How Math Explains the World.pdf

consisting of five and two people, respectively. Of the four candidates for
chair, your faction wholeheartedly endorses A, would settle for B, and
loathes and detests D.
Everyone in your faction casts an identical ballot: their first choice is A,
followed by B, C, and the detestable D. The other two factions have al-
ready cast their ballots as follows.

Number of Votes First Place Second Place Third Place Fourth Place

5 D C B A

2 B D A C

Glumly, you note that if you cast your four ballots, the results will look
like this.

Number of Votes First Place Second Place Third Place Fourth Place

5 D C B A

2 B D A C

4 A B C D

There will be a runoff between A and D, which D will win, 7 to 4. Intol-
erable. Suddenly, a bright idea occurs to you, and you locate a small room
filled with the requisite amount of smoke in which to caucus. You point
out to the other members of your faction that if they are willing to switch
A and B on their ballots, B will receive six first-place votes (a majority) and
win the election. No ballot they cast will enable A to win, but by switching
A and B they can ensure an acceptable result and guarantee that D will
not win.
This technique also works in more subtle situations. Suppose now that
the other seven ballots are tabulated as follows.

Number of Votes First Place Second Place Third Place Fourth Place

5 D C B A

2 C B D A

If your faction votes as originally intended, the tabulation will look like
this.

224 How Math Explains the World