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According to the 12th Amendment, a majority of "whole number of Electors appointed" is needed to elect a US President or Vice President, or else it's thrown into a contingent election by the House (for President) or Senate (for Vice President).

Under 3 USC 15, when counting electoral votes in the joint session of Congress, an objection to a state's electoral votes can be made by a Representative and a Senator, and then both houses will separately consider the objection. If both houses, acting separately, concurrently decide that the votes are not lawful, those votes are not counted.

In such a case that a state's electoral votes are not counted, does that subtract from the total number of electoral votes of which a majority is needed to elect a President or Vice President? Or is the majority still determined based on the original number of electoral votes (including those not counted)? If the majority is still based on the original number of electoral votes, and the electoral votes that were discarded were needed to put a winning candidate over the half-line, that would mean that once those votes are discarded, no candidate would have a majority, and the election would definitely be thrown to the House and Senate.

Historical precedent doesn't help me here, as the only time electoral votes from a state were thrown out was in the 1872 election, and in that case, it didn't matter -- Grant had a majority of electoral votes based on the original number anyway.

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The 12th Amendment refers to a candidate getting "a majority of the whole number of Electors appointed" (emphasis mine), and so the question will come down to whether the objection is down to the appointment of the Electors, or the votes that they cast.

If the Elector concerned had been appointed legitimately and certified as per 3 USC § 6, but their vote is rejected by Congress, it would not change the fact that the Elector was appointed, and the number of votes required for election would remain unchanged.

If, on the other hand, Congress finds that the Elector concerned had not been appointed legitimately, it is likely that the appointment would be considered null and void, thus reducing the number required for a majority.

The US Archive page for the 1872 election shows 352 Electors were appointed, not including those from Arkansas or Louisiana, with a majority being 177. If their appointments were upheld, a majority would have been 185. It also shows the three votes for Horace Greeley, who was dead at the time, were rejected, but because the Elector himself was properly appointed, the majority required remained at 177.

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