In knowledge bases such as Wikidata, it is possible to assert a large set of properties for entities, ranging from generic ones such as name and place of birth to highly profession-specific or background-specific ones such as doctoral advisor or medical condition. Determining a preference or ranking in this large set is a challenge in tasks such as prioritisation of edits or natural-language generation. Most previous approaches to ranking knowledge base properties are purely data-driven, that is, as we show, mistake frequency for interestingness. In this work, we have developed a human-annotated dataset of 350 preference judgments among pairs of knowledge base properties for fixed entities. From this set, we isolate a subset of pairs for which humans show a high level of agreement (87.5% on average). We show, however, that baseline and state-of-the-art techniques achieve only 61.3% precision in predicting human preferences for this subset. We then analyze what contributes to one property being rated as more important than another one, and identify that at least three factors play a role, namely (i) general frequency, (ii) applicability to similar entities and (iii) semantic similarity between property and entity. We experimentally analyze the contribution of each factor and show that a combination of techniques addressing all the three factors achieves 74% precision on the task. The dataset is available at www.kaggle.com/srazniewski/wikidatapropertyranking.