## Instant Runoff Voting (IRV) "amplification" a.k.a. "chaos" scenarios

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?