lG3c2DVsZ9i1xc5RSgQbvAoQ1waJGUox3g0Ao4tAYOtcChCJxt8utkPBn9cKpmG04EO_C5w6TWvs8NV66b-Cro9xXvG6Mx1T6Owc3TzNWcaeFpyZlR4DZL4ydR7CZcBXEy2CEreZGbXUKF8nys4wi-KfqHkQw4HwwSWHeFEUyrPfK9_jrhzNZUCV_Uxx7h9fcLK6fQOnshYOHl17685T_2yccWogdkZX63MF_JWrScp_d3hxUQ_gHBfYQg |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+the+Tractability+Landscape+of+the+Conditional+Minisum+Approval+Voting+Rule&rft.jtitle=Information+processing+letters&rft.au=Amanatidis%2C+Georgios&rft.au=Lampis%2C+Michael&rft.au=Markakis%2C+Evangelos&rft.au=Papasotiropoulos%2C+Georgios&rft.date=2025-03-01&rft.issn=0020-0190&rft.volume=189&rft.spage=106561&rft_id=info:doi/10.1016%2Fj.ipl.2025.106561&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ipl_2025_106561 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0190&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0190&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0190&client=summon |