# Columnist: It's How Votes Get Counted That Counts

If it stipulates that each first-place vote an actor receives is worth 3 points, each second-place vote 2 points, and each third-place vote one point, then who wins? (Answer below)

There are many alternative systems, including the increasingly popular approval voting system in which voters vote for or approve of as many nominees as they care to. A famous theorem by economist Kenneth Arrow states, however, that all systems satisfying some very simple conditions have their flaws.

It's appropriate that this year's best picture award went to A Beautiful Mind. The movie's protagonist, mathematician John Nash, made seminal contributions to game theory, a discipline not unrelated to voting systems and the ways voters and candidates respond to them. The movie was my favorite, despite the fact that there was less math in it than there is in this short column.

Answer: Given the rankings (37 - W, C, P; 18 - C, W, P; 45 - P, C, W), Crowe wins because his total number of points is (37 x 2) + (18 x 3) + (45 x 2), which equals 218. Penn's point total is (37 x 1) + (18 x 1) + (45 x 3), which equals 190, while Washington's is (37 x 3) + (18 x 2) + (45 x 1), which equals 192.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears every month.

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