This paper introduces a receiver who perceives ambiguity in a binary model of Bayesian persuasion. The sender has a well-defined prior, while the receiver considers an interval of priors and maximizes a convex combination of worst and best expected payoffs. We characterize the sender’s optimal signal and find that the receiver’s payoff differences across states given each action, play a fundamental role in the characterization and the comparative statics. If the sender’s preferred action is the least sensitive one, then the (...) sender’s equilibrium payoff, as well as the sender’s preferred degree of receiver ambiguity, is increasing in the receiver’s pessimism. We document a tendency for ambiguity-sensitive receivers to be more difficult to persuade. (shrink)

We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (IEEE Transactions on Systems, Man and Cybernetics 22(5):1144–1152, 1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian Updating rule. This allows us to characterize two parametric families of convex capacities: ${(\varepsilon,\delta)}$ -contaminations (which were introduced, in a slightly different form, by Huber (...) (Robust Statistics, Wiley, New York, 1981)) and ${\varepsilon}$ -contaminations. (shrink)

We provide a critical assessment of the ambiguity aversion literature, which we characterize in terms of the view that Ellsberg choices are rational responses to ambiguity, to be explained by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. First, admitting Ellsberg choices as rational leads to behaviour, such as sensitivity to irrelevant sunk cost, or aversion to information, which most economists would consider absurd or irrational. Second, we argue that the mathematical objects referred to as “beliefs” in the ambiguity (...) aversion literature have little to do with how an economist or game theorist understands and uses the concept. This is because of the lack of a useful notion of updating. Third, the anomaly of the Ellsberg choices can be explained simply and without tampering with the foundations of choice theory. These choices can arise when decision makers form heuristics that serve them well in real-life situations where odds are manipulable, and misapply them to experimental settings. (shrink)

Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 620-638, November 2021.

On average, “young” people underestimate whereas “old” people overestimate their chances to survive into the future. Such subjective survival beliefs violate the rational expectations paradigm and are also not in line with models of rational Bayesian learning. In order to explain these empirical patterns in a parsimonious manner, we assume that self-reported beliefs express likelihood insensitivity and can, therefore, be modeled as non-additive beliefs. In a next step we introduce a closed form model of Bayesian learning for non-additive beliefs which (...) combines rational learning with psychological attitudes in the interpretation of information. Our model gives a remarkable fit to average subjective survival beliefs reported in the Health and Retirement Study. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

This paper argues that several leading theories of subjunctive conditionals are incompatible with ordinary intuitions about what credences we ought to have in subjunctive conditionals. In short, our theory of subjunctives should intuitively display semantic humility, i.e. our semantic theory should deliver the truth conditions of sentences without pronouncing on whether those conditions actually obtain. In addition to describing intuitions about subjunctive conditionals, I argue that we can derive these ordinary intuitions from justified premises, and I answer a possible worry (...) for my derivation by refuting a subjunctive triviality result modeled on (Lewis 1976). I conclude that the debate over the correct theory of subjunctive conditionals requires settling meta-philosophical questions about the relative value of various virtues of first-order theories of subjunctive conditionals. (shrink)

Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the ambiguous bet (...) and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process. (shrink)

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis : 865–895, 2016) shows that when voters have ambiguous prior beliefs—a set of priors—and follow maxmin expected utility, such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to (...) posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error. In a classical model, Feddersen and Pesendorfer :23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis : 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals. (shrink)

We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural (...) approach to determining the weights. We then show how this representation can be used in decision making, by modifying a standard approach to decision making—minimizing expected regret—to obtain minimax weighted expected regret. We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case. (shrink)