In the last Washington State Governor's race, we had a similar condition, where the margin of victory was well within the margin of error. It seems that in such case, the only way to determine the actual will of the people is to do a re-vote.

Unfortunately, whatever candidate was ahead a any point in time would say "it's time to just move on".

I'm afraid that too many people don't get the concept of "margin of error" and will insist on getting a count that 100% accurate (instead of merely 99% or something).

While appealingly efficient, I don't think this is sound practice. "In the margin of error" does not mean that it's a 50/50 tossup. But you're usually pretty accurate, so what am I missing?

A coin flip is simple, decisive, and immune to political machinations. A proper probability estimate is not.

Further, if you truly believe in democracy, then a candidate with 49.9999% of the vote is probably nearly as good as one with 50.0001%, right? So the cost of an error is low as well.

OK, that seems reasonable as long as one is certain that it's 49.9999% rather than a loose standard of "pretty close". What you wouldn't want is to make possible for the clear loser in a 48% - 52% race to demand a coin toss. Or maybe you do: by the precepts of your argument, maybe that would be fine.

I'm uneasy with the random approach suggested by the article for fear that a truly crazy candidate might win the lottery, but I'd be good with having all the candidates above some large baseline (say, 30% of the vote) get a proportional shot at the win. I think I'd probably want it to be proportional to the counted share even if there is a margin of error, though.

I'd advocate calculating the statistical margin of error [1] before the election (which might, in fact, be +/-2% if the election is small enough) and doing the coin flip if it's within that margin.

[1] Technically margin_of_error(votes_cast).