Justified representation: Difference between revisions

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==Implications==

While [[approval voting]] is strategy-proof for voters with dichotomous preferences, every method passing justified representation is susceptible to strategic voting, even in this setting. <ref>{{cite arXiv | last=Peters | first=Dominik | title=Proportionality and Strategyproofness in Multiwinner Elections|eprint=2104.08594|class=cs.GT| date=2021-04-17}}</ref>
==Comparison==
==Comparison==


Every winner set that provides [[Perfect representation]] also provides [[Justified representation | Proportional Justified Representation ]]<ref> {{Cite|authors=Luis Sánchez Fernández, University Carlos III de Madrid; Norberto Fernandez, Defense University Center at the Spanish Naval Academy; Jesus Arias Fisteus, University Carlos III de Madrid; Pablo Basanta-Val, University Carlos III de Madrid|date=|year=2016|title=Some Notes on Justified Representation|url=https://www.researchgate.net/publication/308022665_Some_Notes_on_Justified_Representation|conference=10th Multidisciplinary Workshop on Advances in Preference Handling|location=New York, USA|volume=|pages=|via=[[ResearchGate]]}} </ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>{{Cite journal|last=Aziz|first=Haris|last2=Brill|first2=Markus|last3=Conitzer|first3=Vincent|last4=Elkind|first4=Edith|last5=Freeman|first5=Rupert|last6=Walsh|first6=Toby|date=2016-09-11|title=Justified Representation in Approval-Based Committee Voting|url=http://arxiv.org/abs/1407.8269|journal=arXiv:1407.8269 [cs]}}</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.
Every winner set that provides [[Perfect representation]] also provides [[Justified representation | Proportional Justified Representation ]]<ref>{{cite web | last=Fernández | first=Sánchez | last2=García | first2=Fernández | last3=Fisteus | first3=Arias | last4=Val | first4=Basanta | title=Some notes on justified representation | website=e-Archivo Principal | date=2016-06-14 | url=https://e-archivo.uc3m.es/handle/10016/25680 | access-date=2022-04-30}}</ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>{{Cite arXiv|last=Aziz|first=Haris|last2=Brill|first2=Markus|last3=Conitzer|first3=Vincent|last4=Elkind|first4=Edith|last5=Freeman|first5=Rupert|last6=Walsh|first6=Toby|date=2016-09-11|title=Justified Representation in Approval-Based Committee Voting|eprint=1407.8269|class=cs.MA}}</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.


Even though Justified representation may appear to be similar to [[Stable Winner Set | core stability]], it is, in fact, a strictly weaker condition. Indeed, the core stability condition appears to be too demanding, as no known voting system is guaranteed to produce a core stable outcome, even when the core is known to be non-empty.
Even though Justified representation may appear to be similar to [[Stable Winner Set | core stability]], it is, in fact, a strictly weaker condition. Indeed, the core stability condition appears to be too demanding, as no known voting system is guaranteed to produce a core stable outcome, even when the core is known to be non-empty.
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