How the interplay between power concentration, competition, and propagation affects the resource efficiency of distributed ledgers

Forks in the Bitcoin network arise as a natural consequence of competition within its Proof-of-Work consensus protocol, but lead to resource inefficiencies and compromise network security. The frequency of forks, therefore, serves as a critical indicator of a distributed ledger's operational efficiency. We model the fork rate in a network of heterogeneous miners as a function of the number of miners, their hash rate distribution, and block propagation times within the peer-to-peer infrastructure. Empirical evidence demonstrates that fork rates are well-approximated by the ratio of the median block propagation time to mining time. Our model provides a theoretical foundation for this relationship while also capturing the fork rate's additional dependency on miner heterogeneity. Our work establishes a robust mathematical setting for investigating factors often unobservable from existing empirical data, such as power concentration, competition, and asymmetric propagation times in distributed networks. Using this as a null model, we can detect anomalies in the historical fork rate-e.g. around 2016-indicating either high concentration of mining power or strongly heterogeneous latency in the Bitcoin network. We also estimate the mining power wasted in mining blocks on top of a nonlatest block, which potentiates accidental forks. The wastage amounts to approximately 16,000 MW in the most recent year, equivalent to half of the power generated in the United Kingdom.