Theory 068/Information & Computation /Reliability engineering
Tolerance Needs a Multiplicity
More replicas are assumed to be safer. Beyond a point they add correlated failure modes.
Fault tolerance requires redundancy of a specific multiplicity set by the failure model rather than by the number of replicas, so adding replicas beyond the requirement adds cost without reliability when failures are correlated.
01The evidence
Distributed consensus requires a quorum, and systems with more replicas than the quorum show diminishing reliability gains and new correlated failure paths.
02The tension
Reliability is often pursued by adding replicas, which assumes independence. Shared infrastructure breaks that assumption and makes extra replicas marginal.
03The mechanism
Tolerance to f failures requires a multiplicity determined by the failure model: crash, omission, or Byzantine. Beyond that, extra replicas do not expand the tolerated set.
That makes the multiplicity the requirement, and predicts that reliability should saturate once the quorum is met, with additional replicas adding correlated risk.
04What this is not
Count models assume independence. This uses a multiplicity requirement, which predicts saturation and correlated risk.
05Predictions
- P1Reliability should saturate at the required multiplicity.
- P2Extra replicas should add correlated failures.
- P3Independence assumptions should fail in shared infrastructure.
06Refutation
Reliability rising indefinitely with replicas would favour count models.
07What it changes
It would change redundancy planning.