The assumption that most participants follow the rules. Not math, just people or companies behaving.
Why it matters: Some protocols are exactly as safe as this is true.
The details
On the map: more than half (or two thirds) of the parties follow the protocol
Not a mathematical assumption: it says more than half (or two thirds, against actively cheating parties) of the participants follow the protocol[1, 2].
It is what lets secret-sharing-based MPC be unconditionally secure. If an attacker controls enough parties, privacy and correctness fail no matter how good the mathematics is.
Rests on
If any of these breaks, this breaks too.
Good randomness(needed by everything in the unconditional box (and everything else))
Michael Ben-Or and Avi Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation. Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88, 1988. doi:10.1145/62212.62213
David Chaum, Claude Crépeau and Ivan Damgard. Multiparty unconditionally secure protocols. Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88, 1988. doi:10.1145/62212.62214