Well, the clock ran out on the recounts, so it's all over now, baby blue. With all the yappery about "counting every vote" and "disenfranchisement of Florida" and equal protetction, I think it's important to disambiguate just what a further recount would have and wouldn't have accomplished. Precisely what did our country lose as a result of this weekend's legal buffoonery?

We count ballots because our system for choosing a President gives each state a certain number of electoral votes, and most states choose to give their electoral votes as a bloc to that candidate preferred by a plurality of their inhabitants. This is the American system as it currently exists, and this system requires that we actually figure out, within each state, who is the most-often preferred candidate. We make this determination by having each person record their preference on a ballot, and then counting up the ballots. Unfortunately, this count may not accurately reflect the numerical preferences of the population, for various reasons.

The zeroth reason that a count may not reflect the will of a majority is that not every person is allowed to vote or chooses to vote. Children, resident aliens, convicted felons, and citizens who have failed to register far enough in advance of the election are all barred from voting. Further, many of those eligible to vote do not. In the U.S., we have decided that the will of the ineligible and non-voting should not count, and so we collectively agree that this kind of "error" is no error at all. Our democracy is based on the will of a plurality of those eligible voters who choose to cast a ballot, and relatively few people object to this restriction.

The first real source of error in an election is that not every voter who attempts to vote succeeds in carrying out their intention. The vote of every African-American voter turned away from the polls for not having two forms of ID falls in this category, so does that of every member of the armed forces whose ballot was lost by the Post Office. In this category, too, we must place the votes of those tricked into voting for Buchanan by the butterfly ballot and the votes of every voter who wrote "I vote for George Bush" on their ballot instead of punching through the chad next to his name. Votes in this category will consistently be miscounted (or not counted at all), across any number of recounts, regardless of the technology or methodology used. [Note also that some of these skews between voter intention and recorded vote result in an "illegal" vote, whereas others result in a "legal" one that will be miscounted. I think this is a false distinction, in that in either case what will be counted is not what the voter meant by their attempt to vote.]

The second source of error is that some ballots may have been correctly executed and correctly counted at least once, but some subsequent error causes irreparable damage in such a way that any further recount will produce the same erroneous interpretation of them. If the handling involved in a manual recount of a perfectly ordinary vote were to fully detatch a second chad, that ballot would become -- permanently and incorrectly -- an illegal overvote. This case is the real screw case for counting boards, since it is a result of their actions and is intrinsically uncorrectable. It is also the case on which the Bush attorneys focused most strongly.

The third source of error in any counting process is that different counting technology or methodology will produce different results. Votematic machines will consistently fail to count half-detatched chads, although almost any method for a manual count will count them. Even within a manual recount, a standard that counts pregnant chads will consistently produce different results than a standard that does not. This counts as "error" in that the results are sensitive to the standards for measurement, but those standards have very little to do with the intent of the voter and a great deal to do with the physical artifact of the ballot. These technique-sensitive differences cause a systemic error, in that the error caused by repeatedly using the "wrong" standard will appear identically in every recount using that standard. You can't fix an unfair method by repeating it: this was the argument most strongly used by the Gore camp during the various state-level lawsuits, and they focused most of their efforts on errors in this category.

The fourth, final, and most disturbing category of counting errors is that two counts conducted according to identical methodology will still differ, due to purely random factors, the unforgiving laws of probability. and human and mechanical imperfection. Such errors are a stochastic component to the measurement error, a threshold of accuracy beneath which no count's resolving power should be trusted. This is the sense in which machine counts are highly "accurate:" two successive machine counts are likely to agree with each other more closely than two successive hand counts. Even still, on fringe cases, the machines will disagree with themselves sometimes.

If your election is riddled with errors in categories one and two, you're kind of stuck with them. Errors of the first kind are variously easy and difficult to allege and to prove, but impossible to correct, short of a revote. Errors of the the second kind are detectable only circumstantially and in the aggregate, and are equally impossible to undo. The physical evidence that might allow for remedial action simply doesn't exist. I think there were pretty substantial errors of the first kind in Florida, but probably very few errors of the second kind. The Bush camp alleges exactly the opposite (although their argument largely collapses under even the most minimal statistical treatment). Either way, nothing much is going to happen about it, other than Jesse Jackson working the streets overtime to make damn sure it doesn't happen again.

Errors in categories three and four are the more difficult ones, because you can do something about them -- and in Florida, the error bars caused by these sorts of errors were large enough that both "Bush wins" and "Gore wins" fell within the range they defined. It was the fight over errors of the third kind -- you get what you measure for -- that sent the case up to the Supreme Court and back down again twice, without resolution. It is, in theory, a question with a resolution (and to this general claim, almost everyone in the case assented, albeit in variously self-serving ways): someone sets a uniform and fully legitimate standard that we generally agree is a reasonable line to draw. Perhaps that line might even be drawn non-ideologically. One can still dream, no?

No, it's errors in the fourth cateogry that are the truly horrifying ones. There's lots of strong evidence from Florida that the systemic errors inherent to Votematic machine counts are sufficiently high that one is forced into the territory of manual recounts, with their higher stochastic errors. In order to eliminate a few thousand miscounted votes caused by category-three failures to machine-count partially-detatched-chad ballots, one has to deal with the category-four failures of manual recounts, on the order of a difference of perhaps a dozen to a few hundred between successive manual counts. And this is why we're so screwed down in Florida: the margin of victory, quite possibly, is comparable in magnitude to these swings betweeen successive counts.

In the world of statistics, we're looking at a problem of measurement error not entirely unlike thpse faced by pollsters who must declare margins of error on every "measurement" they take of the public mood. You can set up statistical models of the differences between recounts, and extrapolate from the standard deviation of a set of counts of the same set of ballots to estimate the intrinsic variability of such counts, then average across larger and larger numbers of counts until your variance becomes acceptably small. Alternatively, you can model probabilistically the likelihood of an error in each individual ballot examiniation, and from this model compute the expected variability in successive recounts, and then compute the number of recounts needed to bring that variability down.

You see the problem, though. It's the tradeoff between accuracy and confidence. Statistics can tell us, given some set of recounts, what the probability is that the "winner" they name really does have more votes (ignoring, for the moment, any of the first three kinds of errors). Usually, for most normal elections, when that set contains exactly one count, we can reject the null hypothesis (the other guy won) with extremely high probability. The odds that Bush really won the national popular vote (but random fluctuations in the counting made it seem that Gore won) are microscopic. Given that we routinely accept as ironclad the margins of error from polls with 95% chance of being correct to their stated accuracy, it's extremely safe to say that Gore won the national popular vote. There's so much numerical leeway on the accuracy that we can have excellent confidence. In Florida, though, the error band around the one (partial) manual count that's been conducted is so large is sufficiently large that we just can't say, with the usual statistical confidence, that Bush really won. He has more votes in this count, it's more likely that he has more votes than Gore, future counts would be more likely to come up for Bush than for Gore, but that's as far as we can go. We just don't have enough evidence, statistically speaking, to call the election. Statistically, it's a tie. To make it otherwise, we need either one really good recount, or a large number of crappy ones.

So, why this excursion into probability? So I can make my real point about the conclusiveness of this election and those fuckheads on the Supreme Court. Bush is to be our next President. Our system has chosen a President. The system works, in the sense that when the gears stopped grinding, one man had won, and it all ran according to the rules laid down in the Constitution, various laws, and courts' interpretations of those laws. A definitive winner, a peaceful transfer of power, a concession from the loser. System working as designed.

What has failed in this case -- what the Supreme Court consigned to failure -- is our electoral system's claim to select the candidate who receives the majority of votes cast in enough states to provide a majority of electoral votes. The bizzare cut-off in Florida has left us without the necessary evidence to safely conclude that Bush got more votes there than Gore. Leave aside the civil rights issues, leave aside the question of the right standards for a count, leave aside the particulars. We don't have even a count that passes a reasonable category-three muster (thanks to the damn 1-2% error rate on the Votematics and their horrid inability to deal with partially-detached chad), let alone one that passes category-four muster.

I say the following as an ardent Gore supporter: there was a best possible result in Florida once the courts started getting involved. That best possible result was a statewide recount, using machines for most of the ballots and hand-examination of those ballots rejected by the machines. It's entirely possible, indeed I think it likely, that such a count would have produced a result sufficiently far away from a 50-50 perfect split that the winner would be unambiguous.

It also seems likely that that winner would have been Bush, but I think that would have been a far better result than what we wound up with, because such a result would have shown off our system working at a more basic and transparent level than the one that ultimately had to step in. It's one thing for the courts and legislatures to go through their hoops to make the election itself work; it's another thing for them to to through their hoops to make the Rube Goldberg device containing the election work. This is the real travesty of the Supreme Court's decision: they all but admitted that we don't have a conclusive set of results from Florida's vote, but did nothing to help us achieve such results.

Does this make George W. Bush illegitimate? Well, I think he's a bastard, but that's a separate issue. He didn't march into D.C. with guns and jackboots; everything was carried out according to Hoyle, in the sense that the Supreme Court signed off on the recount that might have changed the certified totals and the electors will vote and Congress will accept those votes and he'll be duly and properly sworn in. He's not illegitimate; but the simplified "system" of popular-vote-for-electors is, in the sense that it didn't work as specified and can't be trusted to. These last five weeks haven't materially affected my opinion of him or how he ought to be treated. He's acted like an overpriveleged shit, but well, we knew that much already. This whole mess doesn't make him any less President.

Does this make the Supreme Court illegitimate? I don't even think that question is meaningful. I think that Scalia and company are stupid and unimaginative for drafting such a manifestly dumb opinion; I think that O'Connor and Kennedy are craven for not facing up to the issues and for that messy per curiam business. Partisan? Yeah, but that doesn't make them not the Supreme Court. Come on. Reagan appointed Scalia because Scalia has certain opinions, not the other way around. Really. Where this "hurts" the "institution" of the Supreme Court in my playbook is that the 5-4 division is so much more apparent and its consequences so much more severe that I'm going to be pressuring the Senate Democrats to fight tooth and nail for centrist appointments. Which means more fighting over appointments, but jeez, like this is supposed to be any more delegitimizing than the confirmation fights over Bork and Thomas?

Does this make Al Gore illegitimate? If he'd conclusively lost, maybe it would have terminated his political career, a possibility we can only sit back and hope for now. Perhaps once he isn't running for President, he'll go back to fighting for the environment. One is still allowed to hope that something useful may come out of this whole mess.