German translation: HowTrustNetWorksDeutsch
When a new user, who we will call Alice first gets the TrustNet scanner, she has no connections to anybody else. All the people in the list will have a score of 0.0.
If Alice meets somebody she likes, she can give them a positive rating. Once Alice has rated Bob, Bob will appear with a score of 10 on her scanner. Direct ratings always result in a score of +10 or -10. It doesn't matter if Alice knows 20 other people who hate Bob. Once Alice rates Bob directly, her judgement is considered absolute, and her friends' opinions will be ignored.
Now Bob's actions start influencing Alice's scores. Bob meets and rates Carol and Dave positively. The result of this is that Alice now gets a score of 1 for both of them. Your friends' ratings are worth only 1/10 of your own, and their friends' ones only 1/100.
If Carol has a bad encounter with Eve and rates her negatively, it'll also affect Alice's score for her. Due to Carol's rating, Eve's score is -0.1 to Alice.
Ratings add up. If Dave also rates Eve negatively both ratings are added, and Eve's score now becomes -0.2.
Another of Alice's friends - Trent - was attacked by a person named Mallory, whom Trent subsequently rated negatively. Since Trent is closer to Alice than Carol and Dave, he's got a greater influence on Alice's scores. That makes Mallory's score to Alice be -1.
Negative ratings aren't followed. Since what leads to Mallory is a negative rating from Trent, his positive opinion of Eve is ignored by Alice's scanner, and doesn't change Eve's score to Alice.
In more realistic setting, people rate each other, so the actual ratings look more like this:
Ratings are relative, and depend on where you start from. For instance, Mallory views things this way: ??. He and Eve are friendly, which results in him seeing negative ratings for Carol and Dave. Alice, Bob and Trent have no score at all, so they don't appear on the graph. This is because Trent has no positive ratings leading to them, or anybody who rated them.