[EM] [Election-Methods] Can someone point me at an example of the nonmonotonicity of IRV?

[Kristofer Munsterhjelm]

Terry Bouricius wrote:
> Kathy,
> 
> On the monotonicity criterion and IRV. IRV does indeed fail the most 
> common definition of the monotonicity criterion, as do two-round runoffs 
> and all other methods (I believe) that satisfy the later-no-harm 
> criterion. It is a trade off ... Which is more important in the real 
> world, monotonicity or later-no-harm. Different experts have different 
> opinions on that.

Just a note in passing: if you judge electoral methods just by whether 
they fulfill monotonicity or LNHarm, then you should pick Descending 
Solid Coalitions, which passes both.

In practice, though, DSC can give weird results; Chris Benham showed one 
in particular. What the existence of DSC does show is that it's possible 
to make a method that passes both monotonicity and LNHarm.

Plurality also technically passes both of the LNH criteria, as well as 
monotonicity. When I said that was impossible in an earlier post, I 
implicitly assumed one would want mutual majority, which Plurality 
fails. To pass mutual majority, if there's a group of candidates that a 
majority prefers to those not in the group, then the system should 
always pick a candidate within that group.