[EM] Superchargers and Afterburners

[Forest Simmons]

On Thu, 17 Apr 2003, Markus Schulze wrote:

> Dear Forest,
>
> you wrote (16 April 2003):
> > Then for n from 1 to N
> >    If C_(n-1) is a beats-all candidate then let C_n = C_(n-1)
> >       Else let C_n be the candidate with the greatest victory over C_(n-1)
> >    End If
> > Next n.
> >
> > If the sequence of candidates generated by this method cycles, then break
> > the cycle at its weakest link.
>
> When I understand this method correctly then you successively break the
> strongest cycle at its weakest link. Actually, this is Tideman's Ranked
> Pairs method.

Actually, I was thinking of stopping after the first instnace of cycling.

For example, Plurality with Afterburner would start with the candidate
having the greatest number of top rank positions on the ballot as C_0. If
any candidate beats this C_0, then the one with the greatest victory over
C_0 would be C_1, etc. Keep going until you reach a "beaten-by -none"
candidate, or until there is a cycle.  In the latter case break the cycle
at the weakest link to get the winner.

What led me in this direction was the thinking about the Approval winner
as the candidate that has the greatest victory over the NOTB (None Of The
Below) candidate.  Approval with afterburner would continue in this vein.

Forest