  The mechanism of the online user preference evolution is of great
significance for understanding the online user behaviors and improving the
quality of online services. Since users are allowed to rate on objects in many
online systems, ratings can well reflect the users' preference. With two
benchmark datasets from online systems, we uncover the memory effect in users'
selecting behavior which is the sequence of qualities of selected objects and
the rating behavior which is the sequence of ratings delivered by each user.
Furthermore, the memory duration is presented to describe the length of a
memory, which exhibits the power-law distribution, i.e., the probability of the
occurring of long-duration memory is much higher than that of the random case
which follows the exponential distribution. We present a preference model in
which a Markovian process is utilized to describe the users' selecting
behavior, and the rating behavior depends on the selecting behavior. With only
one parameter for each of the user's selecting and rating behavior, the
preference model could regenerate any duration distribution ranging from the
power-law form (strong memory) to the exponential form (weak memory).
