 The second kind of belief relevant for doxastic preference change concerns prospects that influence the preference for other prospects without being probabilistically related. For example, one’s preference for winning a trip to Florida in the lottery will crucially depend on one’s belief about the weather there during the specified travel time, even though these two prospects are probabilistically unrelated. More generally, if \(X\wedge Y\) is preferred to \(X\wedge \neg Y\), with \(X\) and \(Y\) probabilistically not correlated, then a rise of the probability that \(X\) will result in a rise in the desirability of \(Y\) (even if it does not affect the probability of \(Y)\), and vice versa.