[EM] Elimination with Take-Down

[Kristofer Munsterhjelm]

On 5/4/23 22:48, Forest Simmons wrote:
> What started as Chain Climbing has evolved into a Banks efficient 
> take-down Elimination protocol.... whenever you eliminate an 
> alternative, let it take-down with it any alternative it defeats ... an 
> expedient for conferring Banks efficiency on elimination methods.

A thought about this: Could we create a method that works in this way 
but also produces the same result as Smith//Range for a three-way contest?

Suppose we have an ABCA cycle and everybody but that cycle has been 
eliminated. Then there are six possible Range orders: ABC, ACB, BAC, 
BCA, CAB, and CBA, where ABC means that A has the highest score, B is 
next, and C is last.

If C is last, then C is eliminated and takes A with him. B wins.
If B is last, then B is eliminated and takes C with him. A wins.
If A is last, then A is eliminated and takes B with him. C wins.

So this only produces the "proper" outcome if the Range order is ACB, 
BAC or CBA. The other half of the time, it'll be incorrect. So for 
maintaining the VSE of a high-VSE method, it might not be a good idea.

It might be useful for strategy, though. An interesting question is if 
take-down elimination Benham loses any strategy resistance. With IRV 
being as chaotic as it is, we could hardly lose any VSE :-)

And another thought: wanting Banks might be overkill -- at least for 
current versions of the "homotopy method". Although on the hand, if we 
do get large honest Condorcet cycles, that shows there's genuine 
competition. So who knows what could happen after Condorcet has been in 
use for a long time?

-km