If we take seriously the “ambiguity aversion” discussed earlier, when offered the choice between betting on the fair coin’s landing heads as opposed to the unknown-bias coin’s landing heads, it doesn’t seem unreasonable to prefer the former. Recall the preference for unambiguous gambles in the Ellsberg game in section 2.1. But if both coins have the same subjective probabilities attached, what rationalises this preference for betting on the fair coin? Joyce argues that there is a difference between these beliefs that is worth representing. IP does represent the difference. The first case is represented by \(P(H)=\{0.5\}\), while the second is captured by \(P(H)=[0,1]\).