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The Folly of Borda’s Rule, and Giving Approval

Borda’s Rule: With N candidates, your 1st ranked candidate receives N-1 points from you. Your 2nd ranked candidate receives N-2 points from you. And so on. Non-chosen candidates receive zero points. Iterate the tallying and come up with an eventual winner.

Eschewing Borda, the Institute of Management Sciences, the Institute of Electrical and Electronics Engineers (otherwise and more popularly known as IEEE, bestowers of such forgettable numbernames as 1394, now known as Firewire; and 1284, now known as USB), the Mathematical Association of America, and the American Statistical Association all use “approval voting” (wherein each voter may cast single affirmative votes for as many candidates as desired) to elect their officers. Retired Dartmouth Professor (and longtime Sierra Club activist) Robert Norman is also a fan of approval voting.

Meanwhile, the only prominent use I could find of Borda is the baseball MVP election, as noted by Mike Ossipoff, who writes that Borda is actually a quite restrictive method. “Of course Borda wouldn’t be so bad if voters could choose how many candidates to rank,” he writes. “And, to add more freedom to the method, why shouldn’t a voter be able to give any point score to a candidate, instead of a rigid decreasing sequence?” But when this level of freedom is granted, the method is strategically identical to approval voting.

The February 12 “special meeting” of Dartmouth Alumni nears, where a vote (only those in Hanover on that Sunday may vote) will be taken that will make subsequent ratification of a proposed constitution (one which changes from approval to instant-runoff voting) easier. A letter from approval voting supporter Joe Asch went out to the drafters of that constitution this morning, who strongly support instant-runoff voting. This debate is significant because it mirrors ones constantly being had nationally (with some ardent supporters of IRV) and within the Dartmouth studentry, which switched to IRV for the Student Assembly.

Included in the letter is this 1995 article [PDF] from the Journal of Economic Perspectives will convince. It was penned by Robert J. Weber, the Frederic E. Nemmers Distinguished Professor of Decision Sciences at Northwestern’s Kellogg School of Business. Even if you disagree with the hypothesis, Weber offers an enjoyable history of “new” voting methods.

However, what I would like to see is opposing scholarly work from game theorists, mathematicians, or statisticians in support of instant-runoff voting. None has yet been presented, so far as I know, to the Dartmouth community. It seems that this would do much to desteam people like me, who tend to see IRV advocacy as little more than change for change’s sake.


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