How Math Explains the World.pdf

Admittedly, the above tabulation does seem to resemble something you
see when you visit your optometrist, but let’s check the results of each
method of voting.

1. Most first-place votes. A is a clear winner.


2. Runoff between the top two. A and B are the two candidates in the run-
   off, as they have 18 and 12 f irst-place votes, respectively. A is preferred
   to B by only the 18 voters who placed him first; B is preferred to A by
   the other 37 voters, and so B is the winner.


3. Survivor. This takes a little work to determine the winner. E receives
   the fewest first-place votes in the first round, and is therefore elimi-
   nated. The table now looks like this.

Number of First Second Third Fourth

Ballots Choice Choice Choice Choice

18 A D C B

12 B D C A

10 C B D A

9 D C B A

4 B D C A

2 C D B A

It’s the end of the line for D, who received only 9 first-place votes.

The table now reduces to this.

Number of First Second Third

Ballots Choice Choice Choice

18 A C B

12 B C A

10 C B A

9 C B A

4 B C A

2 C B A

At least the table is getting easier to read. B receives only 16 first-

place votes, leaving A and C in a two-person race. Eliminating B

leaves this.

212 How Math Explains the World