[EM] an extra step for IRV (and some other methods?)

[C.Benham]

I have an idea for adding an extra step to IRV which has the effect of 
throwing out its compliance with Later-no-Harm in exchange for Minimal 
Defense, while trying to hang on to Later-no-Help.

*Voters strictly rank from the top  however many or few candidates they 
wish. Until one candidate remains, provisionally eliminate the candidate 
that is highest ranked (among candidates not provisionally eliminated) 
on the fewest ballots. The single candidate left not provisionally 
eliminated is the provisional winner P.

[So far this is IRV, used to find a "provisional" winner. Now comes the 
extra step.]

Interpreting candidates ranked above P as approved and also P as 
approved if ranked, elect the most approved candidate.*

This method might be called "IRV-pegged Approval" (IRVpA). It is more 
Condorcet-consistent than IRV, because when IRVpA produces a different 
winner that candidate must pairwise beat
the IRV winner  (so it keeps IRV's compliance with Mutual Dominant 
Third).  Also the IRVpA winner must be more approved than the IRV winner.

I'd be interested if anyone can show that this fails Later-no-Help.

Some other methods might gain from adding the same extra step, for 
example Schulze(Margins), MinMax(Margins) and Descending Solid Coalitions.
It will fix any failures of  Minimal Defense (and my  Strong Minimal 
Defense criterion) and Plurality.

Chris Benham