Beyond Cumulated Gain and Average Precision: Including Willingness and   Expectation in the User Model
  In this paper, we define a new metric family based on two concepts: The definition of the stopping criterion and the notion of satisfaction, where the former depends on the willingness and expectation of a user exploring search results. Both concepts have been discussed so far in the IR literature, but we argue in this paper that defining a proper single valued metric depends on merging them into a single conceptual framework. 
Benjamin Piwowarski and Georges Dupret and Mounia Lalmas
cs.IR