Despite its problems as being demonstrated in Minnesota, I think the way it's done now is still the right way to do it.
That said, here is an interesting alternative. The vote totals are merely used to determine probability weights for a "coin flip" that determines the election. The advantage of this idea is that the coin flip may be done in one place under the scrutiny of many election observers. Using cryptographic random number generators for the "coin", the process might even be made secure. In contrast to the current system where voter fraud of a hundred votes anywhere in the state (a tremendous area for election monitors to monitor) can decide a close election, such fraud only buys a little bit of advantage in the coin flip.
The scheme I propose is that the vote totals determine the weights of a coin. For example, if 49 votes are cast for candidate A, and 51 for B, then we use a coin biased 49%-51%. We flip this coin a number of times equal to the number of total actual votes cast, in this case, flip it 100 times. Then, count who gets more coin flips in their favor.
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