Probability Matching, a classical violation of expected utility maximization, refers to people's tendency to randomize, or even match their choice frequency to the outcome probability, when choosing over binary lotteries that differ only in their probabilities. Why? I present an experiment designed to distinguish between several broad classes of explanations: (1) models of Correlation-Invariant Stochastic Choice --- randomizing due to factors orthogonal to the correlation between lotteries, such as non-standard preferences or errors, and (2) models of Correlation-Sensitive Stochastic Choice --- deliberately randomizing due to misperceived hedging opportunities, especially when lotteries are negatively correlated. My experimental design differentiates between their testable predictions by varying the correlation between lottery outcomes. The findings indicate that the first class, despite being home to most existing theories, has limited explanatory power. Using additional treatment, I rule out Similarity Heuristics as a competing explanation with the second class. The results indicate that a vast majority of individuals deliberately randomize due to misperceived hedging opportunities.

Optimal portfolios depend on the correlation among asset returns, yet evidence on whether people respond to it is mixed. I show that a key driver is the complexity of two distinct cognitive operations that forming a portfolio requires, mirroring the two-step structure of the expected-utility axioms: canceling common-return states, which are choice-irrelevant (Cancellation Complexity, CC), and evaluating the cross-state tradeoff that remains (Tradeoff Complexity, TC). In an experiment that varies each friction separately while holding the expected-utility prediction fixed, both amplify mis-response to correlation --- participants over-diversify even when the hedging opportunity vanishes --- but through different channels. TC shifts the optimum participants perceive: an evaluation cost distorts choice toward portfolios that are easier to compare. CC shrinks the utility differences among allocations, while leaving the tradeoff unchanged and so carries no such cost. Outside the lab, I find evidence from U.S. stock returns consistent with the TC channel: the behavioral component of the comovement premium rises with the TC of a stock's return distribution relative to the market's, with no detectable change in its rational component.

The same underlying data can be communicated or perceived in different formats. A natural question is whether people prefer the formats that serve them best. We study five different summary reports of a series of binary signals in the canonical belief updating setting: Majority (which signal type appeared more often), Percentage (the percentage of each signal type), Difference (how many more of the dominant type), Count (the number of each type), and Sequence (the raw sequence of the signals). These reports differ in two key dimensions: instrumental value (IV) and information richness (IR). In an online experiment (N=200), we elicit participants’ preference (WTP) for the reports and measure their belief-updating performance across the reports. Our central finding is a systematic misalignment between preference and performance. WTP rises with both IV and IR, although the standard economy theory predicts only IV should matter. Performance, in contrast, improves with IV but deteriorates with IR conditional on IV. That is, participants perform worse with the very reports they pay more to receive. We also find substantial heterogeneity in participants' preferences, but the misalignment between preference and performance is robust across subgroups. Together, these results indicate that demand for information is shaped by features that go beyond instrumental value, and that people have imperfect meta-cognition about their own belief-updating behavior.

Elicited beliefs are compressed toward the midpoint of the response scale, even under incentive-compatible mechanisms. A single-number report, such as a slider, cannot show how much of this compression reflects imprecise perception and how much the format adds. We introduce the Dynamic Binary Method (DBM), in which the participant halves the scale through a sequence of binary comparisons and may stop at any step. In two experiments comparing DBM with a slider, participants who get the first comparison right are more accurate at the second on the extreme truths rather than the intermediate ones. A belief formed orthogonal to the method, compressed toward the midpoint, would produce the opposite ordering. The comparisons instead behave as fresh reads of a noisy signal. Separating the two sources, we find that most of the compression is common to both methods and reflects imprecise perception. The slider adds a smaller component, positive under every estimator and data partition. DBM's first comparison --- above or below the midpoint? --- cannot be changed by a pull toward the midpoint, so it measures perception free of that pull. A participant's first comparisons also measure her perceptual precision and predict her slider errors on other tasks. DBM is not more accurate than a slider, but it shows how a belief is constructed, which a slider hides.