Basic assumption: you trust your friend more than a stranger. A friend of your friend is probably more trustworthy than a random stranger as well (at least because your friend trusts her). For example, in the context of movies tastes, if all your 10 trusted cinema-friends trusts "mary" (that you don't know) about her movies tastes, can we predict that you will find her opinions about movies useful as well? I think so.
Imagine you have the following information: ME trusts Ben, Me trusts Mena, Ben trusts Cory, Mena trusts Cory. (This is a simple SocialNetwork).
QUESTION: Should I trust Ben? How much?
A trust metrics is nothing but about finding and answer (and maybe a numerical value) to this question.
You can easily imagine millions of issues/complications and this is what makes trust metrics interesting:
Trust depends on the context (I trust Bob the mechanic to fix my car but not to look over my son)
You can add weights to every trust statements (I trust Mena as 9 out of 10)
Trust is transitive? How much? In every context?
Trust in general is subjective (I trust IndyMedia, you trust CNN) so global trust value (for example the one computed by Google with PageRank) usually don't apply but are usually less computational expensive. When global predicted trust values are enough?
How can i come to know that Mena trusts Cory? Gossiping? Broadcast? DHT? Asking directly to Mena?
How can I be sure that the information "Mena trusts Cory" was really created by Mena? Here it comes into play public key cryptography ... a very interesting topic but we can just assume that every information we receive is reliable because digitally signed
The setting (people/trust connections) is very similar to (web sites/links): what are the similarities? what the differences?
Can trust metrics help in detecting malicious users? (rhetorical, this is infact one of the main advantages of trust metrics)
As long as trust values are just total or missing (I trust Alice and Bob, I express no trust statement to all the other people), it is pretty easy to imagine a trust metric. What happens when you can have real value trust statements (I trust Bob as 8/10 and Spammer as 0/10 and Mary as 9.95/10)?
What really a negative trust value represent?
Are users willing to give negative ratings to other users (some papers say that the negative ratings in eBay are really a few [xxx find the paper])
Negative trust values just stop the trust chain or I can use them to infer something such as "I should not trust this guy"?
How users can easily provide trust statements? What are the best way to explain it? (Some reports say that eBay users find too complicated the very very simple metric used now, it can be an error to introduce a more sophisticated but more complicated metric!)
What the representation of trust statements can be to facilitate users? What about explanation of the results ("You should trust "Mena" as 9.4/10 because ..."
What can be the better representation and VisualiZation of the social network? (I like touchgraph.com a lot but many people say that this kind of interfaces are just very intriguing but then people don't use them because too complicated and not very handy)
Trust metrics can help in detecting paradox. "I trust Controversial, I trust Hanna, Hanna totally distrusts Controversial". Should I be warned of this? What if *all* my "friends" distrust him?
Sociologial concerns (you trust all your friends? what if a friend of you see that she is not in your "web of trust"?)
Add a new one! (just free your mind and write down the most unconfessed questions you always had abut trust metrics!! ;-)
Trust is only transitive if we know beforehand that all invloved use fearly the same trust metric and that the metric is independent of who is being trusted and who is trusting. http://www.sics.se/~tol.