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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==
Every winner set that provides [[Perfect representation]] also provides [[Justified representation | Proportional Justified Representation ]]<ref> {{Cite|authors=Luiscite Sánchezweb | last=Fernández, University| Carlosfirst=Sánchez III| delast2=García Madrid;| Norbertofirst2=Fernández Fernandez,| Defenselast3=Fisteus University| Centerfirst3=Arias at| thelast4=Val Spanish| Navalfirst4=Basanta Academy;| Jesustitle=Some Ariasnotes Fisteus,on Universityjustified Carlosrepresentation III| de Madrid; Pablo Basantawebsite=e-Val,Archivo UniversityPrincipal Carlos| III de Madrid|date=|year=2016-06-14 |title=Some Notes on Justified Representation|url=https://wwwe-archivo.researchgateuc3m.netes/publicationhandle/308022665_Some_Notes_on_Justified_Representation|conference=10th10016/25680 Multidisciplinary Workshop on Advances in Preference Handling|location=New York, USA|volumeaccess-date=|pages=|via=[[ResearchGate]]2022-04-30}} </ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>{{Cite journalarXiv|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|urleprint=http://arxiv.org/abs/1407.8269|journalclass=arXiv:1407cs.8269 [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.
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