Justified representation: Difference between revisions
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Sorry this is a bit of a work in progress. Need to transfer from linked papers |
Sorry this is a bit of a work in progress. Need to transfer from linked papers |
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[[File:Justified Representation.png|thumb]] |
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==Justified representation== |
==Justified representation== |
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| [[w:Sequential_proportional_approval_voting|Sequential Proportional Approval Voting]] || No || No || No || in P |
| [[w:Sequential_proportional_approval_voting|Sequential Proportional Approval Voting]] || No || No || No || in P |
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| [[Ebert's Method]] || Yes|| No || No || NP-hard |
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| [[Sequential Phragmen]] || Yes|| No || Yes|| in P |
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| Example || Example || Example || Example || Example |
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| Example || Example || Example || Example || Example |
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==Comparison== |
==Comparison== |
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Every winner set that provides [[Perfect representation]] also provides [[Justified representation | Proportional Justified Representation ]] <ref> https://www.researchgate.net/publication/308022665_Some_Notes_on_Justified_Representation </ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>https://arxiv.org/abs/1407.8269</ref> It is easily seen that PJR is a weaker requirement than EJR, and a stronger one than JR |
Every winner set that provides [[Perfect representation]] also provides [[Justified representation | Proportional Justified Representation ]] <ref> https://www.researchgate.net/publication/308022665_Some_Notes_on_Justified_Representation </ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>https://arxiv.org/abs/1407.8269</ref> It is easily seen that PJR is a weaker requirement than EJR, and a stronger one than JR. A method satisfying EJR also satisfies PJR, and that a method satisfying PJR also satisfies JR. |
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The following |
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==References== |
==References== |
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Revision as of 18:33, 8 January 2020
Sorry this is a bit of a work in progress. Need to transfer from linked papers
Justified representation
In linked papers. Need to sort out how to do formatting
Extended Justified Representation
In linked papers. Need to sort out how to do formatting
Proportional Justified Representation
In linked papers. Need to sort out how to do formatting
Compliant systems
| System | JR | EJR | PJR | Coplexity |
|---|---|---|---|---|
| Proportional approval voting | Yes | Yes | ?? | NP-hard |
| Sequential Proportional Approval Voting | No | No | No | in P |
| Ebert's Method | Yes | No | No | NP-hard |
| Sequential Phragmen | Yes | No | Yes | in P |
Comparison
Every winner set that provides Perfect representation also provides Proportional Justified Representation [1]. In contrast, Extended Justified Representation may rule out all winner sets that provide perfect representation. [2] It is easily seen that PJR is a weaker requirement than EJR, and a stronger one than JR. A method satisfying EJR also satisfies PJR, and that a method satisfying PJR also satisfies JR. The following