[EM] Is this method monotone? (Or: finding dynamics of STV nonmonotonicity)

[Kristofer Munsterhjelm]

Consider the following method:

First calculate the Ranked Pairs social ordering.
Then repeatedly:
	- Check if any candidate has more than a Droop quota of first preferences.
	- If so, elect that candidate and eliminate him.
	- If not, eliminate the currently uneliminated candidate who's ranked 
last on the RP social ordering.
	- Repeat.

This should minimize the effects on nonmonotonicity due to loser 
elimination. In IRV, the nonmonotonicity is entirely due to the loser 
elimination effects, but Ranked Pairs passes LIIA and so loser 
elimination should have minimal effect.

So, would this method be monotone? Probably not (maybe it has a failure 
mode similar to the QBS), but it could be instructive to see just how 
much monotonicity failure is due to *winner* elimination.



This method would be quite centrist/consensus biased in practice. 
Whether that's a feature and a bug would be for people to decide. In one 
dimension, imagine the distribution of support being divided into bins 
that are each a Droop quota large. This method would (if I'm not 
mistaken) elect the candidate closest to the center - i.e. closest to 
the edge of the bin facing the distribution's median - in each bin.

Better would be this:

Repeatedly:
	- Check if any candidate has more than a Droop quota of first preferences.
	- If so, elect that candidate and eliminate him.
	- Otherwise, do Ranked Pairs with the reduced ballots (currently 
eliminated candidates removed), and eliminate the loser.
	- Repeat.

That's more likely to fail monotonicity, but should be less 
center-biased, and the nonmonotonicity events would be limited to when 
the Ranked Pairs ordering changes due to a winner being eliminated.

(On a side note, if we had a method that would place candidates ranked 
first by more than a Droop quota above any other candidates *and* would 
pass LIIA, then we would definitely have monotonicity. But I don't think 
that's possible, because this property implies majority in the 
two-candidate case, and LIIA plus majority implies Condorcet, which is 
incompatible with the DPC.)

-km