I'm surprised that nobody has mentioned any of the 3 attacks from Prosperity on their ban list.
I don't think that having an intersection of both players ban lists would be too hard to program or explain to users. You could phrase it as "pick up to 5 cards to never play with. Now you can pick as many cards as you want that you won't play with if your opponent agrees not to". At the same time, it being game-able is a valid concern.
I will say this though, the Union list is, in my opinion, at a greater risk of being gamed in a more unscrupulous way. For instance, when crafting my list, why would I bother to put Possession on there if I believe the chances of my opponents doing so on their list are high? Why don't I just create a bot that goes through every player's ban list (assuming they're public), find the most common cards, then be sure that I don't put them on my list. Now I have confidence that I'm X% likely to not encounter all of those cards I would actually want to ban, and I can still ban 5 additional cards that I'm bad with.
And if we overcome the above problem by making the ban lists private, I can still keep a log of all of the banned cards from every game I play. The only solution to that problem that comes to mind is to not tell players what cards are being banned at all, which I'm not a fan of.
I question whether solving these issues would even be worth it. The very nature of Dominion means that I won't actually see my least favorite card often because the card pool is always growing. If we ignore the possibility of a Bane card, the current odds that one specific Kingdom card will be in the game is 4% (which will decrease to 3.53% when Nocturne comes out). Granted, the odds that one of my 5 least favorite cards comes out is 17.25% (15.51% once Nocturne comes out). But if that sounds like a lot to you, remember that not all cards are hated equally. I may have 3 cards I despise and 2 that I feel "meh" about, and that 17.25% just refers to the odds that 1 of those 5 comes out to play.
There's also the issue that it could cause resentment from players who like certain unpopular cards. If I buy Alchemy because I really love Possession (and am apparently a statistical anomaly), and then it never comes out on the table, I'm gonna be frustrated that I spent money on something I don't get to use. There's already only a 4% chance that I get to play with Possession in a game. Now consider if 80% of the community bans it. That means I only have a 20% chance of playing a game where Possession is even an option (ignoring any matchmaking probabilities), just to get a ~4%* chance that it shows up. So in total I would have less than a 1% chance of ever seeing Possession.
I don't agree with the notion that we only have to worry about the hated cards that do get played, and not the beloved cards that don't get played. There are certain cards that I get really happy to see, and if I paid for them, I don't think it's fair that I have lower odds of seeing them just because the people I play against online can't deal with them on the rare occasions they come out.
Final point: I worry that this kind of thing will lead to increased community group think. Surely Donald is familiar with our occasional tendency to just decide that a certain card is broken, too strong, too weak, too worthless, etc. only to later realize that maybe we made a bigger deal about it than it really was. I think that that moment of realization only happens when we play with those cards more. So if the community just decides "this new card from Nocturne is stupidly broken, it's just an auto-buy every game", and everyone starts banning it, then it's going to take far longer for people to start using it enough to fairly assess it.
*The reason this is phrased as approx 4% is because now in this scenario we're using bans, which decreases the card pool by up to 10 cards, depending on if my opponent and I have duplicates or not. So the odds that Possession shows up if neither of us have banned it becomes anywhere from 4%-4.17% before Nocturne, and 3.53%-3.66% after Nocturne
