Implementing reliable pairwise average in distributed systems
Full reliability is simply not possible in (distributed) systems; at some point of fractional system failure you reach a level where system state and/or data is no longer recoverable. You should consider that this is dependent not only on node failure, but also on data distortion (bits might flip as they travel across the network, etc.). As a result, you can reach very high levels of certainty about correctness but it's very difficult if not impossible to guarantee it.

One of the most well known examples of this is the Byzantine Generals/Byzantine Fault problem, which deals with consensus in networks (https://en.wikipedia.org/wiki/Byzantine_fault).