In leader-based consensus protocols, the leader must distribute each block to all processors. Without erasure coding, the leader sends full copies — a data expansion rate equal to the number of participants. Erasure coding reduces this by sending fragments that collectively reconstruct the block. The data expansion rate — total data sent divided by payload size — determines how close throughput approaches the network bandwidth limit.
Protocols with two-round finality (one voting round) cannot achieve a data expansion rate below approximately 2.5 (arXiv:2603.11797). This bound is tight — existing protocols match it. The constraint is fundamental: with one voting round, the leader must ensure that any honest quorum can reconstruct the block, and the overlap requirements between quorums force redundancy.
Three-round finality breaks through. With two voting rounds, the data expansion rate approaches 1 — essentially no overhead. The mechanism: the second voting round provides a recovery path. The leader attempts an aggressive erasure code (low redundancy, high efficiency). If reconstruction fails — because Byzantine processors withheld their fragments — the second round detects the failure and falls back to a more conservative code. Consistency is never compromised because the protocol doesn't commit until reconstruction succeeds.
Two protocols realize this. Carnot 1 requires n >= 4f+1 processors and achieves clean design with no additional fragment dissemination. Carnot 2 operates at optimal resilience n >= 3f+1 but needs extra fragments when Byzantine processors interfere. Under favorable conditions, both approach expansion rate 1; under adversarial conditions, they revert to 1.33 and 1.5 respectively.
One additional voting round buys a factor-of-2.5 improvement in bandwidth efficiency. The extra round is not delay — it is a recovery mechanism that makes aggressive coding safe.