Note that, according to Gibbard and Satterthwaite, all of the systems I am considering here are sometimes vulnerable to voter manipulation. Satisfying the criteria I find important tends to minimize chances for manipulation.

Baldwin | Borda | Bucklin | Carey | Coombs | Copeland | Dodgson | Hare | Nanson | Raynaud | Schulze | Simpson | Tideman | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Pareto-optimal? | YES | YES | YES | YES | YES | YES | YES | YES | YES | YES | YES | YES | YES |

majority? | YES | NO | YES | YES | NO | YES | YES | YES | YES | YES | YES | YES | YES |

Condorcet? | YES | NO | NO | NO | NO | YES | YES | NO | YES | YES | YES | YES | YES |

monotonic? | NO | YES | YES | NO | NO | YES | YES | NO | NO | NO | YES | YES | YES |

clone-independent? | NO | NO | NO | NO | NO | NO | NO | YES | NO | YES | YES | NO | YES |

mutual majority? | YES | NO | YES | NO | NO | YES | NO | YES | YES | YES | YES | NO | YES |

Smith? | YES | NO | NO | NO | NO | YES | NO | NO | YES | YES | YES | NO | YES |

reverse-symmetric? | NO | YES | NO | NO | NO | YES | NO | NO | NO | NO | YES | NO | YES |

reinforcing? | NO | YES | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO |

Schwartz? | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO | YES | NO | NO |

nonmanipulable? | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO | NO |

# Coombs fails reinforcement |

# precinct 1 |

8:B>C>A>D |

6:C>D>A>B |

4:D>B>C>A |

# precinct 2 |

8:B>A>D>C |

2:B>C>D>A |

6:C>A>D>B |

2:C>B>D>A |

2:D>B>C>A |

Back to Ranked-ballot voting methods

Robert Hampton “Honky” LeGrand III ’98