Instant runoff takes care of that concern.
How is that going to work? Revote every day or just every Tuesday until somebody wins? Who prepares the new ballot and reprograms the voting machines? How much paid time off from work should people be granted to go vote? Should there be a floor on voting participation else the vote doesn't count? Could I think of at least 3 or 4 more objections?
Instant runoff is simple, you get a list of candidates, and you rank them in your order of preference.
In the event that in the first pass a candidate gets a majority vote, no actual second "runoff" is required.
If nobody gets to 50%+1 in the first pass, then the candidate with the least number of votes is eliminated. The people who voted for that candidate then have their ballots re-tabulated based on their #2 pick. Rinse and repeat eliminating each successively more popular candidate(working up from the bottom) until somebody crosses the 50% threshold.
Thanks to the wonder of technology, this is something that can be computerized and automated easily enough, and still leave a paper trail behind.

Not quite sure how IR would handle an edge case where say, you have 6 candidates, and somebody only ranked 4 of them, and none of those 4 were the most popular candidates if it makes it down to the final 2 in order to cross 50%+1 vote. I'd assume a non-selection would turn their vote into a non-vote of sorts at that point. (It would still appear in the tallies for the eariler rounds, but not count towards the final round(s) should they have chosen strangely. But I have no idea if that edge case is addressed, and too lazy to check)
Although it should be noted, since I like the Electoral College, I'd only support this application on the state level.
Doing some checking against this election, it is a safe bet that Colorado would have comfortably flipped from Hillary to Trump.
Maine is admittedly questionable, but likely to have gone majority Trump under IR rules, assuming 100% of the libertarian vote went Republican before going Democrat, if it was only 98% of them who did so, Hillary would win. (Maine went for Hillary, except for 1 district which Trump carried)
Pennsylvania and Wisconsin would have likely remained Trump wins. So those "upsets" would stand.
Michigan would have likely been an even more comfortable Trump win. (Trump had 47.5% of the vote, the Libertarians had 3.6% of the vote, giving a combined 51.1% of the vote. Although he'd still need just barely under 70% of Libertarian voters in Michigan to have picked him over Hillary under IR)
Minnesota is also a close one to call under an IR scenario. A combined Trump/Libertarian/McMullin IR tally would net Trump an additional 5.6% of the vote, boosting his tally to 50.5% of the vote from 44.9% assuming no "Democratic defectors" in the mix(Trump would need to keep 92% of the Libertarian&McMullin voters from selecting Hillary ahead of him. Of course, Hillary would need to likewise not suffer from the people who didn't vote for one those three options voting for Trump over her, as she only netted 46.4% herself), but it is another potential Electoral flip in Trump's favor.
Nevada would actually be an edge case for the IR system. 2.56% of the voters evidently opted for "None of these candidates" as their choice. Hillary had 47.92% of the vote, Trump had 45.50% of the vote, and the Libertarians netted 3.32% of the vote. Assuming a 100% transition from Libertarian to Trump, however unlikely that is, neither candidate would make it 50% of the vote. Although Trump would potentially have Majority support in Nevada at 48.82%.
New Mexico looks like it would likely be an edge case as well(Trump at 49.38% once combined with the Libertarians, McMullin voters could bring him to 50.11% in theory, but requires "0 defectors" to Hillary) while Hillary would hold 49.5% once combined with the Green Party), so New Mexico becomes a possible flip.
Virginia likely remains in Hillary's hands with her getting 49.75% and the Green party getting 0.69% of the vote, making an IR tally of 50.44%.
New Hampshire is a likely electoral flip, a combined Trump/Libertarian IR tally getting him 51.5% of the vote. C/o the Libertarians holding 4.2% of the popular vote there.
Arizona, Florida, and Utah would also likely remain in Trump's hands.
Before someone blinks too much at the number of states that seem to suddenly "turn red" under a potential IR scenario for this past election where "Hillary won the popular vote." Keep this in mind:
As per Wikipedia as of this writing:
Hillary: 65,844,610 votes, 48.06%
Trump: 62,979,636 votes, 45.97%
Libertarian: 4,488,912 votes, 3.28%
Green: 1,457,038 votes, 1.06%
McMullin: 725,902 votes, 0.53%
Other: 1,549,765 votes, 1.13%
So going with the IR scenario of:
Hillary/Green we net 66,301,648 votes cast. For 49.12% of the vote.
Trump/Libertarian we net 67,468,548 votes cast. For 49.25% of the vote.
Trump/Libertarian/McMullin we net 68,194,450 votes cast. 49.78% of the vote.
Which means getting to 50% of the popular vote would require digging into the 20-someodd presidential tickets that ran across the nation and deciding which constituency would be likely to split which way, if any.
But for the Democrats bellyaching about the EC this time around, the above tally of the national polls are something to take note of. Hillary may have won a simple Plurality of the popular vote, but she didn't win a clear majority. Likewise, based on where many of the other votes went, it's highly unlikely most of the people who did vote, would have ever voted for her. The only question is if all those third party voters would have gone for Trump or Hillary if they actually had to make that choice.