users' percentile similarity measure
As I understand it, you don't want to use the dot product, because it is unbounded.  Yet you also don't want to use the cosine similarity metric:



, which is just the dot product normalized by the length of the two vectors being dotted because it does not take magnitude into account e.g. $(1,1)\cdot(1,1)=1=(1,1)\cdot(2,2)$

Perhaps you could therefor use the sorensen dice coefficient or possibly 1-soresen:



This varies from 0 to 1 and accounts for magnitudes of the constituent vectors e.g.:

$$s_{\nu}[(1,1),(1,1)]=1$$

, where as 

$$s_{\nu}[(1,1),(2,2)]=\frac{4}{5}$$

Hope this helps!