but in case there shall arise the question which of two or more of such State authorities determining what electors have been appointed, as mentioned in section 5 of this title, is the lawful tribunal of such State, the votes regularly given of those electors, and those only, of such State shall be counted whose title as electors the two Houses, acting separately, shall concurrently decide is supported by the decision of such State so authorized by its law; and in such case of more than one return or paper purporting to be a return from a State, if there shall have been no such determination of the question in the State aforesaid, then those votes, and those only, shall be counted which the two Houses shall concurrently decide were cast by lawful electors appointed in accordance with the laws of the State, unless the two Houses, acting separately, shall concurrently decide such votes not to be the lawful votes of the legally appointed electors of such State. But if the two Houses shall disagree in respect of the counting of such votes, then, and in that case, the votes of the electors whose appointment shall have been certified by the executive of the State, under the seal thereof, shall be counted. When the two Houses have voted, they shall immediately again meet, and the presiding officer shall then announce the decision of the questions submitted.