During World War II, many fighter planes returned from bombing missions in Japan full of bullet holes. The decision was made to reinforce the planes, and their natural tendency was to bolster the hardest-hit sections in the body of the plane. However, the mathematician George Danzig suggested that it was precisely the parts that were hit less that needed to be armored. Was he right?



Furthermore, why do coalition negotiations continue to last until the last minute, even in cases in which the results look clear-cut? Do negotiations express the swollen egos of politicians more than the good of the country? Can their results be anticipated? And in general, do politicians act rationally?

Game theory deals with the attempt to use mathematical models to understand the behavior of several parties, all of them acting to promote their own individual interests. It's rare for game theory to offer unilateral, quantitative solutions of practical value, but it can provide important qualitative insights regarding rational behavior in general.

Danzig, it turns out, was right. The sections of the planes that had returned pockmarked with bullet holes were the sections that could survive being hit; the sections that needed to be armored were those that would cause the plane to crash if they were damaged.

As for Clinton, she acted perfectly rationally. Admission of defeat when she still had a slight chance of victory would have reduced her chances to zero, and the same holds for Netanyahu and Livni on election night.

Meretz supporters who voted for Kadima did not act irrationally either, because their votes increased Livni's chances of forming a government (though, of course, Meretz supporters who voted for Meretz also acted rationally).

In game theory, voters who choose a party whose positions do not most closely resemble their own are said to engage in manipulative, or strategic, behavior. An important insight of game theory is that there is no electoral method in which each voter would benefit the most from voting solely according to ideological preference. That means the entire democratic method is open to manipulation, though there are still both better and worse voting systems.

The system proposed recently, whereby the head of the largest party would become prime minister, is a bad one, since it would increase the need for voters to engage in manipulative behavior and make it more difficult for them to use their votes as a way of genuinely expressing their political positions and values.

Game theory offers an important insight when it comes to coalition talks as well: Even if a coalition agreement is beneficial for both sides, it won't hold up from the moment it's worthwhile for one of them to violate it. This also has a positive side, showing that any agreement - whether a coalition deal, a peace accord or a commercial transaction - needs to create a mechanism that makes it worthwhile for all the parties to keep it. Creating such mechanisms is one of the major fields of game theory.

But game theory is unable to predict or recommend an answer to the more interesting question of which parties will be part of the ruling coalition. Are the results really known in advance? It's worth thinking about that possibility again, because no one - not commentators, not mathematicians and not even the politicians themselves - knows what the results will be.

The prevailing popular feeling is that our politicians are clearly acting irrationally - but my impression is different. The problem is not irrational behavior but a real difficulty in making decisions under conditions of uncertainty, especially in a reality made up of multiple players with genuine - and sometimes immeasurably great - differences in terms of goals, interests and values.

The writer is a professor of mathematics and member of the Center for the Study of Rationality at the Hebrew University of Jerusalem.