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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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    I scanned the record from the 1872 count yesterday and didn't see any evidence that the question of the validity of the electors' appointment as opposed to the validity of their votes was considered. That distinction could be significant to this question. Furthermore, even an invalid appointment could arguably be different from a failure to appoint in the first place (although a failure to appoint altogether would not fall under congress "discarding" votes as contemplated in this question).
    – phoog
    Dec 12 '20 at 16:04
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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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    Link to the "US Archive page for the 1872 election" redirects to a general page. Nowadays, it doesn't show what is claimed. (Note: I don't say the claim is invalid, just that the link doesn't support it anymore)
    – Sjoerd
    Dec 11 '20 at 20:50
  • It is clear from the answer of @RickSmith that there is (was?) an error in the US Archive data.
    – user
    Dec 12 '20 at 22:09
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If Congress discards a state's electoral votes, does it change the number needed for a majority?

In the 1872 presidential election, the discarded votes of Arkansas and Louisiana were counted to determine the majority. In cases where the vote was "not given" by an elector, the total was reduced and the majority adjusted to reflect that reduction.

From the Congressional Research Service report, Counting Electoral Votes: An Overview of Procedures at the Joint Session, Including Objections by Members of Congress, Updated November 15, 2016.

The Majority Required for Election

The 12th Amendment requires the winning candidate to receive “a majority of the whole number of Electors appointed.” That number normally becomes the same as a majority of the number of electoral votes counted by the tellers.

One exception that has been identified occurred in 1873 when the Vice President announced that President Ulysses S. Grant had received “a majority of the whole number of electoral votes,” even though he also indicated that not all of those electoral votes had been counted. In that case, the two houses, under procedures similar to those described below, had decided not to count the electoral votes from Arkansas and Louisiana. Nonetheless, the number of electoral votes allocated to Arkansas and Louisiana evidently were included in “the whole number of electoral votes” for purposes of determining whether President Grant had received the majority required for election.8 It should be noted that President Grant was victorious by whichever standard was used. He received 286 electoral votes out of the 352 electoral votes counted, or out of the potential 364 electoral votes (if the contested votes from Arkansas and Louisiana were included in the whole number).

In 1865, by contrast, only two of the three Nevada electors cast their electoral votes. In the joint session, only two Nevada votes were counted and included in the “whole number of electoral votes.”9 Similar instances of votes “not given” by electors not being included in the “whole number” of electors reported, thus reducing the so-called denominator and the “majority” needed to elect, occurred in 1809, 1813, and 1817.

We are not aware of instances in which this issue has become a source of contention or was determinative of which candidate was elected. If electoral votes from a state or the District of Columbia were not available to be counted during the joint session (and if the question were raised in a timely fashion), the joint session might be called upon to address the effect of this situation on what number of votes would constitute the “majority of the whole number of Electors appointed.”

——
8Congressional Globe, vol. 46 (February 12, 1873), pp. 1305-1306.
9Congressional Globe, vol. 35, February 8, 1865, pp. 668-669

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