Eliciting Rankings for Attributes of Goods

The preference elicitation literature often examines ordinal rankings over n goods. However, when the number of goods n is large, this can be prohibitive, and mechanism designers often resort to eliciting top-q rankings, where q ≪ n. When goods are characterized by k binary attributes describing them (e.g., “a school with a gifted program”, “a dorm with air conditioning”, etc.), we juxtapose when it might be preferable to elicit rankings over the k possible attributes instead of a top-k ranking over the goods themselves. In this preliminary work, we examine for which sets of goods preferences over attributes can yield strictly more complete rankings than top-k rankings over goods, and vice versa.