[EM] Re: DMC,AWP,AM

[Forest Simmons]

On Wed, 30 Mar 2005, Forest Simmons wrote:

> Chris,
>
> I wonder if the following Approval Margins Sort (AMS) is equivalent to your 
> Approval Margins method:
>
> 1. List the alternatives in order of approval with highest approval at the 
> top of the list.
>
> 2. While any adjacent pair of alternatives is out of order pairwise ...
>   among all such pairs swap the members of the pair that differ
>   the least in approval.
>
> This method is clone independent and monotonic, and yields a social order 
> that reverses exactly when the ballots are reversed.
>

AMS is monotonic in a strong sense: if ballots are changed so as to 
increase alternative X's approval or to give X a victory that it didn't 
have before, while leaving all of the other approvals and pairwise defeats 
the same, then X cannot move down in the social order produced by this AMS 
method.

In other words, AMS is monotonic with respect to the entire social order 
it produces.


> If AMS and AM are the same, it might be useful to have this alternative 
> description.
>
> If they are not the same, it would be interesting to see how they compare in 
> properties and performance.
>
> I haven't had the time to run AMS on your examples below, but I will soon if 
> you don't beat me to it.

After one example it is pretty obvious that AM and AMS are equivalent when 
there are only three alternatives, since they both yield the CW when there 
is one, and they both preserve the approval order if the only upward 
defeat arrow is from the bottom to the top, and they both reverse the 
closest approval margin pair, otherwise.


Forest