## Borda Voting Explained

In the Borda election method, voters rank the candidates as first, second, third, etc. The first choice of each voter gets a number of points one less than the number of candidates. Each subsequent choice then gets one less point than the preceding choice, until the last choice get no points at all. If the number of candidates is four, for example, the first choice gets three points, the second gets two points, the third gets one, and the last choice gets none. The points from each voter are added together to determine the winner. In the most common form of the Borda system, each voter must rank all the candidates; truncation is not allowed.

The Borda election method is one of the better known methods for tallying ranked ballots. It is used by the Associated Press (AP) and the United Press International (UPI) to rank teams in NCAA college sports, for example. It is also used in various scientific and technical applications such as handwriting recognition and space navigation, where the votes come from unbiased sensors or systems rather than people. The Borda system has few advocates for use in actual public elections, but they have received perhaps a disproportionate share of attention in the popular press.

When voters can be trusted to vote sincerely, the Borda method can be very effective. The coaches and sports writers who rank college football teams, for example, vote openly and are expected to vote honestly, without trying to unfairly stack the deck in favor of their favorite teams. Also, when the votes come from mechanical sensors or computer algorithms, then the Borda method can also do a good job. However, the Borda system tends to have problems when the voters are free to stack the deck, and it tends to encourage strategic and insincere voting.

How does the Borda method encourage insincere voting? Suppose my true preferences are for candidates (A,B,C) in that order. But suppose I know that A and B are in a tight race and C is not a serious contender. I may as well rank the candidates (A,C,B), contrary to my true preferences, because then I am giving A two points over B rather than just one, doubling the effect of my vote. Similarly, the voters whose true preferences are (B,A,C) may as well rank them (B,C,A) for the same reason. If too many voters try this strategy, they might just end up inadvertently electing candidate C, but as long as not too many do so, C will not be a threat.

The situation is even worse with a larger number of candidates, because then voters can increase the point differential even more. Consider, for example, a general election with Republicans, Democrats, and four minor parties. As long as the minor parties are weak, many voters will be tempted to insincerely rank the Republican first and the Democrat last, or vice versa, essentially using the minor parties as a wedge to increase the point differential between the Democrats and Republicans. The strategy could backfire if too many voters try it, but otherwise it can leverage a voter's influence significantly. A good election method should not even tempt voters to try such strategy.

The Borda voting system also has other serious problems. It is the only seriously proposed method that can actually fail to elect a candidate selected by a majority as their favorite. Another serious problem with the Borda method is that it fails to satisfy the Condorcet criterion, which can be stated as follows: if all votes are sincere, and if one candidate is preferred over each of the other candidates individually by more voters than prefer the other candidate, then that candidate should win. The Condorcet criterion seems like common sense, but the Borda system fails to meet it even though it allows voters to rank the candidates.