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8.1.5 Properties Ostra’s system of credit balances observes the following invariant: At all times, the sum of all credit balances is 0 The conservation of credit follows from the fact that (i) users have an initial zero balance when joining the system, (ii) all operations transfer credit among users, and (iii) credit decay affects positive and negative credit at the same rate. Table 8.1 details how each operation leaves the overall credit balance unchanged. Thus, credit can be neither created nor destroyed. Malicious, colluding users can pass credits only between themselves; they cannot create additional credit or destroy credit. The amount of unwanted communication that such users can produce is the same as the sum of what they can produce individually. We have already shown that each user can produce unwanted communication at a rate of no more than d ∗ L + S. We now characterize the amount of unwanted subset of the user population can produce. Let us examine a group of users F. Owing to the conservation of credit, users in this group cannot conspire to create credit; they can only push credit between themselves. Thus, the users in F can send unwanted communication to users not in F at a maximal rate of |F|∗d∗L+SF (8.2) where SF is that rate at which users in F (in aggregate) receive communication from users not in F that they mark as unwanted. 158PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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