Too Long, Didn’t Read
Instead of giving both players the option to end the game by server decision if either passes 3 times consecutively, it is proposed that only the player who passes 3 times in a row be given the option to end the game by server decision, the player who is still playing stones be not given that option
Reasoning
There are two most likely explanations when one player is playing useless moves after all dame and teire are filled: the player is new to the game, or the player is trolling (specifically by stalling)
New Player
I encounter new players more often than I encounter stallers, but even if I didn’t, they still warrant consideration. I am always excited to help beginners, and as the best way to learn is by doing, I am generally willing to play well past the end of the game if the beginner isn’t sure why something is dead (or alive). In such situations, it completely undermines the didactic value for the server to end the game, and if the beginner in this situation wanted the game to end, they wouldn’t even have to resign: they could just pass and agree to your scoring proposal (if you’re refusing to pass back, then see the next section on how this proposal handles trolls)
If the player is new, you have three things you might want to do in some combination: explain to them in chat why the game is over, let them play out their useless attempt to live until they’re satisfied that they can’t live, and/or force the game to end by server decision
However, as it stands now, you cannot repeatedly pass while letting them attempt hopelessly to live if you’re more than 10 points ahead, not because you would be given the option to end the game (you can just choose to ignore it), but because they will be given that same option, and being new, are likely to take it, thus unwittingly wasting the time you have invested in giving them the chance to better understand why removing dead groups at the end of a game works and cheating themselves out of that learning experience
This proposal would simply not give them that option: they have to keep playing, because they’re not passing. If they start passing, you can pass back and go to scoring. If you feel like there’s no point in continuing but they won’t pass, you can just take the option to score the game by server decision then. If they keep playing and you’re willing to play on to help them, you can continue passing and/or playing moves as needed, until you decide to take one of the previous two options
Troll
I do not encounter stallers as often as new players, but I have encountered them before, and it bears noting that this proposal will in no way interfere with the ability to force games to end by server decision against a staller
In such a situation, you want the game to end, and thus after filling all dame and teire, you must simply pass 3 times. Since you are the one passing, you do get the option to force-end the game by server decision, exactly as intended