What's happening with this idea then? Any developments?
I think it is an interesting idea which could probably be developed in a number of ways. I can understand the points about subjectivity, collaboration, cheating, etc., but I can't think of many mathematical models that do not have to cope with some contaminants.
Most businesses play the roles of both supplier and demander. We could form a network of "trust-lines" between them and use Duane's "diminishing trust" idea to try and solve the problem below, and even to arrive at a "trust level" for each member in the system. Here is a diagram (there are notes about the diagram at the bottom of this message):
http://img15.imgspot.com/?u=/u/06/348/08/TRUST1166190337.GIF
Suppose we wanted to find out how much A can trust C. There are a number of routes through the diagram from A to C. There are routes with 3 hops and routes with 2 hops. There are two routes with 2 hops, A->B->C which evaluates to 0.85 x 0.67 = 0.57, and A->E->C which evaluates to 0.77 x 0.95 = 0.73. So which trust level do we choose, 0.57 or 0.73? Do we take the average? And why shouldn't the 3-hop routes be used in the calculation of the trust level? For example, the 3-hop route A -> B -> E -> C evaluates to 0.85 x 0.94 x 0.95 = 0.75, which is higher than both of the 2-hop trust levels.
I think I might pinch your idea if you don't mind Duane, and have a little play around to see if I can get a trust level for each member.
Dave
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Some notes about the diagram.
Draw an arrow from A to B with arrowhead touching B, and label the arrowhead 0.85. This denotes that A has bought from B, and has placed 0.85 of "trust" in B.
(All trust values are between 0 and 1 inclusive, i.e. if t is the trust value, then 0 <= t <= 1).
Do the same for all the other members that A has bought from.
Notice that some trust lines have an arrowhead at each end. For example, the trust line between A and D is a double headed arrow. This means that A has bought from D and places 0.93 trust in D, and D has bought from A and placed 0.59 trust in A.
You don't need to use seperate trust-lines to show mutual trust between two members. It will be clearer if you use double arrowheaded lines (as in the diagram) to show mutual trust between two members.
