[EM] Re: Election-methods Digest, Vol 9, Issue 87

[Forest Simmons]

> Date: Fri, 1 Apr 2005 01:25:36 +1000 (EST)
> From: Chris Benham <cbenhamau at yahoo.com.au>
> Subject: [EM] Re: DMC,AWP,AM
>
> Forest,
> You wrote:
>
>> "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.
>
...

>
> CB: AMS doesn't seem very "intuitive", especially to
> the uninitiated, but I like it!   (My other worry is
> that I even understand it.)
> So how is this method worse than the best of the
> methods you currently advocate?

1. It's deterministic.

2. It's not quite as easy to describe or motivate as Definite Majority 
Choice.

> A perhaps ridiculous question: does the AMS  process
> always stabilize?
>

Not a ridiculous question: it's the pigeon hole principle: there are only 
finitely many permutations of the alternatives, and you cannot return to 
any of these after you have left it, because once X and Y have been 
swapped, they are never swapped back, since only out-of-order pairs get 
swapped.

Forest