I think you mean Patriarchs, not Patriarchates - Patriarchates are churches, not bishops. The short answer is that a Patriarch is elected by the Holy Synod of their Patriarchate. The Holy Synod can also depose a Patriarch, has the right to accept or decline a Patriarch's resignation (the Holy Synod of Romania for instance, declined to accept Patriarch Teoctist's resignation after the December Revolution) etc. It's therefore up to the Jerusalem Holy Synod whether Irineos is deposed or not. I believe (but really am not sure because of the appalling ignorance of westerners who report on Orthodoxy) that the Holy Synod have indeed deposed him, though I'm not sure if this was done officially or not. If this is the case Irineos should just go, especially as all the other Patriarchs refuse torecognise him.