authority, proof of space, proof of burn, or proof of elapsed time. Contrasting with the above permissionless participation rules, all of which reward participants in proportion to amount of investment in some action or resource, proof of personhood protocols aim to give each real human participant exactly one unit of voting power in permissionless consensus, regardless of economic investment. Proposed approaches to achieving one-per-person distribution of consensus power for proof of personhood include physical pseudonym parties, social networks, pseudonymized government-issued identities, and biometrics. Consensus number To solve the consensus problem in a shared-memory system, concurrent objects must be introduced. A concurrent object, or shared object, is a data structure which helps concurrent processes communicate to reach an agreement. Traditional implementations using critical sections face the risk of crashing if some process dies inside the critical section or sleeps for an intolerably long time. Researchers defined wait-freedom as the guarantee that the algorithm completes in a finite number of steps. The consensus number of a concurrent object is defined to be the maximum number of processes in the system which can reach consensus by the given object in a wait-free implementation. Objects with a consensus number of can implement any object with a consensus number of or lower, but cannot implement any objects with a higher consensus number. The consensus numbers form what is called Herlihy's hierarchy of synchronization objects. According to the hierarchy, read/write registers cannot solve consensus even in a 2-process system. Data structures like stacks and queues can only solve consensus between two processes. However, some concurrent objects are universal (notated in the table with ), which means they can solve consensus among any number of processes and they can simulate any other objects through an operation sequence. See also Uniform consensus Quantum Byzantine agreement Byzantine fault tolerance References Further reading Bashir, Imran. "Blockchain Consensus." Blockchain Consensus - An Introduction to Classical, Blockchain, and Quantum Consensus Protocols. Apress, Berkeley, CA, 2022. Distributed computing problems Fault-tolerant computer systems