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Proof of stake (PoS) is a method for cryptocurrency verification through distributed consensus. In a proof of stake system, stakeholders are chosen as creators of a block through analyzing criteria combined with randomization.
The general idea of proof of stake is meant to provide an algorithm that equalizes probability for figuring out a selection process for block creators. Some additional elements include delegated proof of stake protocols that use various nodes, and randomized proof of stake which, again, uses the principle of randomization.
An alternate method is to use proof of work, where the mining work is actually documented and acts as proof of transaction or asset status. However, proof of work is more energy intensive, and so proof of stake can be a way of saving resources.