It's become a ritual of our democracy that when the outcome is close, each side usually accuses the other of trying to steal the election. In some cases, it's obvious that we should double-check the count. Our mantra is, as it should be, to make sure every ballot is counted fairly and accurately. It's a noble democratic goal. The trouble is, we don't know how to accomplish it.

Seriously.

We've been counting objects since we were toddlers playing with blocks, and we ought to be pretty good at it. We're not — at least when we're counting ballots. The tally from election night (what cognoscenti have come to call the —preliminary— count) is almost certainly wrong. Let's be very clear about that. Counting errors are a given, no matter what system is used. We humans miscount paper ballots, but machines aren't much better. Ballots get mangled, they stick to each other, they get counted twice or not at all. So we count again. Of course we do. The trouble is that the recount — known as the —official— or the —certified— count — is also almost certainly wrong.

It's true that recounts are often more careful than the preliminary tallies, but the complicated systems for checking ballots can themselves lead to potential errors. In one commonly used method, four auditors work together. The first reads the ballot aloud, the second checks to be sure the ballot has been read correctly, and the other two keep a hand count, pausing at regular intervals to be sure they are in sync. Other systems involve three auditors per ballot, or two, but no matter which we choose, it's easy to imagine the count getting tangled.

And that's exactly what the research suggests will happen. A widely cited study of New Mexico's 2006 election found that machine counts and hand counts of the same ballots differed enormously, with agreement ranging from just above 50 percent to just below 80 percent — meaning that even in the best case, there was disagreement more than 20 percent of the time. The study also found that successive hand counts of the same ballots usually yield differing results.

This isn't to say that either count is —right— — only that they differ. But let's not leap to the conclusion that partisanship or corruption are to blame for the errors. Laboratory tests in which subjects tabulate ballots bearing the names of imaginary candidates without party identification also show high rates of disagreement about the number of votes for each.

All of which is to say that we might never be able to get the correct count — if by —correct— we mean true and accurate totals of the number of ballots actually cast for each candidate. In other words, the second, —official— tabulation doesn't give us the true numbers; it just gives us different numbers.

But of course we'll keep doing recounts. We have to. Suppose that on Election Day, state officials announce that my candidate lost. If there's no recount, the chances of my side winning are exactly zero. Now add a recount. Here the research is unclear, but let's suppose the odds are overwhelmingly against the recount changing the result. I won't care about that. All that's necessary to make the recount worthwhile from my point of view is that there be a non-trivial possibility that the result will flip. When the margin of victory is less than 0.5 percent, research tells us that there is indeed a nontrivial probability that the official count will change the result. We just don't know what the probability is.

But as long as the probability is nontrivial, the precise figure hardly matters. Suppose it turns out that, say, 95 percent of recounts produce the same winner announced on Election Day. This figure sounds quite overwhelming, until we realize that if the count is the same in 95 percent of the cases, then in 5 percent of the cases — one out of 20 — the count is different. And a 5 percent chance that my candidate wins is infinitely larger than a zero percent chance. So if my candidate loses a close election, it's entirely rational for me to favor a recount.

We could avoid all of this if we were confident of getting the count right the first time. But we're not. Sure, at the margin there are ways of reducing the error rate. For example, paper ballots are counted more accurately than the old-fashioned lever machines that have almost gone out of use — and also more accurately than many electronic voting machines. No counting method, however, ensures that we will get the right answer when the election is close. We've been counting all our lives but we still mess it up.

In truth, the only solution to the recount problem is not to have such close elections. If the outcome isn't close, we don't have to worry about the errors. We know that they exist, but we're confident that counting again wouldn't change the outcome. Nobody thinks the landslide winner cheated the loser.

But in our deeply divided country, narrow election victories and the attendant suspicion and anger look to be a part of the unruly present and, in the near term, the unruly future. (And, no, it turns out that we can't motivate voters by warning them that the election will be close. Public knowledge that the outcome will be decided by a small percentage seems not to improve turnout.)

So we'll keep doing recounts, and with good reason. Let's not kid ourselves, however. Let's be very clear about the two things that will always happen as a result.

We won't ever satisfy the partisans whose candidate loses the second time around; they'll believe to their dying day that the election was stolen by the other party. In a close election, we'll never really know who —really— won. We'll just know that the second, error-filled count decided. We can certainly decide to make a rule holding that this second count is the official one. But let's not delude ourselves into believing that we're going to get the numbers right. Because we're not.

Stephen L. Carter is the William Nelson Cromwell Professor of Law at Yale, where he has taught since 1982. Among his courses are law and religion, the ethics of war, contracts, evidence, and professional responsibility. His most recent book is The Violence of Peace: America's Wars in the Age of Obama (2011). He is an author and Bloomberg View columnist.