I think we should ban recounts. Hold an election. Count the votes. Declare a winner. The end. You lost by one vote out 20,000,000 cast? Sucks to be you.
I came to this conclusion the other day as I was reading a book on probability ("The Drunkard's Walk" by Leonard Mlodinow). In it he discusses briefly the 2005 governor's election in Washington. After 2 recounts the Democrat was declared the winner. The first count had the Republican up by 261 votes out of 3,000,000 cast. The second had the Republican up by 41. The third had the Democrat up by 10. Then 700 "lost votes" were found which brought the Democrat up by 129 votes.
In reality, a swing of 399 votes out of three million is little more than statistical noise. Assuming that the first count and all of the recounts are done scrupulously and impartially, then there is no reason to think that any of the recounts is more accurate than the first count. All counts of large numbers are approximate.
In the modern world, however, there is actually reason to think that recounts may be less accurate than the original count. Since 2000, at least, both sides "lawyer up" for recounts. Ballots are found, ballots are disqualified. Local and state elected officials must make decisions, giving rise to the real threat of partisan tampering. lawyers for a campaign will argue with a straight face that certain ballots from areas dominated by the opposing party should not be counted while identical ballots from their strongholds should be. Tempers rise and accusations come from both parties that the other party is trying to steal the election. The final result may well be governed by which side had the better lawyers and the partisan sympathies of state and local officials (including judges.) One thing is certain though, bitterness will ensue.
I see two alternate possibilities. The first is to call any contest within certain statistical parameters a tie and settle the election by random means. (Preferably Bear, Ninja, Cowboy). The downside here, is that the party that had the "most" votes will feel cheated. The second is just accept the result. Since in very close elections who actually has the most votes is a random matter, there really is no need to add another random test. Just declare the person who had the most votes the winner and move on.