What are we trying to achieve? It’s very simple actually — all we’re trying to do is maintain a simple table of balances on a piece of paper. This table will show how many coins each of our heroes has. The trick is, because we can’t have one piece of paper that holds the only source of truth — we’re going to have to keep things equal and let each of the gang maintain their own version — this is the decentralized part. And naturally, we’re also going to hope that all 4 pieces of paper eventually show the same thing — this is the consensus part.
So what would this piece of paper look like?
This paper is the first one we agree on — that’s why it’s marked as day 1. Where did these balances come from? We’ve previously agreed it’s fair that each of the gang starts with 100 coins. We’re also going to need one of the survivors to write this paper. It doesn’t really matter who, so let’s take Hugo. He will be the one to publish this paper to everybody and make sure they each save a copy (the island has an amazing photocopy machine, I forgot to mention).
Since coin balances are expected change, we’re going to create a new updated piece of paper at the end of every day. It may not always be Hugo who publishes the update though — we want to keep things as fair as possible after all.
Another important part, due to the lack of mutual trust in the group, is having each of the gang confirm the status update individually. An easy way to achieve this is having each one of the survivors sign each of the papers — but only if they agree with what’s written on it.
How many people need to sign a paper for it to be considered final and approved? We need to reach consensus, so a majority will do. Since we have 4 people in total, a majority is at least 3 out of 4. The paper above was signed by all four so it’s definitely final. Why don’t we want to require all four signatures on all papers? Because this will allow one individual to jeopardize the entire process. If Sawyer goes on a fishing trip for a few days, the gang can’t update balances until he gets back — this gives one person too much power. Why do we even need a majority? Why isn’t 2 out of 4 signatures enough? Because if we only require 2 out of 4, we may end up with 2 people (like Hugo and Sawyer) signing one version of balances, and the other 2 people (Kate and Jack) signing a different version that doesn’t match. We can’t have two conflicting versions of reality both considered final.