Lists of ordered objects are widely used as representational forms. Such ordered objects include Web search results or best seller lists. In spite of their importance, the methods of processing orders have received little attention. However, research concerning object ordering is becoming more common. Some researchers have developed various methods to perform almost the same task: a learning function used for sorting objects from examples of ordered sequences. We call this task the estimation of Attributed Central Orders (ACO for short). The performance of this task is useful for sensory surveys, information retrieval, or decision making. We performed a survey of such methods, empirically compared the methods’ properties, and discuss their merits and demerits.