Decision factors that support preference learning

Decision factors that support preference learning Alan Jern and Charles Kemp {ajern,ckemp}@cmu.edu Department of Psychology Carnegie Mellon University Abstract People routinely draw inferences about others’ preferences by observing their decisions. We study these inferences by char- acterizing a space of simple observed decisions. Previous work on attribution theory has identified several factors that predict whether a given decision provides strong evidence for an un- derlying preference. We identify one additional factor and show that a simple probabilistic model captures all of these factors. The model goes beyond verbal formulations of attri- bution theory by generating quantitative predictions about the full set of decisions that we consider. We test some of these predictions in two experiments: one with decisions involving positive effects and one with decisions involving negative ef- fects. The second experiment confirms that inferences vary in systematic ways when positive effects are replaced by negative effects. Keywords: preference learning; decisions; probabilistic model; attribution Suppose your friend Alice orders a boxed lunch that in- cludes an eggplant sandwich and you are curious how much Alice likes eggplant sandwiches. The conclusion you reach could depend on several factors. If there were many other boxed lunches available, perhaps Alice’s preference for egg- plant sandwiches is relatively strong. If all boxed lunches ex- cept the eggplant sandwich box come with a free cookie, per- haps Alice’s preference for eggplant sandwiches is extremely strong. On the other hand, if the eggplant sandwich is part of the only box that contains a cookie, perhaps Alice’s pref- erence for eggplant sandwiches is relatively weak and she really wanted the cookie. As these examples suggest, any given choice could potentially have many different explana- tions, and deciding which of these explanations is best is often a challenging inductive problem. In cases like these, observing someone make a decision provides information about his or her desires or prefer- ences. Two classic proposals along these lines are Jones’s and Davis’s (1965) correspondent inference theory of attri- bution and Kelley’s (1973) ANOVA model, both inspired by Heider (1958). Both proposals identify some normative principles that predict when an observed decision provides strong evidence for an underlying preference. The ANOVA model has influenced subsequent computational accounts of learning and reasoning (Cheng & Novick, 1992), but there have been few computational accounts that address the issues emphasized by correspondent inference theory (see Medcof, 1990). Here we show that a simple probabilistic model cap- tures some of the key principles of the theory, along with some additional principles not identified by Jones and Davis. To explore the factors that support preference learning, we work with a space of what we call decision events—observed decisions among discrete choices. Each event involves a set of options, and each option may have one or more effects. For example, a restaurant may offer three boxed lunches (three options), and one of these lunches may include an eggplant sandwich and a cookie (two effects). One principle of corre- spondent inference theory asserts that unique effects are max- imally informative: for example, if Alice chooses the only boxed lunch that includes an eggplant sandwich, perhaps her preference for eggplant sandwiches is relatively strong. A second principle asserts that as the number of chosen effects increases, the less strongly one can conclude that an actor sought one particular effect. For example, if Alice’s choice happens to be the only box that contains an eggplant sand- wich and the only box that contains a cookie, perhaps she likes the cookie rather than the eggplant sandwich. Both of these principles, along with several others that we discuss, are captured by a simple probabilistic model known as the multinomial logit model (McFadden, 1973). This model is common in the economics literature, and has re- ceived some attention in the psychological literature (Bergen, Evans, & Tenenbaum, 2010; Lucas, Griffiths, Xu, & Fawcett, 2009). The model assumes that an actor assigns some utility to each effect, and chooses probabilistically among the op- tions in proportion to the total utility assigned to each one. Given these assumptions, it is possible to work backward from an observed decision to infer the likely utility assigned to each effect. Lucas et al. (2009) showed that the model helps to explain how children use statistical information to make inferences about others’ preferences (Kushnir, Xu, & Wellman, 2010). We build on this work and suggest that the model provides a comprehensive account of preference learn- ing over the full space of decision events. A space of decision events The first step is to formally characterize the space of decision events. We will use a running example where an actor is given a choice between bags (i.e., options) that contain candies of different brands (i.e., effects). The actor chooses a bag con- taining a Brand x candy, and our goal is to infer the strength of the actor’s preference for Brand x . Figure 1a shows the 14 distinct decision events that involve up to four effects. The event on the far left is a case where the choice set includes a single bag that contains only a Brand x candy; the event on the far right is a case where the choice set includes four bags each containing a candy from a different brand. Since the la- bels of the candies are not important in this example, a single representative is included for all decision events that are the same up to relabeling. For example, the event that involves a single bag containing x and a is equivalent to the event that