This 2025-voter 12-candidate IRV election is won unambiguously by "A" despite the fact that only 2 voters consider A their favorite. (For simplicity we have only shown the top or top-two choices by each voter.)

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

1000 | Z |

512 | P>A |

256 | Q>A |

128 | R>A |

64 | S>A |

32 | T>A |

16 | U>A |

8 | V>A |

4 | W>A |

2 | X>A |

1 | Y>A |

2 | A |

This election demonstrates an "exponential chain of amplifications."
Using this sort of idea you can make IRV do practically anything.
Notice how *every* round of this IRV election is 1 vote away from being a tie,
and if that tie had gone the other way then A would *not* have won. That
illustrates the potential of IRV for generating complete "chad counting" near-tie
election nightmares, where every round can be a near-tie, and every round – even
those between apparently "unimportant" candidates with "no hope" – can affect
the ultimate outcome.

The above example was not intended to make IRV look bad, but merely to demonstrate this exponential chain phenomenon. A defender of IRV could justifiably argue that since A was the second choice of a majority of the voters, A was not a bad winner.

A modification which *is* intended to make IRV look bad is
**below**. Now **A wins** despite only having two voters (perhaps A and A's spouse?) with
favorite A, *and* despite the fact A is ranked either *bottommost* or second-worst
by 75% of the voters, and A is rated in the bottom-half of all candidates, i.e.
worse than the average random winner-choice selected by a monkey,
in the view of 98.4% of the voters.
Indeed, A would lose pairwise to *every* opponent other than Z – all 10 of them –
and by a huge "landslide" margin (75-25 or larger) in each case.

"FairVote," the IRV propaganda group, refers to this as "A is a majority winner." FairVote informed me that because they have their own special private definition of the term "majority winner," this was not a "lie," it was merely a "legitimate difference of opinion."

Probably the best winner in this scenario would be P (rated top or second-top by 75% of the voters, beats every opponent pairwise by 75-25 or larger "landslide" ratio, except for Z whom P only beats by 51-49 ratio). But IRV never awards P any transfers and hence never regards P as a serious contender; the only two serious contenders are A and Z. Actually in this situation if forced to choose between A and Z, I would probably pick Z because of strength-of-preference, but IRV always ignores preference-strength information. So in this example IRV is electing the candidate A who objectively is probably the worst of the 12.

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

1000 | Z>P>Q>R>S>T>U>V>W>X>Y>A |

512 | P>Q>R>S>T>U>V>W>X>Y>A>Z |

256 | Q>R>S>T>U>V>W>X>Y>A>P>Z |

128 | R>S>T>U>V>W>X>Y>A>P>Z>Q |

64 | S>T>U>V>W>X>Y>A>P>Z>Q>R |

32 | T>U>V>W>X>Y>A>P>Z>Q>R>S |

16 | U>V>W>X>Y>A>P>Z>Q>R>S>T |

8 | V>W>X>Y>A>P>Z>Q>R>S>T>U |

4 | W>X>Y>A>P>Z>Q>R>S>T>U>V |

2 | X>Y>A>P>Z>Q>R>S>T>U>V>W |

1 | Y>A>P>Z>Q>R>S>T>U>V>W>X |

2 | A>P>Z>Q>R>S>T>U>V>W>X>Y |

While, of course, this *particular* maximally-dramatic
scenario is unlikely to arise,
this kind of "amplification" *phenomenon* is *not*
terribly unlikely; in fact it is commonplace. Authors such as Dummett and
Saari have called this "chaos."

To dramatize things in another way, we now fill in the top *five*
voter preferences (not merely the top two)
in the first example:

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

1000 | Z |

512 | P>A>Y>X>W |

256 | Q>A>Y>X>W |

128 | R>A>Y>X>W |

64 | S>A>Y>X>W |

32 | T>A>Y>X>W |

16 | U>A>Y>X>W |

8 | V>A>Y>X>W |

4 | W>A>Y>X>V |

2 | X>A>Y>W>V |

1 | Y>A>X>W>V |

2 | A>Y>X>W>V |

In this "nightmare" IRV election, the "no hopers" based on their top-rank vote counts would
seem to be A,Y,X,W, and V, who *combined* own less than 1% of the vote.
The lowest of the low would seem to be A, X, and Y.
Meanwhile the "top dog" would appear to be Z with 49.4% of the vote.
However,

- A wins the election.
- But if two more voters came and voted for Y, then Y would win.
- On the other hand, if the two extra voters went for X, then X would win.
- On the third hand, if W got the two extra votes, then W would win.
- But if V (or U, or T, or S, or R, or Q, or P) had the two extra votes, then Z would win.
- But even if Z were granted 20 more votes, then Z still would not win!

Can you imagine the lawsuits?