# Re: [EM] 03/29/02 - Rob Richie Letter and Non-Monotonicity:

Alex Small asmall at physics.ucsb.edu
Fri Mar 29 10:55:22 PST 2002

```Blake wrote:

>the only realistic example wouldn't have people perfectly splitting the
>vote, so it wouldn't prove that a result occurs only from vote
>splitting, so it wouldn't prove anything at all.

Perhaps examples are too anecdotal.  The case I made last night can be
stated in terms of general principles rather than "look, for these
particular numbers I can get this paradox."  I should have done that.  Let
me now explain the origin of non-monotonicity in IRV with 3 candidates:

Suppose A beats B, and B beats C (A vs. C is irrelevant for now).  Non-
monotonicity will occur under the following conditions:

2)  In the count of first place votes, the difference between B and A is
greater than the difference between A and C.
3)  B's supporters are willing to gamble.

Under those conditions, if some of B's supporters "defect" to C, they can
promote C ahead of A, leading to a runoff between C and B.  B now wins,
only because he strategically sent some supporters away to another
candidate.

This paradox can occur with or without a Condorcet winner, since the A vs.
C contest doesn't matter.  The conditions are fairly general, so the
monotonicity violation is hardly a special case.

Alex

```