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Proof-of-Weight (PoWeight) is a blockchain consensus mechanism that gives users a 'weight' based on how much cryptocurrency they are holding. Proof-of-weight consensus mechanisms are based off of the first Proof-of-Weight consensus model used in the cryptocurrency Algorand, which was developed by researchers at the MIT Computer Science & Artificial Intelligence Laboratory.
The Proof-of-Weight consensus mechanism remains secure as long as the majority of weighted users are honest, and protects the network against double-spend attacks. Each time a transaction is made on a blockchain using the Proof-of-Weight consensus mechanism, the network creates a committee of random network members and assigns each member their 'weight' (based on how much currency they hold on the network) which slightly centralizes the consensus process within the random committee.