Public opinion polling is usually done by random sampling from the entire population, treating individual opinions as independent. In the real world, individuals' opinions are often correlated, e.g., among friends in a social network. In this paper, we explore the idea of partitioned sampling, which partitions individuals with high opinion similarities into groups and then samples every group separately to obtain an accurate estimate of the population opinion. We rigorously formulate the above idea as an optimization problem. We then show that the simple partitions which contain only one sample in each group are always better, and reduce finding the optimal simple partition to a well-studied Min-r-Partition problem. We adapt an approximation algorithm and a heuristic algorithm to solve the optimization problem. Moreover, to obtain opinion similarity efficiently, we adapt a well-known opinion evolution model to characterize social interactions, and provide an exact computation of opinion similarities based on the model. We use both synthetic and real-world datasets to demonstrate that the partitioned sampling method results in significant improvement in sampling quality and it is robust when some opinion similarities are inaccurate or even missing.