, Salem, MA


October 16, 2012

Column: How every vote matters


Given the variety of methods, I’m sure voters and candidates would love to know which one would provide the “best” results — a problem that economists, political scientists and mathematicians have been studying for decades. But the question is far older.

In 1433, Nicholas of Cusa, a church lawyer, discovered that the emperor was coming to the church council where he was serving. It seemed an ideal opportunity to push for reform, and he went so far as to create what he called a most “righteous, just (and) honest” way to tally the votes for the emperor.

Fast-forward to today’s local sports page and you’ll find (essentially) his method in the college football polling, where teams are ranked from highest to lowest, and then points assigned based on ranking for each voter. The most points wins. (Vote No. 4.)

Unfortunately, though, just like the plurality vote, Cusa’s method (also called the Borda count) suffers from a basic problem. Namely, you should expect strange paradoxes if you compare head-to-head results (like the exit polling for Bush/Gore without third-party candidates), with the actual election results including all candidates.

In fact, Nobel laureate Kenneth Arrow’s celebrated theorem (along with some extensions) shows that every election procedure is flawed in a similar way long before we even start counting the votes — much less ballot-box stuffing, voter fraud or inept officials.

Along similar lines, recall how some Romney supporters appealed in the primaries to his Republican rivals’ voters. They wanted those voters to misrepresent their true choices by voting for Romney on the basis of “electability” in the final election — presumably leading to a more desirable outcome vis-à-vis re-electing Obama. It turns out one can rigorously prove that every method can give voters the opportunity to get a better (in their perception) final outcome by casting an “insincere” ballot.

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