[EM] How close can we get to the IIAC

[fsimmons at pcc.edu]

Marcus,

you seem to think that the method is to elect the highest approval member of the uncovered set.  That is 
not the case.  Instead, first we check to see if the highest approval candidate C is uncovered.  It is not, 
so then we check to see if the highest approval candidate B that covers C is uncovered.  It is, so B is 
the winner.

The method is monotone:

Sketch of Proof:

Suppose that the method winner is W.  If W moves up in the approval list, then W obviously still wins. 
So we consider the interesting case where W now defeats some candidate C pairwise that beat W 
before.  Suppose that the new method winner is  W' .  Then W' must be some candidate that now covers 
C but didn't before when C covered W.  Why? Because W beats W'.    So W' does not beat W.  That 
means that W' gets into the act before W.  But there was nothing to keep W' from getting into the act 
before W before.  Therefore W covers W', and still wins.

Forest

> From: Markus Schulze 
> To: election-methods at electorama.com
> Subject: Re: [EM] How close can we get to the IIAC
> Message-ID: <7.0.1.0.1.20100417234339.01100e80 at alumni.tu-berlin.de>
> Content-Type: text/plain; charset="us-ascii"
> 
> Hallo,
> 
> > Here's a method I proposed a while back that is monotone,
> > clone free, always elects a candidate from the uncovered
> > set, and is independent from candidates that beat the
> > winner, i.e. if a candidate that pairwise beats the
> > winner is removed, the winner still wins:
> >
> > 1. List the candidates in order of decreasing approval.
> >
> > 2. If the approval winner A is uncovered, then A wins.
> >
> > 3. Otherwise, let C1 be the first candidate is the list
> > that covers A. If C1 is uncovered, then C1 wins.
> >
> > 4. Else let C2 be the first candidate in the list that
> > covers C1. If C2 is uncovered, then C2 wins.
> >
> > etc.
> 
> Situation 1:
> 
> Suppose the order of decreasing approval is CDAB.
> 
> A beats B
> B beats C
> C beats D
> D beats A
> A beats C
> B beats D
> 
> uncovered set: A, B, D.
> 
> The winner is D.