[EM] demonstration, IRV elim order and monotonicity

[Kevin Venzke]

Hello.

I've said (misleadingly) in the past that Approval STV aka Approval-Elim Runoff
is able to be monotonic (mono-raise) because the elimination order is fixed at
the beginning.

I've then had to clarify that I don't believe it is enough to simply fix the order.
Also, the method used to determine the order has to meet a sort of IIA: Raising
a candidate can't change the method's ordering of the other candidates.  This
seems to leave as options just Approval, order based on a random ballot, and a
completely random order.

So to try to prove this second part, here is a scenario where the method fixes
the IRV elimination order, but still fails mono-raise:

The method is IRV with elimination based on initial first preferences.

9 A
2 B>A
6 B>C
7 C

The order is CBA.  C is eliminated and A beats B 9-8.  (A wins.)

But raise A on the 2 B>A ballots, making them 2 A>B.

Now the order is BCA.  B is eliminated and C beats A 13-11.  (C wins.)

When instead Approval is used to set the order, it is not possible for
raising A to have any effect except to move A back in the order.  If A
won before this change, that means the elimination process didn't get as
far as A's initial place in the ordering, let alone some further place.

Kevin Venzke
stepjak at yahoo.fr



	

	
		
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