Point of information: In 33 states + DC, laws require that the counting of votes be audited no matter what the results were. The remedy, if discrepancies are found in a sample audit, is usually a recount, though the scopes and types of those recounts vary. (Yay federalism.)
The hypothetical is interesting, though completely implausible (sorry). I think there are three broad categories of response that I’ll call “bureaucratic,” “political,” and "non-governmental." These names are probably lazy and bad, but here’s what I mean…
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By “bureaucratic” I mean actions taken by government officials under whose purview potential election-related crimes would fall: secretaries of state, registrars of voters, various law enforcement agencies, and the like. I would absolutely expect investigations by many of those officials and agencies in this scenario; they already investigate allegations of election crime – most of which come to naught, but it’s their job, so they do it.
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But legislators at all levels (yay federalism) have the power to conduct investigations, and in these cases it’s going to be a political question, resolved politically, based on the balance of power within each chamber of Congress/state leg/county board/whatever. And, of course, on the specific character/situation/ambition of every legislator who gets to vote on whether to investigate.
I would expect that in the OP’s hypothetical, relatively few elected Republicans would sign on to investigations – sorry, Republican fans, but recent behavior by your legislators makes this a safe inference, IMHO.
Swap the parties, and I’m much less sure about what would happen; “count every vote, even if we lose thereby” has been Democratic rhetoric in contested elections since at least 2000, and I imagine there would be intra- and extra-party pressure to hold them to that. Would that pressure work? Are Democratic legislators more likely to stick to principle before party?
- And of course we have non-governmental institutions that would investigate the election. Media organizations, natch. Also various think tanks and public advocacy groups. The goo-goos (good-government types).
One last point: basically, all of the solutions to any finding of malfeasance in this situation are political – right? Here are some I can think of, details varying by state (yay federalism):
- state legislatures overriding vote counts
- pressure on EC electors to be faithless
- Congress refusing to ratify EC results, taking election to House/Senate
- post-inauguration, impeachment and removal.
The lack of an apolitical solution ultimately means that all investigations are highly prone to politicization. For this reason, the chances of developing a fact-based, bipartisan consensus on what, if anything, went wrong would, IMHO, be pretty low.