Is it fairer to give every candidate points for every rank on the ballot?

It uses more of the ballot, but it comes with catches. The Borda count lets every rank on the ballot count. Each candidate gets a number of points equal to the number of candidates ranked below them: the lowest-ranked gets 0 points, the second-lowest 1 point, and so on. Add up the points on all the ballots and the candidate with the most points wins. Plurality voting, by contrast, assigns one point only to the top candidate.

Try three voters, U, V and W, and four candidates. U and V rank them A-B-C-D, while W ranks them B-C-D-A. With 3, 2, 1 and 0 points for each ballot, A scores 3 + 3 + 0 = 6 and B scores 2 + 2 + 3 = 7. So B is elected, even though A is first choice on two of the three ballots.

The count is named after Jean-Charles de Borda, a French mathematician and naval engineer, who devised it as a fair way to elect members of the French Academy of Sciences. The Academy experimented with it but abandoned it, in part because "the voters found how to manipulate the Borda rule". Borda's reply: his scheme, he said, was intended only for honest men.

A second objection came from the Marquis de Condorcet. Examples led him to argue that the Borda count is "bound to lead to error" because it "relies on irrelevant factors to form its judgments".