This paper studies decision problems under uncertainty where a decision-maker observes an imperfect signal about the true state of the world. We analyze the information preferences and information demand of such decision-makers, based on properties of their payoff functions. We restrict attention to "monotone decision problems," whereby the posterior beliefs induced by the signal can be ordered so that higher actions are chosen in response to higher signal realizations. Monotone decision problems are frequently encountered in economic modeling. We provide necessary and sufficient conditions for all decision makers with different classes of payoff functions to prefer one information structure to another. We also provide conditions under which two decision-makers in a given class can be ranked in terms of their marginal value for information and hence information demand. Applications and examples are given.