Exacting a small subset of data points to represent a large dataset for multi-criteria decision making is an important functionality of modern database systems. The happiness maximization query a.k.a. the regret minimization query has been a popular tool to fulfill this task and overcome the inherent drawbacks of the other two influential tools, namely, the top-k query and the skyline query. Since the happiness ratio of the happiness maximization query is not able to accurately quantify the happiness level of users, the concept rank is introduced to the happiness maximization query. However, in many real applications, data points are frequently inserted or deleted where an update can be considered as an insertion after a deletion. In this paper, we investigate the average form of the rank-happiness maximization query which considers the satisfaction of all users in the dynamic environments. By illustrating that the average rank-happiness ratio function is monotone and submodular, we propose the DynMLS algorithm with theoretical guarantee to answer the query and a multi-layer structure is adopted for the DynMLS algorithm to maintain the data points effectively and efficiently. Comprehensive experiments on both synthetic and real datasets demonstrate that we can efficiently find small subsets with large average rank-happiness ratios of our proposed DynMLS algorithm.