Schedule - Parallel Session 5 - Risk and Uncertainty

Suppose that from time to time you get a coffee from a local cafe. In one scenario (certain), every time you buy a coffee, you receive a $1 discount. In the other scenario (uncertain), every time you buy a coffee, you receive a $1 or $0.50 discount. In which scenario will you buy more coffees from this cafe? There are good reasons to predict that the certain discount is a more effective incentive. For one, you would save more money under the certain discount than under the uncertain discount. For another, if you are like most normal consumers, you would prefer certainty to uncertainty. Yet we predict the opposite. We predict that you will repeat the purchase more if the discount is uncertain than if it is certain. We propose that outcome uncertainty can increase activity persistence due to uncertainty resolution. Uncertainty resolution is a unique mental reward which reinforces the corresponding behavior. We tested this uncertainty effect and its mechanism in diverse contexts, and found that uncertainty in payment (Study 1) increases willingness to repeat in work, uncertainty in discount (Study 2) and uncertainty in price (Study 3) increase willingness to repeat in purchase, and uncertainty in prize (Study 4) increases willingness to repeat in study. All our studies involved real consequences to participants. In Study 3, for example, we ran a sales program for Reese’s Peanut Butter Cups with three versions of pricing: certain low price (10c each), certain high price (15c each), and uncertain price (10c or 15c with equal chances). Each buyer encountered one version and made purchases one by one. In either certain price program, the buyer who decided to purchase drew a cup from a bag and paid its price. In the uncertain price program, the buyer who decided to purchase drew a cup from a bag and paid the price indicated by the cup. We found that (a) adding uncertainty into a price can generate a larger demand than lowering the price, and that (b) price magnitude may influence the initial purchase, but price uncertainty drives purchase along the way. In other studies, we found that (c) people are willing to repeat an activity when they have the opportunity to resolve uncertainty after each outcome but not when they don’t have such an opportunity, (d) they do not decide to repeat because the outcomes they receive are varied, and (e) in prospect, they do not expect they would enjoy uncertain outcomes. In sum, the findings on the positive uncertainty effect are counterintuitive and counter-normative, and they shed light on the intricate relationship between uncertainty and decision-making.

Risk aversion is behaviourally characterised by an inclination to choose any action over one with the same expected benefit but with greater variance in its consequences `(a mean-preserving spread’ of the action). In the orthodox treatment of risk, an agent’s degree of risk aversion is associated with the curvature of the von Neumann and Morgenstern (vNM) utility function representing her preferences over the goods serving as outcomes of lotteries. A common criticism is that this treatment collapses two distinct attitudes: to marginal increases in the quantity of the good in question and to the variance in the outcomes of the lotteries. To which it can be retorted that the criticism is simply senseless unless utility can be cardinalised independently of the rationality conditions on risk preferences built into the vNM framework. A number of recent theories (e.g. Cumulative Prospect, Rank Dependent Utility and Risk-Weighted Utility theory) take up this challenge by deriving a risk function on probabilities and a separate utility function on outcomes from preferences satisfying weaker conditions than the vNM ones. In this paper we explore a different (and more conservative) way of doing so: using Bayesian decision theory to provide the required cardinalisation of utility. Our crucial postulate is that chances (objective probabilities) of outcomes, being objective features of the world, can figure as possible consequences of actions. The application of Savage’s theory to preferences over acts with consequences that include both `ordinary’ outcomes and chances of such outcomes then yields a cardinalisation of the utilities of both without imposing any constraints on how the utilities of chances are related to the utilities of the outcomes of which they are chances of. Within such a framework it is possible to separate attitudes to marginal increases in quantities of a good from attitudes to marginal differences in the chances of a (fixed quantity of) a good. Agent’s preferences over lotteries will then reflect both factors. For instance, risk neutrality, qua indifference between an act and mean-preserving spreads of it, can result from concave utilities for both the good and for chances of the good, or from convex utilities for both, as well as, of course, linear utilities for both. We show that the typical patterns of preferences observed in both the Allais and Ellsberg paradoxes can be explained within such a broadly Bayesian framework, in terms of the dependence of the utility of marginal differences in chances of goods on the chances of other outcomes. We conclude by comparing this approach to modelling risk attitudes with that of Cumulative Prospect theory and related approaches.