The consensus mechanism on Namada provides an algorithmic way for validators to communicate votes and collectively agree on a consistent state. The algorithm, coupled with a cryptoeconomic voting power allocation mechanism called "proof of stake", is designed so that that non-colluding validators acting in their (economic) self interest will follow the consensus algorithm in a predictable manner.
The validity-predicate based execution mechanism is inherited from the architectural design philosophy of Anoma. The fundamental idea is that a "valid state" is defined as that which satisfies a set of boolean conditions. These boolean conditions are encoded by functional "validity predicates", which are invoked whenever a state is being proposed. If all validity predicates in the system return the boolean
true, this defines a valid state which validators can vote on. The validity predicate based mechanism differs from the traditional "smart-contract" based execution model, where a valid state is instead defined as that which results from a series of pre-defined valid execution steps. These execution steps are defined within the smart contract, and verifying the validity of the new state requires each validator to run the series of execution steps.