method to use in a democracy goes back more than two centuries.
Probably the first person to notice that there were problems associated
with determining the preferences of the majority was a French mathe-
matician-turned-bureaucrat who played a significant role in the French
Revolution.
A Voting Paradox
Marie-Jean-Antoine-Nicolas de Caritat, Marquis of Condorcet, was born
in 1743, at a time when it was a very good thing to be a marquis. Among
the numerous benefits conferred upon members of the aristocracy was
the availability of higher education. While at college, he focused on math
and science, and at graduation was well on the way to becoming one of
the leading mathematicians of the eighteenth century. Joseph-Louis La-
grange, a brilliant mathematician and physicist who did groundbreaking
work in the theory of probability, differential equations, and orbital me-
chanics (Lagrange points are locations at which small bodies orbiting two
larger ones appear not to move), described Condorcet’s thesis as being
“filled with sublime and fruitful ideas which could have furnished mate-
rial for several works.”^4 Praise from Lagrange was praise, indeed.
However, soon after the publication of this paper, Condorcet met Anne-
Robert-Jacques Turgot, an economist who later became controller general
of Finance under Louis XVI. The friendship blossomed, and Turgot ar-
ranged for Condorcet to be appointed inspector general of the mint, a
similar position to the one awarded Isaac Newton by the English govern-
ment.
When the French Revolution began, it was considerably less than a good
thing to be a member of the aristocracy, but Condorcet actively welcomed
the forming of the new Republic. He became the Paris representative to the
Legislative Assembly, then later the secretary of the assembly, and helped
to construct a plan for a state education system. Unfortunately for Con-
dorcet, when the French Revolution underwent a sea change, he made
two critical mistakes. He could possibly have survived his first mistake,
which was joining the moderate Girondists and asking that the king’s life
be spared. His second mistake, though, proved to be fatal. Condorcet
failed to recognize that control of the Revolution was about to be seized by
the more radical Jacobins. He argued vigorously for a more moderate con-
stitution, which he had helped to write, and soon found himself on the
French Revolution equivalent of an enemies list. A warrant for his arrest
was issued, and Condorcet went into hiding. He later attempted to f lee,
but was caught and sent to prison. Two days later, in 1794, he was found
208 How Math Explains the World