Yes, Prime Minister, question order does matter -- and it's certainly not classical! But is it quantum?

Response to a poll can be manipulated by means of a series of leading questions. We show that such phenomena cannot be explained by use of classical probability theory, whereas quantum probability theory admits a possibility of offering an explanation. Admissible transformation rules in quantum probability, however, do impose some constraints on the modelling of cognitive behaviour, which are highlighted here. Focusing on a recent poll conducted by Ipsos on a set of questions posed by Sir Humphrey Appleby in an episode of the British political satire textitYes, Prime Minister, we show that the resulting data cannot be explained quite so simply using quantum rules, although it seems not impossible.