We generalize Blackwell’s informativeness order to ambiguous experiments. A decision maker might view a statistical experiment as ambiguous if she faces uncertainty about the data-generating process for its signals. Formally, an ambiguous experiment is modeled as a mapping from an auxiliary state space to the set of unambiguous experiments. Each auxiliary state corresponds to a possible data-generating process. We show that one ambiguous experiment is preferred to another by every decision maker in every decision problem if and only if they are related by a condition called prior-by-prior dominance, which states that for any first-order belief the decision maker entertains on the auxiliary state space, the expected experiment resulting from this belief for the first experiment is Blackwell more informative than that of the second. This equivalence is robust for any class of monotone ambiguity preferences that nests expected utility. We obtain another informativeness order when we restrict attention to decision makers who apply the maxmin criterion to evaluate ambiguous experiments and connect this informativeness order to comparisons of sets of Blackwell experiments.

Empirical evidence suggests that individuals selectively avoid information based on past decisions. We address these findings by studying an agent who behaves as if she trades off two conflicting effects of information. The first is a psychological cost from the regret about past decisions that are revealed to be suboptimal, whereas the second is the instrumental value in guiding future decisions. We take as primitive preferences over consumption-information pairs and provide axiomatic representation theorems incorporating both instrumental value and regret in the value of information. New axioms are posited to connect the agent’s consumption choice with her information choice. We show that all parameters can be uniquely identified from the preference. Defining information avoidance as preferring a Blackwell less informative experiment, we provide comparative statics on the agent’s information aversion attitude.

A decision maker may have several information sources available and choose which one to consult only after learning the decision problem she faces. When is one such set of sources uniformly more valuable than another? For unrestricted Bayesian decision problems, we show that the answer can be stated entirely in terms of Blackwell comparisons. Form a tagged mixture by drawing a source independently of the state and revealing both its identity and its signal. One source set is more valuable in every decision problem if and only if each tagged mixture of the second source set is Blackwell dominated by some tagged mixture of the first. The result applies to compact, possibly infinite source sets and general signal spaces. It also has an exact quantitative counterpart: the largest normalized value shortfall is the directed Le Cam deficiency between the source sets’ tagged hulls. The analogous program for monotone decision problems reveals a boundary. We call the passage from problem-by-problem source-set superiority to a problem-independent pairwise dominance a lifting. The Blackwell lifting does not extend directly to the Lehmann order: mixing sources that individually satisfy the monotone likelihood ratio property (MLRP) need not preserve MLRP, and even when it does, no fixed Lehmann-dominating mixture need exist. Requiring one source to serve a finite bundle of monotone decision problems restores the equivalence.

We study a setting in which an agent receives private information before choosing from a menu and anticipates hindsight scrutiny. Such scrutiny creates a motive for conservatism toward menu expansions. Our key axiom, conservatism, is a direct weakening of preference for flexibility: Adding an option is weakly beneficial whenever it leaves the menu’s hindsight benchmark unchanged. Together with standard axioms, conservatism characterizes a scrutiny representation of preferences over menus in which the agent behaves as if she evaluates each menu by subtracting anticipated scrutiny from the material value of informed choice. Menu preference identifies a unique minimum pair of private information and scrutiny intensity, while incorporating subsequent stochastic-choice data pins down the actual pair. Applications to medical liability and corporate innovation illustrate the implications of our model for accountability design.