When the winner wins
- In the image above 4 people vote for the candidates A, B, and C.
- Who won?
- The first person preferred A to B and B to C.
- You mean he ranked them in the order ABC?
- Exactly. If we give 3 points for first place, 2 for second, and 1 for third, following the suggestion made by Jean-Charles de Borda who, according to Wikipedia, was a French mathematician, physicist, political scientist, and sailor (1733 – 1799) .
- Sailor, eh?
- Then B wins the election with 9 points.
- But if we only look at the voters’ first choice then A wins!
- Isn’t that sad?
- I am wondering how many votes the winner has to get for both methods to give the same result.
- What do you mean?
- I want Borda’s method, that sums the preferences by the voters on all the candidates, and the method that only looks at their first choice, to give the same result.
- So do I!
- But, as we just saw, that will not always happen. The question I am raising is what percentage of voters have to put the winner as their first choice for the two methods to declare the same winner.
The Royal Spanish Mathematics Society is 100 years old this year. The newspaper El País celebrates this with a math problem every week. The problem above is, in essence, one of them. Here is a video presenting the problem (in Spanish).