Jean-Charles de Borda

The Borda Method

Voting is something that has been used for a very long time, so obviously it is the best way right. Wrong, simple voting can be modified and made a lot better. Written sources attest the existence of voting procedures all through the middle Ages. Confusion in choosing the right system was common, nobody really knew what was best for them. In 1130, for example, the ambiguity of voting led to the election of two Popes, an event that created a rift within the Catholic Church. In about 1770 a French mathematician named Jean-Charles Borda (1733-1799) proposed a new idea of voting. He asked that voters rank the candidates, andin turn giving the candidates points on how they want them. For example, in a 3-candidate election, the first ranked on a ballot received 3 points, the second obtained 2, and the third ranked got 1 point. The candidate with more points won. There are many ups and downs of each way of voting, but at the time, The Borda Method was the most appealing. But mathematicians found the answer; they have bad and good news for the voting population. The bad news is Borda's count 3,2,1 is not ideal; it can still lead to distorted results. The good news: within the point method, the Borda count is by far the best. Moreover, our voting rule 1,0,0 is the worst; it gives the least amount of information about what voters want and can yield results that speak against the people's will. This becomes clear from the following examples. In 1970 the centre-right candidate Buckley won the New York senate election even though more than 60% of the votes went for either of the two centre-left candidates. A less obvious but even more disturbing case is the recent Bush-Gore race. If those voting for Nader could have made Gore their second choice (which is a reasonable assumption), the democrats would have won without trouble, as the popular vote suggests. But there are more complicated systems. The run-off method, for example, uses the 1,0,0 point rule in combination with several rounds of vote. Only a more than 50% support makes the winner. Otherwise the last candidate is dropped and the vote is repeated. An alternative is to exclude all but the first two candidates and vote a second time. This system, however, has its flaws too. The first version takes too long to be efficient in a national election, whereas the second can bring weird outcomes. In the 26 November 2000 election for the Romanian Presidency, this method led to a run-off between a left wing extremist and a right wing one. The centre vote had been split among several candidates. The only simple and efficient method that in most cases expresses the will of the majority is the Borda count. Ranking the candidates and assigning a balanced rule of points, as in the 3,2,1 example, would make our elections fairer. We only need to implement this rule. Its time has arrived.