#voters | Their Vote |
---|---|

40 | X>Y>Z |

20 | Y>Z>X |

40 | Z>Y>X |

A majority of the voters (20+40) rank X strictly bottom, so X should be an "irrelevant loser." But with Instant Runoff Voting (IRV), it isn't. IRV elects Y if X does not compete but elects Z if X does compete. This (essentially) actually happened in Louisiana 1991.

There are many other examples, but this is
designed to illustrate that this can happen even if a majority of voters
rank the loser dead *last*. E.g.

- (B wins, but if C drops out then A wins)
- (B wins, but if N drops out then G wins)
- (Bush wins; if Nader drops out Gore wins)
- (A wins; if C drops out A wins; if B drops out C wins)

One can go further by creating artificial elections in which, e.g. H is ranked dead last by 99.9% of the voters, but plays a very important role. (With instant runoff voting: If H runs, then Z wins. If H drops out, then A wins.)

#voters | their vote |
---|---|

1000 | Z>...>H |

512 | P>A>...>H |

256 | Q>A>...>H |

128 | R>A >...>H |

64 | S>A>...>H |

32 | T>A>...>H |

16 | U>A>...>H |

8 | V>A>...>H |

4 | W>A>...>H |

2 | X>A>...>H |

1 | Y>A>...>H |

2 | H>A |