A model of approval with an application to list design

Online technologies enable a host of observable acts, such as wishlisting, that do not quite amount to choice meant as a final selection. Rather, they express interest and a positive attitude towards an item. We gather this type of behaviour under the term approval. With items presented as a list, we propose a model of approval. We completely characterise the model in terms of simple properties of observed approval data. We introduce and study the problem of list design. This captures situations where an interested party can manipulate the approver's behaviour by choosing the list with the aim of maximising an objective.