Tuesday, February 23, 2010

Start Learning About The Borda Count

Remember the 2000 Presidential election, when Florida became a debacle in part because of voters who picked Nader instead of Gore?  Part of the reason why that outcome was maddening was because everyone knew most Nader voters, if they had to pick, preferred Gore over Bush.  Unfortunately the plurality voting rule used in Florida was blind to that information.

Imagine for a moment you're back in college or high school, with a class ranking based on your academic achievement.  How would you like your class rank to be based solely on the number of A's you have received in class?  Of course that plan sounds terrible, because someone with all F's and a single A would beat a kid with all B+'s and no A's!  Well, that's exactly how our plurality voting works in the U.S.  So how about GPA?  It seems to do a pretty good job of measuring overall academic achievement; is there a voting-rule equivalent to GPA?  Yes, it's called the Borda count.

The Borda count, invented by French mathematician Jean-Charles de Borda, works like this: each voter ranks candidates in order of preference.  Most Nader voters, for example, would rank Nader > Gore > Bush.  Points are assigned to the three candidates: two points for the first choice (Nader), one point for the second choice (Gore), and zero points for the last choice (Bush).  Points are added up for each candidate, and whoever captures the most total points wins.

The advantage of the Borda count is its ability to incorporate more information about a voter's preferences, as the GPA analogy shows.  As a result winners selected using the Borda count tend to be more moderate than those picked by plurality rule.  The Borda count, as with all voting systems, has flaws, but its ability to more accurately reflect the will of the voters makes it far superior to the current plurality-rule regime.  I will return to this topic in the future to discuss the strengths and weaknesses of other voting systems, as well as the academic field of social choice theory, which studies the mathematical properties of voting rules.

1 comment:

  1. A very interesting idea, but I wonder how well it would work in our two-party system. The Wikipedia page states that the Borda count "affords greater importance to a voter's lower preferences than most other systems." I am imagining a scenario where the two major party candidates roughly divide the As (borrowing your GPA analogy), but due to the binary (yes/no) mentality within the two-party system voters are unwilling to give their B votes to the candidate of the opposing party. If an independent candidate receives only 5% of the As, but ends up with 90% of the Bs, could he/she steal the show?