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When a Bayesian learns new information and changes her beliefs, she must on average become concomitantly more certain about the state of the world. Consequently, it is rare for a Bayesian to frequently shift beliefs substantially while remaining relatively uncertain, or, conversely, become very confident with relatively little belief movement. We formalize this intuition by developing specific measures of movement and uncertainty reduction given a Bayesian’s changing beliefs over time, showing that these measures are equal in expectation and creating consequent statistical tests for Bayesianess. We then show connections between these two core concepts and four common psychological biases, suggesting that the test might be particularly good at detecting these biases. We provide support for this conclusion by simulating the performance of our test and other martingale tests. Finally, we apply our test to data sets of individual, algorithmic, and market beliefs.

We model two agents who wish to determine if their types match, but who also desire to reveal as little information as possible to non-matching types. For example, firms considering a merger must determine the merger's profitability, but would prefer to keep their information private if the deal fails. In the model, agents with different traits reveal information to a potential partner to determine if they share the same type, but face a penalty depending on the accuracy of their partner's posterior beliefs. With limited signaling, there is a universally-preferred dynamic communication protocol in which traits are sequentially revealed depending on the sensitivity of the trait. Interestingly, the rarity of an agent's traits plays no role due to the balance of opposing effects: although revealing a rare trait reveals more information immediately, it also screens more partners from later learning information about other traits.

We experimentally investigate the time-inconsistent taste for immediate gratification and future-preference misprediction. Across 7 weeks, 100 participants choose the number of unpleasant transcription tasks given various wages to complete immediately and at different future dates. Participants preferred 10–12% fewer tasks in the present compared to any future date, leading to an estimated β of 0.83⁠. Comparing predictions with actual immediate-work choices provides evidence against substantial sophistication, with estimates implying that participants understand no more than 24% of their present bias. Finally, we find evidence of “projection bias”: participants wished to complete 4–12% fewer tasks when decisions were elicited right after completing tasks rather than before.

We model religious faith as a “demand for beliefs,” following the logic of the Pascalian wager. We show how standard experimental interventions linking financial consequences to falsifiable religious statements can elicit and characterize beliefs. We implemented this approach with members of a group that expected the “End of the World” to occur on May 21, 2011 by varying monetary prizes payable before and after May 21st. To our knowledge, this is the first incentivized elicitation of religious beliefs ever conducted. The results suggest that the members held extreme, sincere beliefs that were unresponsive to experimental manipulations in price.

In this paper, we examine the eect of "choice fatigue"on decision making. We exploit a natural experiment in which voters face the same contest at dierent ballot positions due to dierences in the number of local issues on their ballot. Facing more decisions before a given contest signi…cantly increases the tendency to abstain or rely on decision shortcuts, such as voting for the status quo or the …rst listed candidate. We estimate that, without choice fatigue, abstentions would decrease by 8%, and 6% of the propositions in our dataset would have passed rather than failed.

This article theoretically and empirically analyses behaviour in penny auctions, a relatively new auction mechanism. As in the US dollars or war-of-attrition, players in penny auctions commit higher non-refundable costs as the auction continues and only win if all other players stop bidding. I first show that, in any equilibria that does not end immediately, players bid probabilistically such that the expected profit from every bid is zero. Then, using two large data sets covering 166,000 auctions, I calculate that average profit margins actually exceed 50%. To explain this deviation, I incorporate a sunk-cost fallacy into the theoretical model to generate a set of predictions about hazard rates and player behaviour, which I confirm empirically. While players do (slowly) learn to correct this bias and there are few obvious barriers to competition, activity in the market is rising and concentration remains relatively high.