As much as I love reading reconciliation stories, it becomes dramatically more difficult when you understand the underlying reason as to why they left you in the first place.
The basic fact is, if someone leaves you for someone else, it's basically because they saw more value in the person than they did with you, which compelled them to move on.
Looking at things in that context, would you be able to trust a person like that?
A person whose easily willing to swing branches just because they can and forget everything you built together is a person who lacks serious character. If they can do that to you so easily, then it means they see little value in you and the things you could ever do for them. Why would you ever want to take back a person like that?
The only time a reconciliation would ever work with people like this is if they a) Couldn't find anyone better or make things work with the new person or b) Are older, disillusioned and no longer have the options they once had when they were younger and more attractive and are using you as a backup plan to settle with.
As much as I hate to accept any of this, It's basically the facts. Even if you did take them back, it will be very difficult to accept the fact that they could have moved on and not cared about you if things did work out for them.
I don't know about anyone else, but my feelings and love is worth much more than that.