When should iterations end?

[Mike Ossipoff]

Steve Eppley writes:
> 
> 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.

As soon as it happens that a candidate currently tops more
than half of the ballots, isn't that a good reason to say
we've got a winner? If a different winner would result from
continued eliminations, in IR-1, if we continued the eliminations

till someone has a majority of votes cast, or till there's only
1 un-eliminated candidate, that seems less legitimate to me, 
because I don't feel that MPV eliminatations are a legitimate
way to find a winner. So it seems better to quit as soon as
the eliminations give someone a majority. At that time the
eliminations' dirty-work can be stopped.

> 
> >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.

No typo. I'm talking about the distinction between having votes
from a majority of the voters, versus having a majority of votes
cast--two different things, when people can cast more than 1
vote. Having a majority of votes cast is a more demanding requirement.

Say, on the average, people have given votes to about
3 candidates, at a particular point in an IR-1 count. If
a candidate has a vote total equal to at least half the
number of ballots, that means that he currently tops at 
least half of the ballots.

That's what I meant by going by the requirement of being voted
for (topping the ballots of) a majority of the _people_, as
opposed to having a majority of the _votes_ that have been
cast (where a ballot having N candidates in 1st place is
counted as currently giving a vote to each one of them).

Counting people, I claim, is more meaningful than counting
votes cast, when people are allowed to cast more than 1 vote..


But to have a majority of the votes cast would require
3 times as many, as compared to having a vote total
equal to half the number of voters (or, which is the same
thing, topping half of the ballots).

> 
> -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.

But a candidate outside that set (that set now ranked 1st by
a majority) is beaten by every candidate in that set. So,
by Smith//Condorcet, the winner of that round has to come
from that set, provided that the candidates in that set are
the only ones who are 1st choice of a majority.

True, with plain Condorcet, a circular tie among those candidates
in that set can result in somene outside of it winning. But say
the method is Iterative Smith//Condorcet, so that can't happen.

So since the winner of that round can't be anyone outside that
set, no ballot belonging to a member of that voter majority
is going to give 1st place status to anythng that they
like less, anything outside that set. So a member of that
set will be the final winner in Iterative Smith//Condorcet.

Because isn't it true that in Iterative Condorcet, a ballot
doesn't extend 1st place status to its next choice unless
nothing that it so far ranks as 1st currently has a win?
Since one of the candidates that that majority ranks 1st
has a win, that majority won't extend 1st place status again.

> 
> -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.

Iterative Condorcet or Iterative Smith//Condorcet can probably be
said to _virtually_ meet the strong LOE criterion. Only an extremely
contrived situation & prohibitively difficult cheat strategy
could prevent its compliance. Or so it seems to me.

> 
> -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?  

Yes.

> 
> Why not just leave all the candidates qualified and continue
> iterating until no more iterations can be made?  If candidates are 

Because in Iterative Plurality, unlike Iterative Condorcet, 
it's easy to have a situation where, via the next iteration,
some voters will give away the election when their candidate
would otherwise end up as the final winner. Iterative Pluralitly
is an imperfect method, and it seems best to stop as soon
as 1 or more candidates have votes from a majority--which shows
as a vote total equal to a majority of the voters. An imperfect
method's procedure should be stopped as soon as there's a result
that's at all satisfactory, I claim.

> dropped or the iterations are aborted, can the method still satisfy 
> the LOE criterion?

It will still meet LO2E-2. I believe that Iterative Plurality
can't meet LO2E-1 or GMC. Just LO2E-2. Not Truncation-Resistance
either. But I feel that it's better than ordinary Bucklin, because
it has a ballot give a vote to its next choice only if something
lower on that ballot currently has a plurality, where Bucklin
has a ballot give a vote to its next choice unless something
ranked higher on that ballot has a majority.

> 
> >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? 

I meant to say "would win as the final winner of the election,
if certain ballots hadn't extended their approval sets to lower
ranked candidates."

I realize that could result in a mess, with an endlessly repeating
cycle of votes given & taken back, and though that can be
dealt with, by having the involved ballots cancel the
approval set extensions involved in the repeating cycle, it
seems to complicate the method too much, and tends to negate
the simplicity & familiarity advantage of a method based
on Plurality.

About your last question, I agree that it's  not clear what
I meant there, and I don't know if I myself knew exactly.
But the rule could say: "If there's a set of voters who
have extended their approval set to candidate Z, and if
someone that all those votes rank over Z would win as the
final winner of the election, only if those voters hadn't extended
their approval sets beyond that better-liked candidate, then
those voters' ballots shall be counted as dropping Z from
their approval sets." I still can't say for sure if that's
unambiguous & sound, but maybe it is now.


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


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