Examples to demonstrate IRV failure of "irrelevant alternatives"

#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.

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

Similar example but for Borda voting

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