BURLINGTON's TOPSY-TURVY IRV ELECTIONS RESULTS -- New Yorker, "The Mathematics of Voting," Anthony Gottlieb

...At first glance, [IRV] is an appealing approach: it is guaranteed to produce a clear winner, and more voters will have a say in the election’s outcome. Look more closely, though, and you start to see how peculiar the logic behind it is. Although more people’s votes contribute to the result, they do so in strange ways. Some people’s second, third, or even lower preferences count for as much as other people’s first preferences. If you back the loser of the first tally, then in the subsequent tallies your second (and maybe lower) preferences will be added to that candidate’s first preferences. The winner’s pile of votes may well be a jumble of first, second, and third preferences.

Such transferrable-vote elections can behave in topsy-turvy ways: they are what mathematicians call “non-monotonic,” which means that something can go up when it should go down, or vice versa. Whether a candidate who gets through the first round of counting will ultimately be elected may depend on which of her rivals she has to face in subsequent rounds, and some votes for a weaker challenger may do a candidate more good than a vote for that candidate herself. In short, a candidate may lose if certain voters back her, and would have won if they hadn’t.

Supporters of instant-runoff voting say that the problem is much too rare to worry about in real elections, but recent work by Robert Norman, a mathematician at Dartmouth, suggests otherwise. By Norman’s calculations, it would happen in one in five close contests among three candidates who each have between twenty-five and forty per cent of first-preference votes. With larger numbers of candidates, it would happen even more often. It’s rarely possible to tell whether past instant-runoff elections have gone topsy-turvy in this way, because full ballot data aren’t usually published. But, in Burlington’s 2006 and 2009 mayoral elections, the data were published, and the 2009 election did go topsy-turvy.

Read more: http://www.newyorker.com/arts/critics/books/2010/07/26/100726crbo_books_gottlieb?currentPage=3#ixzz0ubmJP3cm