[EM] Approval & CR are 2nd best; Approval STV

[Kevin Venzke]

Forest,

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> > A method I would rank between Condorcet and Approval is AER, or "Approval STV."
> > It's IRV, but the elimination order is based on approval.  Because the approval
> > counts don't change, and the elimination order is thus fixed from the beginning,
> > it's monotonic.  It's intuitive, and gives similar results to WV methods.
> 
> What if you recalculated the approval order after each elimination by
> making a minimal adjustment to the approval cutoff on each ballot so that
> no ballot that still had any candidates ranked would either approve all or
> disapprove all candidates?
> 
> Would the method still be monotonic?

I'd say the answer must be "no," although I'm having trouble thinking of a concrete
example.  In AER, the only effect of raising a winner on some ballots is to
possibly push him back in the elimination order.  But a winner is never eliminated,
and this can't cause any candidate to receive a majority *earlier* than our winner
did, so the winner must still win.

If you raise a winner in the variation you're talking about, you can e.g. cause
some other candidate to receive less approval ("minimal adjustment") and get eliminated 
at an earlier stage.  So the problem is that raising a winner can unpredictably alter the 
order of elimination.  This is a problem of plain IRV, too.

I think only straight Approval can be used to set the order and preserve monotonicity,
because it has the property that "boosting" one candidate can never alter the method's
ranking of the other candidates.

For instance, it wouldn't be enough to have an IRV variant where the elimination
order is based solely on initial first preferences.  This is because giving a winner
more first preferences necessarily takes them away from some other candidate, with
unpredictable consequences.

Kevin Venzke
stepjak at yahoo.fr



	

	
		
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