I was thinking of the problem of naming&shaming, victims don't want to reveal themselves. Yet the public wants to know, and have some confidence in the veracity of statements. Such confidence could arise for instance from multiple victims naming the same person. I was thinking cryptography could come to the rescue.
I'm having trouble even in the formal definition part. Initially I though multi party computation could allow a group of people to each name (or not) and only if a name passes a threshold is it revealed, and all members of the group could attest the name passed the threshold. But thinking of practice issues, we may want a async process, where after setup different people submit their testimony separately with minimal back and forth. We may not know in advance who will participate and want to be able to work with a subset members. The minimal number of people to ensure reasonable anonymity is rather small say 100, but we may want to increase the requirement significantly if we are thinking about minimum number of colluding members to reveal which specific member named someone.
I quickly run into impossibilities, If we allow ad-hoc groups to form and vote together then a not so large malicious group could break anonymity. I'm looking for a solvable variant of this problem.