Only $10 of that $20 is for answering--the other half is just for
reading all the way through the question, I realize it's long and
complicated, but I've tried to provide all, and only, the background
you'll need for a good answer.

There's a Girl and a guy (Devoted) who had a wonderful, monogamous
relationship; honest and caring, for a year and a half.  Girl went on
a trip and was attracted to another, Devoted reluctantly acquiesced to
the fling, and she found herself swept away further and further by
New.  This wasn't just a fling anymore, but she still wanted Devoted
more permanently, even though she wanted New more passionately.

Devoted decided that fidelity wasn't the most important factor in his
relationships--although he was hurt, he still wanted Girl back, and
proposed polyamory since two months after meeting New, and a month
after her trip ended she still couldn't get over him.  Girl loved the
idea, but since New was a pretty traditionally minded guy (she'd
almost lost him for two weeks after telling him about the relationship
she'd already had with Devoted during their fling) she was sure he'd
break off all relations permanently if she suggested polyamory.

How can Girl convince New to accept polyamory?  She tried for two
months to choose one or the other but can't give either up, and she
feels very guilty for the hurt she's caused them both but doesn't want
the loss or pain she may "deserve," so answers involving either of
these two factors won't help.  An alternative solution may be
acceptable, but I consider it a smallish chance.

This looks like a recipe for disaster.

Why is it that the poor, the sick and the benevolent seem not to have
such dilemmas as described? Maybe it's because they don't have any
cake at all, let alone the choice of wanting to eat and also to have
at the same time.

It is not so much a love triangle, but rather a "Y" shaped interlude
as in the forked tongue of a snake. To even suggest such a term as
polyamory can only lead to further mistrust. (I can't find polyamory
in my dictionary, but I get your intended meaning). You already know
that Google will not provide an answer, only comments.

I believe that the wrong question is being asked in the first place.
The question should not be "how to convince?". New was not aware of
Devoted, until after. Hence his admirable values in backing off then.
Devoted's acquiessence creates perhaps an exciting opportunity for him
to suggest the same with a 4th party. (Keeping a card up his sleeve of
"It's OK to do this"). Girl may not like it when the shoe is on the
other foot. Imagine 4th party doing the same, and so on. Girl will
then leave Devoted for New. New will never trust Girl. Devoted will
end up alone. Everyone gets hurt. Bloody wonderful. You are correct.
It's complicated .. but need not be.

The question should perhaps be "Who will have the courage to be honest here?"

Maybe all three can meet to sort it out. I doubt it, as Girl is
enjoying her indecision in being wanted by two men.

Dr. Phil  :)

Thanks for the in-depth commentary, silver777.  I didn't realize I
couldn't tip anyone except the actual answerer, but if you've a paypal
account or some such thing I'll get $10 for the reading and true
thought into it.

There's more honesty going on than you think, though.  Girl has
admitted from the very first that she wouldn't be ok with devoted
doing the same thing, while admitting that made her a very bad
girlfriend.  Devoted's fatal flaw isn't lust, though--long ago he had
a foursome and enjoyed but was underwhelmed--it's just having a little
too much of the invertebrate.

I agree with you, though, that New's only fault was being in the wrong
place, at the wrong time, and being really attractive.  But from all
my analysis the problem isn't a lack of honesty, it's just that,
honestly, it doesn't help here.

Hi Reality,

No thanks, I don't want your money as offered.

I'm now more confused than your stars in your sequel. Perhaps I should
have left Probo's comment as the answer. It's true in summary, to the
point and succint.

Phil

I suggest that Devoted cherish the memories with Girl, and move on. 
The key to influencing the behavior of someone who is "one the fence"
about a relationship decision is to create scarcity.  In other words,
if Devoted met and talked about someone else, and frequently had plans
with someone else, Girl would likely realize that she was in danger of
being left with nothing and would abandon New and try to mend things
with Devoted.

Just demote Girl in your mind to friend status for a while and things
will improve drastically within 6 months.

I think that you're asking these questions in the wrong forum.
Silver777 has never even heard of polyamory, and so is not able to
provide a perspective that is related to any experience about
polyamory. If you ask here, you will get only answers that reflect the
mainstream approach to relationships.

Try the following: 
http://groups.yahoo.com/group/spiritual_polyamory/
http://www.polyamory.org/
http://www.worldpolyamoryassociation.com/

I can personally vouch for some of the relationship coaches that you
can link to at the World Polyamory Association site. (Dawn and Akien)

A couple of comments. Devoted's experience in a foursome is more of a
sexual interlude than an experience of polyamory. However, his
willingness to accept your choice--not to choose between two loves--is
truly polyamorous, and if you think about it, very sweet, considering
that he has not really had the experience of polyamory that would
enable him to make such a decision with full awareness.

In addition, your desire not to make a choice is fully acceptable in
mainstream thinking, if you decide to make it so. Consider the movie
"Casablanca," which is considered one of the most romantic movies in
history. In this movie, the Ingrid Bergman character (Ilsa) refuses to
choose between the two men that she loves. At the end, the Humphrey
Bogart character (Rick) chooses to send her off with Laszlo because of
his love for her. In putting his love for her above his own desires,
he was expressing a polyamorous emotion known as "compersion," which
is defined as "your joy is my joy."

My advice to you: do not allow your programming to override the
choices of your heart. If you truly choose to love both, you are most
integrated as a human being if you hold to your choice. You are not
responsible if one goes away; however, you can potentially negotiate a
win-win-win solution if you contact and use the appropriate
professionals who have experience facilitating situations like this.

Hopefully devoted realises that once a cheater allways a cheater,
there will allways be some "new" come along and catch the cheaters
glad eye. Hopefully mr devoted will pack his bags and leave.