Cw(f(si)) = Cd(f).
Suppose also that f is independent from all other features that characterize s1 and s2. This means that the following equality holds:Cw(si) = Cw(f(si)) + Cw(si | f(si)).
If we apply the chain rule on the description side:Cd(s1 & s2) < Cd(f) + Cd(s1 | f) + Cd(s2 |f & s1)
We can write (after simplification):U(s1 & s2) > Cw(s1 | f(s1)) + Cw(f(s2)) + Cw(s2 | f(s2)) – Cd(s1 | f) – Cd(s2|f & s1).
The existence of a common feature f introduces a positive term Cw(f(s2)), equal to Cd(f), in the expression of unexpectedness. This explains why common features contribute to coincidences, and why more complex common features are more interesting.