# [EM] IRV's nonmonotonicity

Rob LeGrand honky1998 at yahoo.com
Fri Mar 29 17:17:59 PST 2002

```Alex and Adam gave three examples to try to show how IRV can violate
monotonicity.  Alex's second example was

>19% Bill > George > Ross
>18% Bill > Ross > George
>19% Ross > George > Bill
>12% Ross > Bill > George
>16% George > Bill > Ross
>16% George > Ross > Bill
>
>Runoff is still Bill vs. George, and George wins. If 2% from the
>Bill>George>Ross camp list their preference as Ross>Bill>George, the runoff
>is Bill vs. Ross. Bill wins.

But this isn't an example of nonmonotonicity.  George wins, some voters uprank
Ross, and then Bill wins.  The upranking voters benefited from their
insincerity, but monotonicity isn't violated in this example.  To violate
monotonicity, an example must cause a winner to lose by having some voters
uprank him or cause a loser to win by having some voters downrank him.  Alex's
first Bill/George/Ross example and Adam's Al/George/Ralph example have the same
problem.

Here's a nonmonotonic IRV example taken from Philip Straffin's book Topics in
the Theory of Voting:
6:A>B>C
2:B>A>C
4:B>C>A
5:C>A>B

IRV gives the win to A, but if the B>A>C voters uprank A and vote A>B>C, then
IRV gives the win to C.  A went from winner to loser when some voters ranked
him higher.

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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