To study preferences, respondents to a survey are usually asked to select their most preferred option from a set. Preferences can be estimated more efficiently if respondents are asked to rank all alternatives. When some respondents are unable to perform the ranking task, using the complete ranking may lead to a substantial bias. We introduce a model which endogenously describes the ranking capabilities of individuals. Estimated preferences based on this model are more efficient when at least some individuals are able to rank more than one item, and they do not suffer from biases due to ranking inabilities of respondents.