|
Article Excerpt
1. Introduction
Past decisions often serve as input to subsequent related decisions. Specifically, the conclusion reached in a previous decision can potentially shed light on how to approach the decision at hand. For example, an individual who several weeks ago evaluated a certain bouquet of flowers and was in favor of purchasing it at a given price, now has to decide whether to buy a similar bouquet of flowers at a higher price. A football fan who could not secure a ticket for a sold-out game at regular price, now has to decide how much to bid on e-Bay for an auctioned ticket. A young professional who recently accepted a job offer in a large city, rejecting a similar but higher paying job located in a small suburban town, is currently deciding how much to bid on a house located in the suburbs. In all these cases, the question arises as to how knowledge of the prior decision (willingness to purchase the bouquet at a certain price; desire to buy the ticket at regular price; rejection of the job located in a suburban town) affects willingness to pay for the option currently being considered (the value to assign to the new bouquet of flowers; the amount to bid on tickets online; the amount to bid on the suburban house).
When individuals are certain of their preferences, or can establish them effortlessly, previous evaluations should not influence subsequent decisions. In reality, however, individuals may face considerable uncertainty regarding the value of a good to them, or how they should trade off different product attributes. For example, in negotiating payment on a particular floral arrangement for an upcoming dinner party, the host may wonder about the importance of bright versus dark colors, the length of the stems, or the type of flowers in the arrangement (tulips, orchids, etc.). The relative importance of each floral arrangement attribute can depend on a number of aspects relevant for the consumption occasion--such as who will be coming to the party, what activities are planned for the party, or where the flowers will be displayed.
Given that the individual is not sure about her preferences, she may try to reduce the uncertainty in several ways. First she can exert effort, in the form of cognitive thinking or time-consuming research, to ascertain the influence of the different aspects. For instance, the host could reflect on the guest list to determine how the floral arrangement under consideration might impress each of them, and she could contemplate on how the arrangement would appear in different locations in the house. Second, the decision maker might invoke information from past related decisions. For example, the host may recall her conclusion regarding a similar bouquet she saw a few weeks ago in a floral shop. In the context of such sequences of decisions, we ask: How are the incentives to expend effort to determine willingness to pay affected by recalled information from a prior decision? How does incorporating information from a previous decision affect the final valuations used to make future decisions?
The goal of this paper is to answer these questions theoretically and experimentally. We construct a model of individual decision making that has three central features: (a) Individuals are uncertain about their preferences, in the sense of how much utility will be derived from consuming a good or how much each attribute will contribute to overall utility; (b) costly cognitive effort can be expended to reduce the uncertainty; and (c) input from a previous decision can be incorporated. In other words, we investigate how boundedly rational individuals use their own prior decisions as a source of information about their utility structure when making subsequent decisions. We analyze the case of an individual who needs to determine her willingness to pay for a single good that she previously considered purchasing at a given price. We also examine the robustness of the primary forces at work when two alternatives are evaluated and a prior choice between them is taken into account.
We identify the broad conditions under which three central results hold. First, we show that incorporating recall of a prior decision outcome leads to more extreme valuations, that is, valuations that deviate considerably from the individual's ex ante mean. When multiple alternatives are under consideration, taking into account a prior decision will result in a greater spread of valuations between the goods. Second, we find that this increased spread is more pronounced when the decision stakes are higher (that is, when the goods are of higher ex ante expected value). Lastly, we find that the expected amount of effort expended in valuing alternatives is greater when prior decisions are taken into account. This last result is especially intriguing, given that effort has already been expended on making the previous decisions.
The main intuition giving rise to these results is that prior decisions not only convey information about the value of the good in and of themselves, but also affect the incentives to expend effort to gain more information in subsequent related decisions. We show that the objective function that relates costly cognitive effort expended to the amount of variance explained, the effort-accuracy relationship, is altered by recalling past decision outcomes. Specifically, the differing outcomes of prior decisions have an asymmetric impact on how an individual trades off current effort with the desire to arrive at a more accurate valuation. Depending on whether a good was chosen or rejected in a previous decision, the individual considers the good to be of greater or lesser value, respectively, relative to the ex ante mean. In the former case (greater value), the individual perceives a very high marginal return from effort that overshadows the lower marginal return from effort in the latter case (lesser value). Consequently, incorporating prior decisions is likely to yield final valuations that are more informed, that capture more of the variance associated with uncertain preference parameters, and that hence differ considerably from their (uninformative) ex ante mean.
We conducted a series of experiments using actual prizes in a familiar product category: dining at local restaurants. The empirical results largely confirmed the main implications of the theory: A prior decision increased the spread of valuations between subjects' most and least preferred alternatives, and, on average, subjects who made relevant prior decisions took significantly longer time than those who had not to determine valuations. Furthermore, the impact of a prior decision on valuation spread became more pronounced as the average value of prizes increased.
The rest of the paper is organized as follows: [section]2 relates our work to relevant literature; [section]3 develops a theoretical framework for modeling the impact of prior decisions on subsequent valuations; [section]4 formulates the key findings of the model as hypotheses, which are tested in a series of controlled lab experiments; and [section]5 concludes. All proofs are given in the appendix.
2. Literature Review
In a series of papers, Fischer et al. (2000a, b) posit that decision makers can be uncertain about their preferences. Their use of random attribute weights is similar to our approach in [section]3.6. The major difference between our work and theirs is that we allow individuals to reduce preference uncertainty by exerting cognitive effort and by recalling relevant prior decisions. By contrast, in Fischer et al. (2000a, b) uncertainty is exogenously fixed. Our work is thus more in line with behavioral decision theory, which demonstrates that individuals face effort-accuracy trade-offs in making decisions (Payne et al. 1993). Moreover, we find it highly plausible that if an individual makes prior decisions regarding an alternative, those will be taken into account in subsequent decisions. (1)
Hsee (1996) and Hsee et al. (1999) study a specific form of preference uncertainty, whereby an attribute whose importance is ex ante uncertain will receive less weight when an alternative containing the attribute is evaluated separately than when it is evaluated jointly with another alternative. This can lead to preference reversals across the two evaluation modes, but has only been demonstrated between subjects. By contrast, our focus is on the implications for final valuations of the same individual intertemporally combining information from a sequence of decisions. Hence, our analysis is more appropriate for dynamic contexts where decisions are not a one-shot task.
Although we model an individual who incorporates information from her own prior decision, our analysis would be similar if the previous decision were made by some other individual, as long as their preferences and incentives are identical. This links our model to the literature on social learning (e.g., Banerjee 1992, Bikhchandani et al. 1992, Gale 1996), where each agent receives a private and independent signal for the value of undertaking some behavior and agents' decisions are sequential and observable. Our analysis differs from this literature as follows. First, individuals in that literature always face the same kind of decision whereas we consider two different types of related decisions (a purchase decision at a given price and a willingness to pay assessment). Second, and more importantly, in the social-learning literature signal precision is exogenous (with all individuals receiving equally accurate signals), whereas we focus on the case where the individual endogenously determines the precision of each signal. Hence, our approach allows examining the impact of prior decisions on the incentives to invest in the accuracy of future signals. (2)
In our model, individuals may recall only partial details of a past decision. Hirshleifer and Welch (2002) show that amnesic decision makers, who recall only previous actions but not previous signals, may follow their current signal more often than full recall individuals, who remember all previous actions and signals. (3) This happens when there is considerable environmental uncertainty that can change an alternative's true value. We do not incorporate such environmental uncertainty. However, relative to our model, they treat signal accuracy as exogenously fixed, which may be a strong assumption given their managerial focus. In Dow (1991), individuals sequentially search two sellers of a good for the lowest price. Consumers partition prices into categories and remember only the category a previously encountered price belongs to. Chen et al. (2005) go a step further by analyzing a market in which competing firms incorporate such memory limitations in their price-setting strategies. In our analysis, consumers are uncertain about their own valuations but not about prices encountered. Our analysis is hence more relevant when past prices are known (e.g., when price is part of the product description itself, or the individual took note of the prices). Moreover, there is evidence in psychology (Engelkamp 1998, Lingle and Ostrom 1979) that individuals can reliably recall their past actions and the decisions they faced but not the underlying reasoning that led to their actions. This suggests that it is likely that the decision to buy or forgo a good at a given price is recalled but that the informational content of aspects considered and that led to the action are less reliably recalled.
Cognitive effort in our model entails a cost, which can be relevant for a broad set of preference formation problems (Ergin 2003). (4) Shugan (1980) offers a methodology for quantifying the thinking cost of comparing different alternatives. In his model the individual knows her utility function and uncertainty arises from having to examine ex ante unknown attribute levels. Our model is more appropriate when product attribute levels are known (e.g., the specs of a computer) but the individual is uncertain how much each attribute or feature will contribute to her utility.
3. Model and Theoretical Results
This section presents our main theory and results. We first analyze the case of a decision maker who considers a single good of uncertain value to her ([section][section]3.1-3.4). We start by describing the model's characteristics. In particular, we explain the relationship between the amount of effort expended and the information gained about the value of the good. We also describe the process through which new information from subsequent effort is integrated. Next, we establish the optimal effort the individual would choose to incur: (a) When asked to decide between purchasing and rejecting the good at a given price, and (b) when asked to provide her monetary value for the good. Lastly, we analyze how recall of a past decision regarding the purchase of the good would impact a subsequent valuation of the good, in terms of the effort expended and the properties of the final valuation. In [section]3.6, we extend our framework to examine the case of multiple goods that possess multiple attributes.
3.1. Model Setup: Single-Good Case
Consider a consumer who is contemplating whether to purchase a good of ex ante unknown value v to her, which is offered at a given price p. The consumer can make a more informed decision by engaging in introspection. Such introspection reveals information on various consumption aspects that affect her utility from the good, and can be regarded as a mental cost accompanied by disutility. (5) The consumer is thus rational in that she wishes to make an optimal decision that maximizes her expected utility, but she is constrained (or bounded) by the costliness of effort needed to acquire information relevant for resolving uncertainty about her utility. (6)
Given the consumer's uncertainty about the value of the good, we treat v as a random variable and assume without loss of generality that its expected value is E[v] = 1. The consumer may expend effort c (measured in terms of utility) to reduce the uncertainty associated with v. If, based on the information gained from the effort, she chooses to purchase the good at price p, her utility will be
v - p - c.
If she rejects the good after incurring effort c, her utility will be (-c).
One can envision a situation where the value v of the object is a function of many uncertain aspects that are stochastically independent, and that the more effort the individual exerts the more aspects she learns about. Specifically, let
v = [y.sub.0][y.sub.1] ... [y.sub.n] ..., (1)
where [y.sub.n] are independent random variables with mean 1 that reflect the uncertain aspects. By expending effort c, the individual learns the values of some of these random variables. We write N(c) for the set of...
|
