# Selected topics in finite mathematics/Condorcet criterion

[*Give a very very brief overview of the criteria?*]

## Objectives

[edit | edit source]To satisfy the Condorcet criterion, a candidate that is favored to beat ever other candidate in a pairwise race wins. Therefore, if a candidate can defeat every other candidate, then they should win.

## Details

[edit | edit source][*State the definition of the criteria?*]

[*Rephrase the criteria into if-then form?*]

[*Give a prose-explanation of the criteria?*]

## Examples

[edit | edit source]The Condorcet method satisfies the Condorcet criteria. Indeed, this is its namesake: if a candidate wins all pairwise races, that candidate wins by the Condorcet method.

Sequential pariwise elections also satisfies the Condorcet criterion. In particular, suppose A wins in all pairwise races. Then as soon as A comes up in the agenda, A will win every [pairwise] race until declared the winner.

## Nonexamples

[edit | edit source]Plurality fails to satisfy the Condorcet criterion. Consider the following election. A wins in all pairwise elections, but instead B wins by plurality.

1st choice | A | B | C |
---|---|---|---|

2nd choice | B | A | A |

3rd choice | C | C | B |

Number of votes | 2 | 3 | 2 |

Borda count fails to satisfy the Condorcet criterion. Consider the following election. One on one A wins all pairwise races. However, in this election as it is, B wins.

1st choice | B | E | D |
---|---|---|---|

2nd choice | C | A | A |

3rd choice | F | B | B |

4th choice | A | C | E |

5th choice | E | D | C |

6th choice | D | F | F |

Number of votes | 1 | 1 | 1 |

Sequential runoffs fail to satisfy the Condorcet Criterion. Consider the following election. Indeed one on one A could defeat either candidate. But in the election as a whole, A is eliminated first.

1st choice | A | B | C |
---|---|---|---|

2nd choice | B | A | A |

3rd choice | C | C | B |

Number of votes | 2 | 3 | 3 |

## FAQ

[edit | edit source]## Homework

[edit | edit source][*Create two elections: one which satisfies the criteria and one which does not?*]

[*You can add the solution to the problem here!*]

[*You can add the solution to the problem here!*]