There is a further question about the interpretation of IP that cross-cuts the above. This is the question of whether we understand \(P\) as a “complete” or “exhaustive” representation of your beliefs, or whether we take the representation to be incomplete or non-exhaustive. Let’s talk in terms of the betting interpretation for a moment. The exhaustive/non-exhaustive distinction can be drawn by asking the following question: does \(P\) capture all and only your dispositions to bet or does \(P\) only partially capture your dispositions to bet? Walley emphasises this distinction and suggests that most models are non-exhaustive.