Supervised machine learning models for automated essay scoring (AES) usually require substantial task-specific training data in order to make accurate predictions for a particular writing task. This limitation hinders their utility, and consequently their deployment in real-world settings. In this paper, we overcome this shortcoming using a constrained multi-task pairwisepreference learning approach that enables the data from multiple tasks to be combined effectively. Furthermore, contrary to some recent research, we show that high performance AES systems can be built with little or no task-specific training data. We perform a detailed study of our approach on a publicly available dataset in scenarios where we have varying amounts of task-specific training data and in scenarios where the number of tasks increases.