[EM] IRV variants

[fsimmons at pcc.edu]

> I don't get it. (I am confused by your explanation of the 
> algorithm).
> How do you think this is better than your latest version of 
> Enhanced DMC?

It takes care of the chicken problem.  But forget my confusing process; the IRV- Condorcet you 
describe here is a simpler solution, as long as you allow equal rankings, and count them as whole (as 
opposed to fractional):

> 
> I think a good method is the IRV-Condorcet hybrid that differs 
> from IRV 
> only by before any and each elimination
> checks for an uneliminated candidate X that pairwise beats all 
> the other 
> uneliminated candidates and elects the
> first such X to appear.

Yes this is simpler.

> 
> That of course gains Condorcet, and it keeps IRV's Mutual 
> Dominant Third 
> Burial Resistance property.
> So if a candidate X pairwise beats all the other candidates and 
> is 
> ranked above all the other candidates on more than
> a third of the ballots then (as with IRV) X must win and a rival 
> candidate Y's supporters can't get Y elected (assuming
> they can somehow change their ballots) by Burying X.
> 
> Does your method share that property?
> 
> > 49 C
> > 27 A>B
> > 24 B
> >
> > Candidate A starts out as underdog, survives B, and is beaten 
> by C, so 
> > C wins.
> 
> 
> From what I think I do understand of your algorithm 
> description, 
> doesn't candidate B start out as "underdog"?

Yes, I was in too much of a hurry when I wrote that.

Also contrary to my hopes the method turned out to be non-monotonic, because the IRV elimination 
order can eliminate a candidate earlier as a result of more first place support.  Only elimination orders 
without this defect can be used as a basis for a monotone method.

Forest