When I made a walk through Paris, two weeks
ago, with the intention to take pictures of statues of philosophers, Condorcet
was not on my list. I passed his statue by chance, simply because I had turned
into the wrong street. But once I saw the statue, of course, I knew that he was
an important Enlightenment philosopher from the 18th century. His ideas were
and are still modern. He stood for a liberal economy; he was an advocate of
human rights, especially women’s rights and Black’s rights (he actively worked
for the abolition of slavery); he opposed the death penalty; he stressed the
importance of education and wished free public education for all citizens,
including women; and he strived for a constitutional republican political
system. When Condorcet criticized the new French constitution of 1793, he was
considered a traitor and he had to flee. In 1794 he was caught and he died in
mysterious circumstances in prison.
Marquis de Condorcet was not only an
important and progressive political thinker, he was also a mathematician.
Combining both interests, he developed a voting system, which came to be known
as the Condorcet Method, but he also discovered that this method can sometimes lead
to what is now known as Condorcet’s Paradox or the Paradox of Voting. Let me
concentrate on the paradox.
In an electoral system based on the
Condorcet Method the voters vote for candidates by arranging them in their
order of preference. For keeping it simple, let me assume that there are three
voters, namely X, Y and Z, and three candidates for a certain political function,
namely A, B and C. Look how the voters vote:
X
prefers A to B and B to C
Y
prefers B to C and C to A
Z prefers
C to A and A to B.
Let’s compare the candidates pairwise:
A > B (= A is preferred to B) by two
voters, namely X and Z, against one (Y).
B > C (= B is preferred to C) by two
voters, namely X and Y, against one (Z).
This would make that A > B > C, or A
is preferred to B and B to C.
However, C has also received two votes, for
C > A (= C is preferred to A) by Y and
Z, while only X prefers A to C.
This would make that A > B > C >
A, which is not possible, of course, since nobody can be preferred to himself
at the cost of himself (resp. herself). Voilà the paradox: Everybody becomes
first but no one wins. Currently nowhere in the world a Condorcet Method of
voting is used in government elections. However, some private organisations do.
I suppose that usually these elections function well, but nevertheless the risk
remains that everybody wins, although everybody is a loser.
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