Bitcoin demonstrated the possibility of a financial ledger that operates without the need for a trusted central authority. However, concerns persist regarding its security and considerable energy consumption. We assess the consensus protocols that underpin Bitcoin's functionality, questioning whether they can ensure economically meaningful security while maintaining a permissionless design that allows free entry of operators. We answer this affirmatively by constructing a protocol that guarantees economic security and preserves Bitcoin's permissionless design. This protocol's security does not depend on monetary payments to miners or immense electricity consumption, which our analysis suggests are ineffective. Our framework integrates economic theory with distributed systems theory, and formalizes the role of the protocol's user community.