My inclination is to think that in the short term (and assuming that there is some desire to get back together) the dumpee is more likely to want to get back together. But long term, I think the dumper decides they want to get back together.
So in that sense, the dumpee will make the first move. But five years from now, look out world, the dumper is going to try to get back on the scene.
Here's why: getting dumped is a major shot to one's ego. Nobody wants to get dumped and most of us don't have the capacity to understand why the person we've spent all of this time with doesn't recognize how great a catch we are. Most of us take it as a direct shot to our pride and ego. So when you get broken up with, you may be inclined to see if you can work it out, both because you care and because you want to prove that you're not a failure at something. The person who did the dumping has already made a decision and for all intents and purposes, is happy with it. So they're less inclined to want to make a "first move" when they kind of already did. They booted you.
So early on, your pride (as the dumpee) takes you on a rollercoaster of emotions and you may very well make several (failed) attempts to reconcile - even offering to fix whatever it was that caused the breakup. But at some point, you're forced to move on. And you do.
Which is where the longterm problem comes in. Years later the dumper may (or may not) realize that they made a mistake and attempt to get back in touch and/or reconcile at which point you've moved on - because you were forced to - and will rebuke their advances, if you're happy anyway.
It just depends on the timing. Dating is no hard science. If it was, it wouldn't be a gazillion dollar industry. Just ask physics.