What makes a person pick certain tags over others when tagging an image? Does the order that a person presents tags for a given image follow an implicit bias that is personal? Can these biases be used to improve existing automated image tagging systems? We show that tag ordering, which has been largely overlooked by the image tagging community, is an important cue in understanding user tagging behavior and can be used to improve auto-tagging systems. Inspired by the assumption that people order their tags, we propose a new way of measuring tag preferences, and also propose a new personalized tagging objective function that explicitly considers a user's preferred tag orderings. We also provide a (partially) greedy algorithm that produces good solutions to our new objective and under certain conditions produces an optimal solution. We validate our method on a subset of Flickr images that spans 5000 users, over 5200 tags, and over 90,000 images. Our experiments show that exploiting personalized tag orders improves the average performance of state-of-art approaches both on per-image and per-user bases.