Local trust metric

A local trust metric predicts trust scores that are personalized from the point of view of every single user. For example a local trust metric might predict "Alice should trust Carol as 0.9" and "Bob should trust Carol as 0.1", or more formally trust(A,C)=0.9 and trust(B,C)=0.1

On the other hand, a global trust metric computes a single global trust value for every single user. For example, a global trust metric might predict "the trust of Carol is 0.4" and this value is indepedent of the user which is asking the prediction. In fact this global value is often called the reputation of Carol and represents what the community as a whole on average think about Carol. Formally, trust(C)=0.4 since the source user is not relevant.

Local trust metrics start from the assumption that every single trust statement is an equally worthy subjective opinion and that there are no wrong opinions and that there are no global reputation values on which all the users must agree. This characteristics is especially useful when dealing with controversial users which receive very different trust statements from the other users.

Local trust metrics are particularly useful also in order to avoid the tyranny of the majority risk. However they might suffer from a risk on the other side of the personalization scale, daily me or echo chamber, that means that the user loses the point of view of the community at large but just relies on the opinions of few trusted users.

Computing Local Trust
One reason why local trust metrics may be less popular in real systems is that they are significantly more complex than compute than global trust metrics. The number of trust links that must be stored increases exponentially as the number of trust nodes increases.

Calculating local trust is significantly more complex because the trust between User A and User X is different from the trust between User B and User X. Every trust level must be calculated uniquely for each user against each other user. In large scale systems, with millions of users, this becomes a huge computing task.