[EM] Plausible IRV example showing non-monotonicity

Bart Ingles bartman at netgate.net
Sat Mar 10 00:38:58 PST 2001

```Here is a more-or-less plausible example showing both the no-show
paradox and a monotonicity violation in an IRV election.  You could
think of the added/changed votes as being the result of either absentee
ballots, or of a recount (possibly including discovery of mislabeled
ballot containers, as happened in New Mexico).

This assumes the usual one-dimensional issue space, with the centrist
voters evenly split over their 2nd choice:

votes      candidates (in order of preference)
----------------------------------------------
900         A  B  C
300         B  A  C
300         B  C  A
575         C  B  A

After C is eliminated, B wins 1175 to 900.

50         C  B  A

Now C has 625 first-choice votes, eliminating B.  C loses the 2nd round,
with 925 votes to A's 1200.  The additional C voters would have been
better off staying home -- a no-show paradox.  By voting, the C voters
helped elect their least favorite candidate.

Finally, suppose the absentee ballots were miscounted, and a recount
awards them all to A:

50        A  C  B

C is once again eliminated first, and B wins 1175 to 950.  Giving the 50
votes to A causes A to lose -- a very plausible monotonicity violation.

The above was adapted from Fishburn's 7-6-5 example.  The main thing I
wanted to add was a realistic centrist vote, with split 2nd choices.
The only thing remotely unusual about the election is the fact that B
and C are in a close race for 2nd place (in the first-round tally).

Bart Ingles

```