Yes, this seems like the most likely arrangement - in a poker game if a significant fraction of your opponents are colluding without your knowledge then you're in trouble anyway, so you already have that level of trust. If you can use the same level of trust to claim the prize as you already implicitly have - maybe that 2/3rds of the players systems agree that a particularly player won, that would probably be good enough.

Another approach might be that everyone playing a game also automatically randomly observes another game somewhere, and their view of what happened is added to the trust calculation.