Looking into it, this is something that has disturbed me to be honest. Both views seem pretty lousy to me, but the Orthodox view seems almost absurd. A limit of three marriages? Where are the patristics to support this? It is entirely abominable. We only have this doctrine because of some event involving an emperor a long time ago? That seems very silly to me; like the founding of the Anglican Church. How do we really support a view like this? On the other hand, I think that the Roman Catholic view seems more 'on the right track' seeing that divorce is much more frowned upon and Christ's words about it taken more seriously, but this whole Annulment system is entirely cruel seeing the effects that it has on some families and how it pretty much just seems to be an 'easy way out' to offer people divorce without technically divorcing them.
"it is entirely abominable"?
Frankly, and unfortunately having experienced it, it seems quite reasonable to me. At some point, multiple marriages begats the question of how seriously it is taken.
In my case, my first marriage didn't work out. I had to go through the spiritual court to have it dissolved. Was not fun, and the Priests asked some very pointed questions. My ex ended up re marrying in the Catholic Church. They ended up annulling our marriage due to a "marital defect". Even though it didn't affect me, it still made me angry in that they pervert a reason to grant annulment.
As for me, I've been married for 25 years, so I'm thankful we have a Church that grants "economia" in these situations. We are fallible, so if we can learn from our mistakes that's a good thing. Making the same mistake over and over is a different story.
Now, to hijack the thread, I have more of an issue with Priests not being able to remarry after the death of a Prebytera, especially if they have small children. There has to be a better answer than they either remain celibate or leave the Priesthood.