Trust - Peer-to-Peer Computing: Applications, Architecture, Protocols, and Challenges - page 131

6.2 EigenTrust
Kamvar et al. [Kamvar et al., 2003] proposed the widely cited EigenTrust
system. In EigenTrust, each peer i keeps track of the number of satisfactory
transactions it has had with peer j, denoted by sat(i, j) and the number of
unsatisfactory transactions it has had with peer j, denoted by unsat(i, j).
With these parameters, s ij is defined as:

s ij = sat(i, j)−unsat(i, j) (6.1)

Kamvar et al. pioneered to point out an insight that the challenge for
reputation systems is how to aggregate the local trust values s ij without a
centralized storage and management facility. Accordingly, EigenTrust is based
on the notion of transitive trust: A peer i will have a high opinion of those
peers who have supplied authentic files to it previously. More importantly,
peer i is likely to trust the opinions of such peers. Such transitivity of trust is
based on the premises that peers who are honest about the files they provide
are also likely to be honest in reporting their local trust values.
In quantitative terms, the global reputation of each peer i is given by the
local trust values assigned to peer i by other peers, weighted by the global
reputations of the assigning peers. Specifically, in EigenTrust, the normalized
local trust value, c ij , is defined as:

max(s ij , 0)

c ij = (6.2)

j max(s ij , 0)

However, there are several potential drawbacks in the local trust compu-
tation. Firstly, the normalized trust values do not distinguish between a peer
with whom peer i did not interact and a peer with whom peer i has had poor
experience. Secondly, these c ij values are relative, and there is no absolute
interpretation. Specifically, if c ij = c ik , we know that peer j has the same
reputation as peer k in the opinion of peer i. However, there is no way to tell
if both of them are very reputable, or if both of them are just mediocre.
Thus, aggregation of local trust values is necessary. To achieve this, peer
opinions are also factored in the weighted evaluation:

t ik = c ij c jk (6.3)

j

where t ik represents the trust that peer i places in peer k based on asking
the trusted peers. Let us denote C as the matrix [c ij ] and t i as the vector of
values t ik . Thus, the aggregation is given by:
t i = C T c i

(6.4)

If a peer i carries out this aggregation process for n times, then we have