That’s where Bueno de Mesquita began programming his computer model. It is based loosely on Black’s voter theory, and it works like this: To predict how leaders will behave in a conflict, Bueno de Mesquita starts with a specific prediction he wants to make, then interviews four or five experts who know the situation well. He identifies the stakeholders who will exert pressure on the outcome (typically 20 or 30 players) and gets the experts to assign values to the stakeholders in four categories: What outcome do the players want? How hard will they work to get it? How much clout can they exert on others? How firm is their resolve? Each value is expressed as a number on its own arbitrary scale, like 0 to 200. (Sometimes Bueno de Mesquita skips the experts, simply reads newspaper and journal articles and generates his own list of players and numbers.) For example, in the case of Iran’s bomb, Bueno de Mesquita set Ahmadinejad’s preferred outcome at 180 and, on a scale of 0 to 100, his desire to get it at 90, his power at 5 and his resolve at 90.

Image Credit... Ted McGrath

Then the math begins, some of which is surprisingly simple. If you merely sort the players according to how badly they want a bomb and how much support they have among others, you will end up with a reasonably good prediction. But the other variables enable the computer model to perform much more complicated assessments. In essence, it looks for possible groupings of players who would be willing to shift their positions toward one another if they thought that doing so would be to their advantage. The model begins by working out the average position of all the players — the “middle ground” that exerts a gravitational force on the whole negotiation. Then it compares each player with every other player, estimating whether one will be able to persuade or coerce the others to move toward its position, based on the power, resolve and positioning of everyone else. (Power isn’t everything. If the most powerful player is on the fringe of an issue, and a cluster of less-powerful players are closer to the middle, they might exert greater influence.) After estimating how much or how little each player might budge, the software recalculates the middle ground, which shifts as the players move. A “round” is over; the software repeats the process, round after round. The game ends when players no longer move very much from round to round — this indicates they have compromised as much as they ever will. At that point, assuming no player with veto power had refused to compromise, the final average middle-ground position of all the players is the result — the official prediction of how the issue will resolve itself. (Bueno de Mesquita does not express his forecasts in probabilistic terms; he says an event will transpire or it won’t.)

The computer model, in short, predicts coalitions. And computers are much better at doing this than humans, because with more than a few players the number of possible coalitions quickly multiplies. With 40 players, the typical size of one of Bueno de Mesquita’s forecasts, there are 1,560 possible pairs to consider just for starters. This is why, he says, his model often produces surprising results. It’s not that it is smarter than humans. But it methodically works through not only the obvious coalitions we know about and expect but also the invisible ones that we don’t.

For Bueno de Mesquita, the first prominent use of the model came in 1979, when the State Department was canvassing academics with expertise on India, including Bueno de Mesquita, to see how some parliamentary maneuverings would unfold. Bueno de Mesquita decided to use his first version of the software (which was, as he puts it, “barely working”) and his own knowledge of India to determine the power players and each of their numbers. Then the university’s mainframe computer worked on the data all night.

In the morning, Bueno de Mesquita said, he was astonished: the predicted victor was a seemingly minor figure, someone discounted by the experts. Bueno de Mesquita shared their opinion, he told me, but he accepted the computer’s verdict anyway. “So I called the person back at the State Department, and told him what I had concluded,” Bueno de Mesquita went on. “And there was a long, quiet period and some laughing. He said: ‘How did you arrive at that? Nobody’s saying that.’ So I told him I had a little computer model. He just guffawed. He said, ‘I wouldn’t repeat that if I were you.’ ”

Three months later, according to Bueno de Mesquita, his prediction turned out to be right.

The son of Jewish immigrants who arrived from Brussels during World War II, Bueno de Mesquita grew up in Manhattan, where his father ran a small publishing company and his mother managed a women’s clothing shop. He went to Queens College when he was 16 — “way too young,” he says — and read history and literature voraciously. (Bueno de Mesquita spent years researching and writing a short novel that defends Ebenezer Scrooge as a kindhearted man.) “He is one the most remarkably intelligent human beings I’ve met in my life, and Bruce does not hesitate to tell you that,” Kevin Gaynor, an environmental lawyer who has twice hired Bueno de Mesquita to advise his corporate clients on “extremely sensitive” government negotiations, told me half-jokingly. “He’s not self-effacing. But he’s not self-effacing in a charming way.” Bueno de Mesquita’s voluminous academic work — he has published 16 books and more than 100 papers — is credited with helping to move game theory and mathematical modeling into the mainstream of political science; according to one count, by 1999 fully 40 percent of papers in the American Political Science Review used modeling. (The figure was so high it prompted deep consternation among non-game-theory political scientists.) While few perform the consulting work he does, other game theorists have produced models very similar to Bueno de Mesquita’s, and he actively promotes his technique, including training N.Y.U. undergraduates to do similar predictions.) He spends half the year at N.Y.U., where he recently finished a four-year stint as the chairman of the political-science department, and half the year at the Hoover Institution at Stanford. Under the terms of his academic contracts, he is permitted to spend one day per week during the academic year doing outside consulting.

It is this consulting, more than his academic work, that has made Bueno de Mesquita both well off and controversial. He began offering predictions to the private sector in 1982, when A.F.K. Organski, a former professor of his, suggested they go into business using Bueno de Mesquita’s model. Business negotiations, they reasoned, were like international relations in that they involved players trying to wheedle and coerce one another. Soon Bueno de Mesquita and Organski (who died in 1998) acquired clients ranging from Arthur Andersen to Union Carbide, which tapped them for advice on placating the Indian government after the Bhopal chemical spill. Today Bueno de Mesquita’s firm essentially consists of himself and Harry Roundell, a former banker at J. P. Morgan who met Bueno de Mesquita when Roundell hired him in 1995 to help the bank figure out how to push for new, favorable regulations in the U.S. They charge $50,000 and up to do a prediction and offer negotiating tips, and they take on 18 to 20 of these assignments a year. Beyond saying it was “a reasonable amount of money,” Bueno de Mesquita would not describe his income from the company.