How Math Explains the World.pdf

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13


The Smoke-Filled Rooms


The Art of the Possible
Otto von Bismarck, the German chancellor, might be most famous for
the warrior’s approach he took to unifying Germany, but he was a
shrewd—and quotable—politician in all respects. “Laws are like sau-
sages: it is better not to see them being made,” he once advised. Not sur-
prisingly, then, that he considered politics “the art of the possible.”^1
During a long career that saw both military victories and political tri-
umphs (Bismarck was responsible for engineering the unification of Ger-
many), he undoubtedly witnessed and participated in many back-room
negotiations. Bismarck probably would have been quite familiar with the
following scenario.
A committee to which you belong needs to elect a chair, and you and
your fellows have decided to use an instant runoff setup to do so. Four
candidates are running for the position. If any candidate receives a major-
ity of the first-place votes, he is elected; otherwise, there is a runoff be-
tween the two candidates who received the most first-place votes. You
head a faction consisting of four people, and there are two other factions

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