# Putting It Together: Voting Theory

There are four candidates for senior class president, Garcia, Lee, Nguyen, and Smith. Using a preference ballot, [latex]75[/latex] ballots were cast, and the votes are shown below.[latex]20[/latex] | [latex]3[/latex] | [latex]8[/latex] | [latex]16[/latex] | [latex]28[/latex] | |

1st choice | Garcia | Garcia | Lee | Nguyen | Smith |

2nd choice | Lee | Nguyen | Nguyen | Garcia | Lee |

3rd choice | Nguyen | Lee | Garcia | Lee | Garcia |

4th choice | Smith | Smith | Smith | Smith | Nguyen |

*Now that the votes are in, it should be a simple matter to find out who won the election, right? *

*Well that depends on which voting system you choose.*

Garcia | Lee | Nguyen | Smith | |

1st choice (4 pts) | [latex]23\times4=92[/latex] | [latex]8\times4=32[/latex] | [latex]16\times4=64[/latex] | [latex]28\times4=112[/latex] |

2nd choice (3 pts) | [latex]16\times3=48[/latex] | [latex]48\times3=144[/latex] | [latex]11\times3=33[/latex] | [latex]0\times3=0[/latex] |

3rd choice (2 pts) | [latex]36\times2=72[/latex] | [latex]19\times2=38[/latex] | [latex]20\times2=40[/latex] | [latex]0\times2=0[/latex] |

4th choice (1 pt) | [latex]0\times1=0[/latex] | [latex]0\times1=0[/latex] | [latex]28\times1=28[/latex] | [latex]47\times1=47[/latex] |

Total Points | [latex]212[/latex] | [latex]214[/latex] | [latex]165[/latex] | [latex]159[/latex] |

[latex]20+3=23[/latex] | [latex]8+16=24[/latex] | [latex]28[/latex] | |

1st choice | Garcia | Nguyen | Smith |

2nd choice | Nguyen | Garcia | Garcia |

3rd choice | Smith | Smith | Nguyen |

[latex]23+24=47[/latex] | [latex]28[/latex] | |

1st choice | Nguyen | Smith |

2nd choice | Smith | Nguyen |

Garcia | Lee | Nguyen | Smith | |

Garcia | [latex]36[/latex] | [latex]24[/latex] | [latex]28[/latex] | |

Lee | [latex]39[/latex] | [latex]19[/latex] | [latex]28[/latex] | |

Nguyen | [latex]51[/latex] | [latex]56[/latex] | [latex]28[/latex] | |

Smith | [latex]47[/latex] | [latex]47[/latex] | [latex]47[/latex] |