[EM] A Comparison of the Two Known Monotone, Clone Free Methods for Electing Uncovered Alternatives

[Jobst Heitzig]

Hi Kristofer,

you wrote:
> I think Short Ranked Pairs also passes all these. To my knowledge, Short
> Ranked Pairs is like Ranked Pairs, except that you can only admit X>Y if
> that will retain the property that every pair of affirmed candidates
> have a beatpath of at most two steps between them.
> 
> See
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-November/014255.html
> . The definition of a short acyclic set of defeats was later changed,
> and the new definition is at
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-November/014258.html

Thanks for unearthing this old idea of mine -- I had forgotten them
completely already.

Unfortunately, I fear Short Ranked Pairs might not be monotonic. One
would habe to check. And I'm not sure your description of an algorithm
for Short Ranked Pairs is valid -- after all, I only defined it
abstractly by saying that one has to find the "lexicographically maximal
short acyclic set" without giving an algorithm to find it.

I propose to proceed as follows: Check how that lexicographically
maximal short acyclic set can be found in the simpler case in which we
define defeat strength as approval of defeating option. This will also
allow us to compare the method to DMC since DMC is the result of
applying ordinary Ranked Pairs with this definition of defeat strength,
so applying Short Ranked Pairs to them should not be too much different.

The resulting short acyclic set will contain all defeats from the
approval winner to other options, but I don't see immediately whether
one can somehow continue to lock in defeats similar to ordinary Ranked
Pairs, skipping certain defeats that would destroy the defining
properties of a short acyclic set. I somehow doubt that since that
defining property is not that some configurations must not exist but
than some configurations must exist. Anyway, in the case where defeat
strength is approval of defeating option, all might be somewhat simpler.

Jobst



> 
> 
> I also guess you could make methods with properties like the above by
> constraining monotone cloneproof methods to the Landau set (whether by
> making something like Landau,Schulze or Landau/Schulze). I'm not sure of
> that, however, particularly not in the X/Y case since the elimination
> could lead to unwanted effects.
> 
> Is one of the two methods you mention UncAAO generalized?
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