I have a couple of times likened MoV to a social consensus mechanism, but I think that may be inaccurate. If compared to blockchain technology, MoV is used to enforce laws, to go from one state to the next, the state transition function.

Proof-of-work, proof-of-stake, or proof-of-power, are used to select what state to use, just like majority consensus in nation-states (proof-of-power is exact equivalent, majority consensus), they are social consensus mechanism to decide which state to follow, whereas a monopoly on violence is used to enforce laws, a very primitive state transition function.

Government without a monopoly on violence

Proof-of-power is majority consensus, exact equivalent to what has existed in nation-states, supporting a free market for government within a permissionless state, a "network-state".

Whitepaper: https://github.com/resilience-me/proofofpower/blob/master/Proof-of-power.pdf