When should iterations end?

[Steve Eppley]

Mike O wrote:

>In IR-1, my reason for stopping the count when 1 or more
>alternatives occupy or share highest position in half of the
>rankings is because I consider a majority to be a compelling thing. 

But why should the "largest majority as soon as someone has a
majority" be so compelling?  Maybe another candidate would end up
with the largest majority after further iterations.

>If we were to express it in terms of votes, so that you're giving
>1 whole vote to each alternative occupying or sharing highest
>position in your ranking, at any particular time in the count,
>and if we were to say that we won't stop the count until some
>alternative has a majority of votes cast, that seems to be
>not in the spirit of majoritarianism, and it seems an unreasonably
>high requirement for winning by majority. It's a majority of the
>_people_ that counts.

I don't understand this paragraph.  Is there a typo?  Perhaps an 
example will help me understand it.

-snip-
>As for Iterative Condorcet, no one gives 1st choice status to
>their next choice unless nothing they've ranked higher has a 
>win. But if a set of alternatives all are now included as 1st
>choices by a majority, then they beat everything else, and 
>one of them has a win. 

Not necessarily, I think, since one of the other candidates who is
currently beaten by a majority may receive more "approvals" after
the next iteration.

-snip-
>So it doesn't seem to me that Iterative Condorcet needs a
>rule to stop the iterations, other than stopping them when
>every ballot has given 1st choice status to every 
>alternative that it lists higher than the one currently
>the winner, and that it opts to extend the use of that option
>down to. In other words, I feel that Iterative Condorcet
>doesn't need a special rule to stop the iterations before
>they naturally stop under the basic rules of Iterative
>Condorcet that Steve initially specified.

Stopping the iterations early would also take away the guarantee that
Iterative Condorcet satisfies the strong LOE criterion (if it turns
out that our preliminary analysis that it satisfies LOE is indeed
correct), I think.

-snip-
>But, it does seem that Iterative Plurality could use a rule
>to drop from the election any alternatives other than the
>ones that occupy highest position in at least half of the
>rankings. As in IR-1.

I don't understand this paragraph.  When would this rule apply?
After the first iteration in which at least one candidate has a 
majority?  

Why not just leave all the candidates qualified and continue
iterating until no more iterations can be made?  If candidates are 
dropped or the iterations are aborted, can the method still satisfy 
the LOE criterion?

>In fact there's another enhancement that could be very helpful
>in Iterative Plurality: Cancelable votes. So the method would
>be "Cancelable Iterative Plurality":
>
>If your ballot has given a vote to candidate Z, and it later
>turns out that a candidate higher in your ranking would win
>had you & others not extended their approval set down to
>that candidate, then your ballot takes back the vote it
>gave to that alternative. 

What does it mean to say that another candidate would win?  By
"would win" do you really mean "would lead after the iteration"? 
How can this (or some other interpretation) be calculated when there
are so many ballots which might or might not simultaneously cancel
their iteration-caused approvals? 

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