## The Borda Count method

The Borda count method was designed to avoid some of the problems with the simple
plurality method.

The idea is pretty simple: give the candidates points according to their places on each
ballot. Give 1 point for last place, 2 for next-to-last and so on up to N points for
a first place vote (if there are N candidates).

For our Math Anxiety Club election, recall the summary of the ballots:

Number of voters | 14 | 10 | 8 | 4 | 1 |

1st choice (4 points) | A (56) | C (40) | D (32) | B (16) | C (4) |

2nd choice (3 points) | B (42) | B (30) | C (24) | D (12) | D (3) |

3rd choice (2 points) | C (28) | D (20) | B (16) | C (8) | B (2) |

4th choice (1 point) | D (14) | A (10) | A (8) | A (4) | A (1) |

So we will conclude that

A gets 56 + 10 + 8 + 4 + 1 = 79 points

B gets 42 + 30 + 16 + 16 + 2 = 106 points

C gets 28 + 40 + 24 + 8 + 4 = 104 points

D gets 14 + 20 + 32 + 12 + 3 = 81 points

So the winner with this method is B (Boris) -- a different result that will make
Alisha unhappy!

### A problem -- the majority criterion

Here's a different election, involving A, B, C and D:

Number of voters | 6 | 2 | 3 |

1st choice | A | B | C |

2nd choice | B | C | D |

3rd choice | C | D | B |

4th choice | D | A | A |

Check that even though A has a majority of the first-place votes, B wins under the
Borda count method.