Abstract

Budish 2025 derives a deterrence condition for proof-of-work consensus under a no-rule-of-law scope condition. This paper extends his framework along two dimensions: it replaces the monolithic anonymous attacker with a pool-centred coalition whose effective capacity depends on member retention, and it admits legal sanctions into the attacker’s payoff. Setting both extensions to zero recovers Budish’s baseline exactly. The model introduces a value-dependent legal term subject to an enforcer participation constraint: below the enforcement threshold, protocol costs alone determine deterrence. As transaction value rises, the legal term becomes positive and the model distinguishes payout-distortion exit from liability-driven exit. Pool-level data for March 2026 show that the coordination layer is concentrated among publicly attributable operators in a small number of jurisdictions. Pure flow-cost security applies where the enforcer participation constraint binds; for large-value attacks, deterrence is jointly determined by protocol costs, legal sanctions, reputational loss, capital destruction, and longest chain exclusion.

Keywords: Rule of law, Legal enforcement, Blockchain security, Mining pools, Reputational sanctions, Double-spending