The value of cost-free uncertain evidence

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility (inaccuracy).

Multiple Beliefs, Dominance and Dynamic Consistency

This paper investigates multiperiod decisions under multiple beliefs. We explore the dynamic consistency of both complete and incomplete orderings. We focus on a dominance concept that supports decision-making under multiple characterizations of uncertainty by ruling out strategies that are dominated across a set of beliefs. We uncover a distinction between two types of dynamic inconsistency, which we label fallacious and fallible inconsistency. Fallacious inconsistency occurs when an a priori optimal strategy is suboptimal in the second period, thus requiring the decision-maker to depart from the original strategy. Fallible inconsistency occurs when an a priori suboptimal second-period action ceases being suboptimal from the perspective of the second-period preferences. We introduce corresponding definitions of dynamic consistency and show that the two types of consistency are equivalent for complete orderings, but differ for incomplete orderings. Subjective expected utility is dynamically consistent and non-expected-utility decision rules, such as minmax, are not. We show that the dominance relation over beliefs falls between these two: it is immune to the more severe fallacious inconsistency, but not to the less problematic fallible inconsistency. We illustrate the method and concepts using a numerical example addressing a focal, real-world problem of risk and ambiguity regarding climate change. This paper was accepted by Ilia Tsetlin, decision analysis.

Revisiting Ellsberg’s and Machina’s Paradoxes: A Two-Stage Evaluation Model Under Ambiguity

In this paper, a two-stage evaluation (TSE) model for decision making under ambiguity is proposed. Events in state space are classified into risky and ambiguous events, which correspond to different types of uncertainty generated by different sources. In this TSE model, uncertainty of two different types are evaluated by decision maker (DM) in different stages. In the first stage, DM evaluates more uncertain consequences of an act locally by applying local subjective expected utility (SEU) models, which are then embedded into the second-stage evaluation based on SEU defined globally over all events. To axiomatize such a model, the small domain SEU over risky acts is extended to both risky and nonrisky (ambiguous) acts. When evaluating a risky act, TSE model reduces to Savage’s SEU with one stage. When evaluating an ambiguous act, local SEU with a different uncertainty aversion defined on ambiguous events gives TSE model some flexibility in describing preferences. It can be shown that TSE model can accommodate Ellsberg’s paradoxes and Machina’s paradoxes in the literature. When applied to portfolio selection problem, TSE model enjoys some nice properties other models do not have. This paper was accepted by Manel Baucells, decision analysis.

Dynamic consistency, valuable information and subjective beliefs

Ambiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior.

Efficiency, equity, and social rationality under uncertainty

In a simple model where agents’ monetary payoffs are uncertain, this paper examines the aggregation of subjective expected utility functions which are interpersonally noncomparable. A maximin social welfare criterion is derived from axioms of efficiency, ex post equity, and social rationality, combined with the independence of beliefs and risk preferences in riskless situations (Chambers and Echenique in Games Econ Behav 76:582–595, 2012). The criterion compares allocations by the values of the prospects composed of the statewise minimum payoffs evaluated by the certainty equivalents. Because of this construction, the criterion is egalitarian and risk averse.

Going, going, gone: competitive decision-making in Dutch auctions

In a Dutch auction, an item is offered for sale at a set maximum price. The price is then gradually lowered over a fixed interval of time until a bid is made, securing the item for the bidder at the current price. Bidders must trade-off between certainty and price: bid early to secure the item and you pay a premium; bid later at a lower price but risk losing to another bidder. These properties of Dutch auctions provide new opportunities to study competitive decision-making in a group setting. We developed a novel computerised Dutch auction platform and conducted a set of experiments manipulating volatility (fixed vs varied number of items for sale) and price reduction interval rate (step-rate). Triplets of participants ($$N=66$$ N = 66 ) competed with hypothetical funds against each other. We report null effects of step-rate and volatility on bidding behaviour. We developed a novel adaptation of prospect theory to account for group bidding behaviour by balancing certainty and subjective expected utility. We show the model is sensitive to variation in auction starting price and can predict the associated changes in group bid prices that were observed in our data.

Strategyproof Choice of Social Acts

We model uncertain social prospects as acts mapping states of nature to (social ) outcomes. A social choice function (or SCF ) assigns an act to each profile of subjective expected utility preferences over acts. An SCF is strategyproof if no agent ever has an incentive to misrepresent her beliefs about the states of nature or her valuation of the outcomes. It is unanimous if it picks the feasible act that all agents find best whenever such an act exists. We offer a characterization of the class of strategyproof and unanimous SCFs in two settings. In the setting where all acts are feasible, the chosen act must yield the favorite outcome of some ( possibly different) agent in every state of nature. The set of states in which an agent’s favorite outcome is selected may vary with the reported belief profile; it is the union of all states assigned to her by a collection of constant, bilaterally dictatorial, or bilaterally consensual assignment rules. In a setting where each state of nature defines a possibly different subset of available outcomes, bilaterally dictatorial or consensual rules can only be used to assign control rights over states characterized by identical sets of available outcomes. (JEL D71, D81, R53)

Reasonable Care under Uncertainty

This chapter develops decision-theoretic principles for reasonable care under uncertainty. It discusses some reasonable ways to choose among undominated actions. When addressing this issue, decision theorists have distinguished three primary situations regarding information that a decision maker may or may not have beyond specification of the state space: decisions with rational expectations, maximization of subjective expected utility, and decisions under ambiguity. When making a choice under ambiguity, a reasonable way to act is to use a decision criterion that achieves adequate performance in all states of nature. There are multiple ways to formalize this idea. The two most commonly studied are the maximin and minimax-regret (MR) criteria.