Consensus is how strangers agree on one history with no referee. Every design answers the same attack: what stops someone from voting a thousand times (Sybil) or rewriting the past? The answers differ — the question never changes.

The three families

Proof of Work — vote with electricity. Miners burn energy guessing hashes; rewriting history means out-burning everyone (mining). Security = physical cost. Cost = energy use.

Proof of Stake — vote with money at risk. Validators lock stake; misbehavior gets slashed. Security = financial cost. Cost = capital concentration (delegation pools, staking/">liquid staking giants).

BFT voting (Tendermint-style) — known validator sets vote in rounds; finality is instant once two-thirds agree. Security = honest supermajority. Cost = capped, permissioned-ish sets.

Forks: what disagreement looks like

When nodes run incompatible rules, history splits — a fork. Soft forks tighten rules compatibly; hard forks break them (Bitcoin → Bitcoin Cash). Forks are governance made visible: the chain follows whichever rules the economic majority enforces.

How to judge any mechanism (the analyst's three)

1. What does an attack cost, in what currency? (Electricity? Stake? Bribing 12 validators?) 2. Who earns the rewards, and how concentrated? 3. What happens on the worst day? (Try the outage simulator on the terminal.)

Consensus is applied game theory: make honesty profitable and attacks
> ruinous, then let strangers act in self-interest. Every mechanism is that
> sentence with different numbers.

Next lesson: public vs private vs permissioned chains.