A small, obvious, mathematical observation about the prospect of a "brokered" Democratic convention:

It won't happen because it virtually can't happen if by "brokered" you mean a nomination contest that continues for several ballots at the Denver convention while the party bigwigs make deals in smoke-filled rooms. (Of course, in the modern case, there would be no smoke in the rooms anyway.)

There are only two candidates.

The rules require only 50 percent plus one to secure the nomination. Unless you have a significant number of delegates not voting, or voting for a candidate other than Sens. Clinton or Obama, someone will have a majority on the first ballot. Do the math.

If you don't want to listen to me gas on about the old days, when long, multi-ballot, multi-day nomination contests actually were possible and did occur, feel free to bail out here. You have my main point. Second ballot in Denver not likely to happen (although at the bottom, I concede a couple of unlikely scenarios where it could). Fellow history nerds, please read on.

The 103rd ballot
You read that right. The 1924 Democratic convention took 103 ballots before the nomination was awarded to the relatively undistinguished lawyer, former congressman, former ambassador John W. Davis.

The convention was deadlocked during all those ballots between the leading contenders, New York Gov. Al Smith and former Treasury Secretary William Gibbs McAdoo. But note this: On the first ballot, 19 Democrats received votes for the nomination. No one had 40 percent. Davis ran seventh with 2.8 percent of the votes.

Most of the other candidates weren't really candidates at all, but "favorite sons," who had the support and loyalty of all the delegates from their own states and no support from anywhere else. This favorite son practice, which is no longer a factor, was a recipe for a brokered convention. The favorite sons and other state party bosses were in an ideal position to wheel and deal between ballots, offering to drop from the race and deliver their delegations to one of the leaders in exchange for — well, whatever they could negotiate.

The other problem in 1924 was that McAdoo and Smith stood on opposite sides of two huge issues that divided Democrats — booze and the Klan. Smith was a "wet," who opposed Prohibition, and McAdoo was a "dry." The Dems were then, as they had been since before the Civil War, the more racist of the major parties.

The Ku Klux Klan had a significant following and backed McAdoo, who never rejected their support. An effort by Smith backers to get a statement into the platform condemning the Klan was defeated by a vote of 543 to 542. Because of these two issues, McAdoo was completely unacceptable to Smith supporters and vice versa. The differences between Clinton and Obama backers pale by comparison.

The deadlocked 1924 convention lasted for 16 days. SIXTEEN DAYS. Davis finally nudged into second place on the 100th ballot. McAdoo and Smith realized that neither of them had any chance, withdrew their candidacies, and the party "united" behind Davis on the 103rd ballot, setting by far the record for a marathon convention.

Davis went on to get crushed in the general election by incumbent Republican President Calvin Coolidge. (People sometimes use this case to argue that big fights at the convention lead to losing candidacies, but there's little reason to believe any Democrat was going to beat Coolidge that year.)

The two-thirds rule
Another huge change from then to now is the abolition of the two-thirds rule. At their first-ever nominating convention in 1832 (before that the nominee was chosen by a caucus of party leaders, mostly the parties members of Congress), the Dems adopted a rule requiring a two-thirds vote for the nomination.

It wasn't such a big problem in 1924, because neither Smith nor McAdoo could get even a majority of the delegates, amidst all those favorite sons. But in 1912, the rule had a huge impact that history nerds like me like to know and tell.

New Jersey Gov. Woodrow Wilson (talk about your thin resumes, he never ran for public office before 1909; before that he had been a professor and then president of Princeton University) won the Democratic presidential nomination.

The leader on the early ballots was Speaker of the House James Beauchamp "Champ" Clark of Missouri.  On the ninth ballot, Clark received the support of a narrow majority of the delegates, but nowhere near the two-thirds required.

By tradition, but not by rule, once someone got the majority, the opposition would stand down. Not this time. William Jennings Bryan, who had been the Dem nominee in three of the previous four elections, held the ranks for Wilson. Clark continued to receive a small majority until the 16th ballot. Yes, he won a majority vote on seven ballots. But once he dropped below 50 percent, his chances were almost over.

Wilson was nominated on the 46th ballot, went on to win the presidency (over the very fractured Republicans), and named William Jennings Bryan as secretary of state.

The two-thirds rule was dropped in 1936. You think the superdelegate stuff is a wild card? Think about what scenarios might be possible this year if the two-thirds rule was still in effect.

A brief return to now
So, there's the math, the majority rule, the lack of additional candidates, and the oft-stated desire of both of today's candidates to avoid a party-wrecking fight.

As a matter of policy, it's unwise to pretend to know the future, and especially in this year's presidential contest. My point is a mathematical, not a political one, and I can imagine scenarios for getting to the second ballot. Clinton and Obama could be so close that 10 or 20 delegates who vote for John Edwards or Al Gore could briefly hold the balance. Someone could assemble a group of superdelegates who will announce that they will vote "present" or for some placeholder candidate on the first ballot, with the understanding that they will move as a bloc to the winner of the first ballot, if necessary. These are at least theoretical possibilities that cannot be ruled out based on the simple math above.

But if you listen to the messages coming out of the DNC leadership, there is a strong desire to force a clear conclusion to the contest well before the convention. Chairman Howard Dean said in early February:

"The idea that we can afford to have a big fight at the convention and then win the race in the next eight weeks, I think, is not a good scenario. So, after the primaries are over, the last primary is June 8th in Puerto Rico, there may be another state with there, and after that if we don't have a nominee, I think we will have a nominee sometime in the middle of March or April. But if we don't, then we're going to have to get the candidates together and make some kind of an arrangement. Because I don't think we can afford to have a brokered convention…"

That "make some kind of arrangement" comment is a little creepy. More recently, Dean put it more diplomatically but the meaning is pretty similar.