When should iterations end?

[Steve Eppley]

In basic Instant Runoff where either equal rankings aren't allowed
or N equally ranked candidates each receive 1/Nth of a vote, the
shortcut of stopping the iterations when one candidate has more than 
50% of the votes gives the same result as the nonshortcut of 
iterating until there's only one candidate left.

But in some iterative methods (Instant-Runoff-1 and the new class of
iterative methods we've recently been exploring for their strong LOE
protection) it's possible for more than one candidate to have
a majority while it's still possible to iterate further, and this
candidate might not win if the iterations are allowed to continue.

In some of Mike O's recent messages he's suggested stopping the
iterations as soon as one or more candidates have a majority, and
then picking the one with the largest majority.  Is that better than
iterating further?  I can see its time-saving advantage when the
ballots are being counted by hand, but that's not by itself a
compelling reason. 

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)