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 \textit{Yes, Prime Minister}, we show that the resulting data cannot be explained quite so simply using quantum rules, although it seems not impossible.