I disagree with the comment “that the process is playing out in an reasonably fair way.” Months have been wasted in the clawing for straws. Is the desired position so casual that the incumbent can spend months totally dedicated to staying in office? Is it possible that some duties have been delayed or ignored that define the functions of the position?
Also, the contention between the opposing camps is nothing but exacerbated. Reducing the likelihood for future compromise.

Besides, I think your list of election objectives unfairly excluded a point that I would personally wish were at its forefront: “choosing the socially optimal candidate” (that is, let’s say, one who would implement the best policies), and, to be frank, I do not think that that objective is being met at all, except sometimes by chance.
Forgive me while I drift further off-topic, but, perhaps the real option that should be considered is a radical change in the system as a whole instead of a minor tweak. And, in breaking with the somewhat pervasive formality and thoughtfulness of this discussion thread, I move for a declaration of me as dictator. I promise I’ll be benevolent.

Also, I did not mean to speak ill of statistical methods; I’m a believer in statistics, too. I’m also a mechanical engineer, though, and my comments were written from the perspective of improving the fidelity of the voting system.

Statistics are good for analyzing the will of a population; but it should not require analysis to determine the will of an individual voter. The machines are not measuring devices, they are congnitively controlled discreet-input devices. The designers should therefore hold themselves to a very high standard of accuracy in the mechanical functioning of the system.

I also took some of the same economics and math classes. There are lots of ways to use statistics to analyze the problem. There are also lots of alternate voting mechanisms which may be improvements over the current standards. Like alcatholic I like Instant Runoff voting but it introduces a new level of vote tracking (the reassignment of votes) that I understand haven’t been well-implemented in the few locales that have tried it so far.

But back to the reality of deciding an election. The standard for winning isn’t statistics. It’s greatest number of votes. 1,250,001 wins over 1,250,000.

I know that’s a daunting goal in a world of imperfect ballots and election machinery. Acknowledging those imperfections, it should be remembered that voting devices are not the same as scientific detectors (which are trying to detect the state of a system without disturbing it). These are input-and-recording devices which are (supposed) to log a single unambiguous response (write-ins add some complications). From a machine-design standpoint, it should be possible to apply high-standard methodologies like six sigma to get a very low vote-logging failure rate. Likewise the transfer of votes from the voting stations to the central counting location.

(I’d also like to put in a word for the importance of transparency of the vote counting software. Nothing in the process should be hidden.)

Naturally, reality won’t approach the high-tolerance vote counting goal even if the machines are well designed because humans are imperfect. Some will have comprehension problems, and some have physical difficulties (imagine trying to vote with advanced Parkinson’s). Allowances for assistance won’t always be heeded.

It is possible that 21st century technology may eventually step in to help with human imperfection. If Stephen Hawking can communicate with a computer, the folks in the nursing home should be (eventually!) be able to get there votes into a voting machine. Making that level of interface reliable and affordable is one of the technical challenges for this century.

For a vote where the candidates get roughly 1 million votes each, every 100 votes of margin translates to about a negligible three days out of a six year term. It wouldn’t be worth fighting for.

I continue to agree with you that legitmacy of the result in a close election is a paramount consideration.

Based on this discussion, I’m leaning to this idea;
If the election is within the tie confidence interval, the outcome should be to elect the challenger candidate. If, after a full term of office, you can’t get better than a tie vote, change should be the favored outcome.

Not sure whether or not I would want this to apply at the presidential level, where the stakes domestically and internationally are at the maximum.

(The old rule for classic-chess world championships was that ties went to the incumbent. That had the unfortunate consequence that incumbents tended to play very conservatively, hoping to force challengers to play very risky approaches with a higher risk of losing games.)

The intent of either the coin flip, or my suggestion of a revote, is not to prevent or obviate recounts, or even the legal contest of close votes. These would still be carried out to their end (thought perhaps not the bitter end of an endless legal contest) in order to arrive at the vote difference that would count in determining if a revote, or coin flip, is necessary.

The intent of the revote for elections so close that the vote difference is smaller than the counting and tallying variance, is to prevent elections being decided essentially ex post facto, on the basis of counting or n0t counting unforeseen classes of vote so small that no pre-existing rules unambiguously cover them. You have to finish an election under the same rules you started it with for it to carry legitimacy. But if you get out your electron microscope, you can find tiny packets of votes that you can’t honestly categorize as valid or invalid under the rules you started with. In races where such tiny packets of votes matter, whether the court ends up counting such packets or rejecting them, either way, it has advanced the case law on the subject by making up new law to cover such unforeseen cases. So I say, let the courts have at that process of creating new law. But let’s not let this election be decided by the courts on the basis of new law. If the result is so close that you need that microscope to discern the winner, if the winner needs some new judgment on vote validity to squeek past his opponent, then you just do the election over again until you have a difference large enough that it does not rest on unforeseen classes of disputed votes.

I see in your objection raising the infinite regress, that would apply to coin tosses as well as revotes for close results, that you have studied Zeno the Eleatic and his paradoxes. Whatever assessment of the reality status of apparent change the Zenonic paradoxes might be thought to force us to, I think that, for revotes or coin flips, a simple legislative fiat would suffice to decide results contested as close to the revote (or coin flip) confidence limit. The law would say they go to revote unless the courts are through with the contest by a certain date after the election.