3.1 New product forecasting

New product forecasting models for frequently-purchased products (deodorants, laundry detergents, juice drinks, etc.) incorporate a construct that is related to recognition. The construct is awareness. Specifically, let a _w be the percent of consumers aware of the new product, a _v be the percent of consumers who will find the new product available in the stores or on the web, T be the percent of consumers who will try the new product (conditioned upon awareness and availability), and R be the probability of becoming a repeat consumer (conditioned upon trial).Footnote ⁴ Then, to a first order, the market share of a new product is given by:Footnote ⁵

(1)

In frequently-purchased categories, consumers repurchase often, so a product cannot succeed if it does not satisfy consumer needs—if it does not earn R. But it also cannot succeed if it is never considered—if it does not earn a _w and T. (For this paper we ignore availability, a _w.Footnote ⁶)

In marketing two awareness constructs are measured and used in managerial decision making: unaided awareness and aided awareness. Unaided awareness is a more stringent criterion than aided awareness. For example, try to recall without aids the brands of deodorants on the market. When I ask MBA students to name deodorant brands (unaided awareness), each student can rarely name more than three brands. However, when I read a list of brands (aided awareness), the same students can easily recognize twenty or more brands. Unaided awareness is an excellent predictor of the brand the consumer will consider (Silk & Urban Reference Silk and Urban1978; Urban & Katz Reference Urban and Katz1983), and brand consideration is an excellent predictor of brand choice.Footnote ⁷ For example, in one study consideration explains approximately 80% of the uncertainty in deodorant choice (Hauser, Reference Hauser1978).Footnote ⁸

In marketing contexts it is important to distinguish whether consumers recognize brands with or without cues. If a consumer is given two or more brands and asked to choose among them, he or she is likely to use recognition as a first screen. If the choice is made in the laboratory, recognition is based on aided awareness because the consumer is given the brands to choose among. On the other hand, in real markets the consumer might make a shopping list or ask an agent to buy (spouse, parent, roommate, etc.). The consumer might even look through shelf facings in the supermarket or drug store and choose to examine those brands most recognizable. Shopping lists are likely based on unaided awareness, shelf-facing examination is likely based on a hybrid of aided and unaided awareness.

In laboratory test markets (also called “simulated test markets”), consumers complete tasks that provide estimates of T. Repurchase, R, is measured post laboratory. Brand plans for advertising and other communications provide data with which to estimate a _w. While practice is not univocal, it is more likely that awareness is an analog that is related to recognition. Real managerial decisions, and possibly millions of dollars in brand communications, are based on the goal of achieving aided and unaided awareness. For example, Proctor and Gamble spent $5.2 billion in 2008 on advertising and Unilever spent $7.8 billion in 2007.Footnote ⁹

While we argue below that recognition analogs are not the only decision rules used by consumers, simple recognition-based decision rules are clearly applicable in frequently-purchased product categories. In non-frequently-purchased product categories, such as consumer durable goods (automobiles, computers, furniture, appliances), recognition may be a screening rule but, before choosing a product, consumers are more likely to seriously evaluate those brands that are not screened out. In durable goods the (initial) purchase is relatively more important to consumers than repeat purchases which may occur years hence rather than weekly or monthly. Such variation in relevancy is consistent with the adaptive-toolbox paradigm. Consumers use recognition-based heuristics when such heuristics are likely to help consumers make good decisions. They use other decision rules in other situations.

3.2 Are recognition-based heuristics ecologically rational in brand choice?

We have argued that consumers use recognition as a screening rule, but, for recognition-based screening to be ecologically rational, the information in the environment should be such that consumers can exploit recognition to make better decisions. Simple heuristics often serve consumers well (Marewski, Gaissmaier, & Gigerenzer Reference Marewski, Gaissmaier and Gigerenzer2010). Some theories in marketing science suggest why consumers can rely on simple heuristics.

One theory of advertising, called “burning money in public”, is a signaling theory. Advertising is ephemeral; once money is spent there is no salvage value. Clearly a large advertising campaign (including web-based and social-media advertising) causes consumers to become aware, but it might also be rational for consumers to infer quality from the advertising campaign. The theories themselves are based on formal game theory and are carefully developed (e.g., Milgrom & Roberts Reference Milgrom and Roberts1986, Nelson Reference Nelson1974; Erdem & Swait Reference Erdem and Swait1998),Footnote ¹⁰ but the basic intuition is simple. A brand will succeed if it is sufficiently high quality to earn repeat purchases (R in Equation 1). If the firm advertises the brand and consumers try the brand, the firm can recoup its advertising expenditures through repeat purchase. On the other hand, if the brand is low quality it cannot recoup its advertising expenditures and will choose not to advertise. Through experience, consumers learn that heavily advertised brands are high quality and infer from advertising alone that the brand is high quality. It is only a small step from these signaling theories to recognition-based heuristics. Because advertising causes awareness of the brand name, and awareness is an analog of recognition, the consumer can infer high quality from recognition.

Even without game theory, we can see intuitively that firms with high quality brands will advertise more (and that it is rational for consumers to use recognition-based heuristics). In a simple model, profit (π ) is equal to the margin, m, from a sale times the sales volume, minus the cost of advertising (A). We continue to use the model of Equation 1 in which share is equal to awareness (a _w) times availability (a _v) times trial (T) times repeat (R). If there is a fixed volume, V, in the market, this abstract model gives us:Footnote ¹¹

(2)

It is reasonable that there are decreasing marginal returns to advertising spending.Footnote ¹² If advertising only affects awareness, then decreasing marginal returns implies that a _w(A) is concave in A. (By concave we mean the second derivative of a _w with respect to A is negative.) We maximize profit by setting the derivative of π equal to zero and solving for A. In symbols:

which implies

(3)

If the higher quality brand gets a higher trial and/or repeat, then TR is larger. Equation 3 implies that it is optimal for the firm to set A such that is smaller because it must equal TR, which is smaller when TR is larger. This condition implies that optimal advertising for a high-quality product (vs. a low-quality product) occurs where the a _w(A) curve is flatter. A concave curve is flatter when A is larger. Figure 1 provides a visual perspective of the implications of Equation 3. The slope of a _w(A ₂) is lower than the slope of a _w(A ₁) because higher quality implies that is lower than . The first-order conditions in Equation 3 can be satisfied only if A ₂ is greater than A ₁. In other words, the higher quality brand will advertise more and the consumer can infer quality from recognition.

Figure 1:

Concave Advertising Response Curve Implies More Advertising Spending for Higher-Quality Products.

Learning by observing other consumers (observational learning) reinforces recognition as a rational screening mechanism. Specifically, if many other consumers use a product, then a consumer might infer that the product is of high quality. But if many other consumers use a product, then it is more likely that the consumer will see the product being used. This usage will lead to recognition. Following this chain backwards the consumer might then infer that products are recognized if and only if they are higher quality. This argument is related to the “criterion ↔ mediator ↔ name-recognition” triangle in Marewski, et al. (Reference Marewski, Pohl and Vitouch2010) by substituting observational learning for media mentions.

Observational learning is common among consumers and affects their behavior. For example, Tucker and Zhang (Reference Tucker and Zhang2010, 2011) describe field experiments in which consumers use information on popularity to choose which websites to visit. Zhang (Reference Zhang2010) demonstrates that organ recipients infer quality from prior rejections and it is rational for them to do so.

Many websites, such as Amazon.com, use collaborative filters to recommend products (Breese, Heckerman, & Kadie Reference Breese, Heckerman and Kadie1998). For example, if I were to purchase Gut Feelings by Gerd Gigerenzer, Amazon.com would recommend other books that “customers who bought this item also bought”. If social networks are such that the consumers I observe most often share my preferences, then it is rational for consumers to rely on observation of their friends and acquaintances to infer which products match their preferences. Such inferences are enhanced when practical or economic constraints limit the feasible combinations of aspects that a brand can offer. (Following Tversky [Reference Tversky1972], an aspect is a characteristic of the brand, such as, “cleans cottons effectively”.)

For example, a laundry detergent that cleans white cotton fabrics well might be less gentle to delicate fabrics. With constraints on the ability to offer aspects, in equilibrium, firms will offer products that are on the “efficient frontier”. (By efficient frontier we mean that no viable brand is dominated by another brand as long as price is considered an aspect of the brand.) When all brands are on the efficient frontier, the consumer need only decide if the brand matches the tradeoffs among aspects that he or she wishes to make. For example, if there were only two aspects that described laundry detergents, “gentleness” and “effectiveness”, then I can choose the laundry detergent that is best for me by only considering “effectiveness”. I can do this because, among efficient-frontier products, the negative correlation of “gentleness” and “effectiveness” enables me to infer the “gentleness” of a detergent from the detergent’s “effectiveness”. Finally, if my friends and acquaintances share my preference tradeoffs, the laundry-detergent brand that they most prefer may be the laundry-detergent brand that I would most prefer. I am most likely to prefer the brand that I recognize because my friends and acquaintances use that brand.

Research on consumer decision rules is consistent with the efficient-frontier story. Non-compensatory heuristics often predict consumer preferences better than linear (compensatory) models in environments where aspects are negatively correlated as they would be if all brands were on the efficient frontier (Johnson, Meyer & Ghose Reference Johnson, Meyer and Ghose1989).Footnote ¹³

3.3 Sometimes recognition is only part of the overall story

Brand consideration is managerially important in the automotive industry. For example, a major US automotive manufacturer (“USAM”) invested substantial resources to study how they might entice consumers to consider their automobiles. Based in part on consumer experiences with past vehicles, one-half to two-thirds of US consumers would not consider USAM’s brands. Even though USAM had excellent new vehicles as judged by independent ratings, this lack of consideration meant that consumers would not observe that improved quality. After testing a variety of strategies, USAM determined that focused competitive test drives and putting unbiased competitive brochures on their website would enhance trust which, in turn, would enhance consideration (Liberali, Urban & Hauser Reference Liberali, Urban and Hauser2011). For example, competitive test drives were projected to increase consideration by 20% if implemented nationally. Strategies such as unbiased online advisors and community forums did not enhance consideration. Although they might have signaled trust, they also communicated aspects of USAM’s past vehicles that were of lower quality. USAM’s field experiments suggested that USAM needed strategies that did more than increase brand recognition; USAM needed marketing strategies that made it cost-effective for the consumer to obtain the information needed to evaluate a USAM brand.

Using extensive qualitative interviews, USAM came to understand that the majority of consumers (76%) were making consideration decisions based on non-compensatory heuristics—not recognition alone but rather conjunctions (and disjunctions of conjunctions) of aspects. To design vehicles and to design marketing campaigns based on consumer decision rules, USAM invested substantial resources to identify the heuristic decision rules consumers use when deciding whether to consider brands. In a decision problem with 53 aspects, non-compensatory models proved to be a much better description of consumers’ decision rules than additive models (Dzyabura & Hauser, Reference Dzyabura and Hauser2011). USAM used these data to identify clusters of consumers who share decision heuristics. That is, consumers were clustered based on the aspects that they used in their decision rules and whether they used a conjunctive or a compensatory decision rule. The main clusters were (1) conjunctive using primarily brand and body-type aspects, (2) conjunctive using brand aspects, (3) conjunctive using body-type aspects, and (4) compensatory using a larger number of aspects.Footnote ¹⁴ Consumers in these clusters also used other automotive aspects in either their conjunctions or compensatory rules. In automotive markets, recognition of a brand and its aspects serves as a cue and consumers infer quality from advertising and from observing other consumers, but consideration is more than recognition. Almost all consumers recognize USAM’s brands (even unaided); the majority of consumers would just not consider USAM’s brands. In order to move from recognition to consideration (and then to purchase), consumers need more-detailed information about the aspects of USAM’s brands—information such as body type, quality, crash-test ratings, fuel mileage, ride and handling, style, and other features. Rather than using recognition alone, consumers use heuristic decision rules based on these aspects to screen brands, typically to less than 10% of the brands on the market (Hauser & Wernerfelt, Reference Hauser and Wernerfelt1990).

The difference in the use of recognition-based heuristics between frequently-purchased products and automotive products is due, in part, to the magnitude of the consumer’s decision. Purchasing a vehicle is one of the most significant consumer decisions. Consumers might eliminate a few brands because the consumer does not recognize the brands (e.g., Tata), but it is rare that recognition will be part of the heuristic decision rule. Using decision rules with more aspects is rational in automotive decisions even though search costs are substantial (visiting a dealer, searching the Internet, talking to other consumers, paying close attention to advertising, etc.). For example, a consumer who wants to consider all sporty luxury coupes may begin his or her search for a new automobile by actively seeking to learn which brands have sporty luxury coupes.

3.4 Evaluation-cost model of brand consideration

The evaluation-cost model of brand consideration provides insight into how consumers might match heuristic decision rules to problems. Let ũ_j be the consumer’s beliefs about the utility of the j ^th brand. The tilde ( ˜ ) over the ũ_j indicates that, prior to second-stage evaluation, the consumer is uncertain about the utility he or she will receive from the j ^th brand. Let s _j be the search cost for the j ^th brand. We’ve assumed that the consumer knows the search cost, but allowing search cost to be a random variable does not change the basic argument. Then, in a sequential search, it is rational for the consumer to consider the n + 1^st brand if:Footnote ¹⁵

(4)

That is, if the consumer could anticipate the maximum values, the consumer would compare the expected return from choosing the best from n + 1 brands to the expected return from choosing the best from n brands. If that increment is larger than the search cost, the consumer will consider the n + 1^st brand; if not, stop. Even if all brands had the same expected utility, it is easy to show that the left-hand side of Equation 4 is decreasing in n. If the consumer uses an heuristic so that earlier-searched brands have larger expected values, the decrease is exacerbated. Equation 4 implies conditions where we expect recognition-based heuristics to be rational for brand consideration. Let m be the number of recognized brands. Recognition-based heuristics will be rational for consideration if the search cost of an unrecognized brand is larger than the expected utility that might be gained if the consumer were to choose from the m recognized brands plus an additional unrecognized brand rather than if the consumer were to choose from only the m recognized brands. It is not unreasonable that this condition holds for deodorants: the expected increment from choosing (long term) from a slightly larger consideration set, say four deodorants, is likely to be small. The search cost, while not large, is not inconsequential. The consumer has to purchase the deodorant and try it, perhaps in odor-critical situations. If some of the conditions discussed earlier hold (advertising as signaling, observational learning, assumption of an efficient frontier among a relatively few brand aspects), then the consumer might stop after considering the brands that he or she recognizes. In automotive decisions the search cost is much larger, but so are the differences in expected utility. Automotive brands vary on a large number of aspects and the consumer may need a larger consideration set to be comfortable about having enough exemplars of key brand aspects. Adding another brand to the consideration set might make new aspects available (all wheel drive, adaptive cruise control, city-safety-auto-stop, etc.). The value of choosing from a consideration set with an additional considered vehicle can be quite substantial. In many situations this increment in value exceeds the search cost the consumer incurs when he or she does not know the aspects of the unfamiliar brand. (Consumers may have mere brand-name recognition, say of Hyundai, but have little knowledge of Hyundai’s aspects.)

Ding et al. (Reference Ding, Hauser, Dong, Dzyabura, Yang, Su and Gaskin2011) summarize qualitative research by describing a consumer who they call “Maria”. Maria used a conjunctive decision rule based on nine aspects to select her consideration set: sporty coupes with a sunroof, not black, white or silver, stylish, well-handling, moderate fuel economy, and moderately priced. Maria was typical. Ding, et al. used an incentive compatible task in which over 200 consumers described their decision rules. Most decision rules were simple and most rules had a non-compensatory component, but not a single consumer used brand recognition.

Automotive decision rules are best for the situation in which the consumers are asked to consider or choose a vehicle. Consistent with the paradigm of an adaptive toolbox, consumers might rely on recognition when selecting which deodorants to consider but rely on a many-aspect decision rule when selecting which automotive brands to consider.

3.5 Summary of marketing science experience

In real markets recognition-based heuristics can be ecologically rational. They are more likely rational and more likely to be observed as decision rules for products that are low cost and do not vary on many aspects. They are less likely to be used for products that represent a substantial purchase decision and which vary on many aspects. Consumers are likely to adjust their decision rules accordingly and managers can use the knowledge of such adaptation to design and market products more successfully.

4.1 Search is endogenous

Automotive purchase decisions illustrate that the magnitude and complexity (number of aspects) of a decision affect the heuristic that consumers use. In real markets consumers can choose either to continue to search or to make a purchase decision with no additional search. Said another way, choosing to use recognition-based heuristics as evaluative decision rules is itself a decision that depends upon the information structure of the problem. In marketing science terms, this makes the decision rule endogenous (choosing the decision rule is part of the decision problem) rather than exogenous (the selection of the decision rule is pre-determined or determined by variables outside the problem at hand). The information structure can influence the decision rule, hence firms can take actions to influence the decision rule. If we observe a consumer using a decision rule in a real market it might be that we are observing the end result of firms’ optimal actions to influence a decision rule. For example, if we observe a consumer using a conjunctive decision rule based on brand and body-type aspects (only Audi, BMW, or Chrysler brands; only coupes or convertibles), then this might be the result of specific Audi, BMW, or Chrysler advertising or this might be the result of the way a salesperson presented information to the consumer. We must also evaluate whether the consumer will accept the decision rules implied by advertising or salesforce messages or whether the consumer will override those decision rules based on the consumer’s own preferences and experience.

Endogeneity means we must study how the consumer decides how to decide. The consumer’s decision rule is not automatic, although it may be a subconscious rule learned by prior experience or by analogy to other situations. Firms should expect to be able to manipulate the use of recognition-based heuristics (and other heuristics) by changing the rewards and costs of information search. USAM’s field experiments were, in part, an attempt to change the search costs for critical information and, hence, change consumers’ consideration decisions. Even in the laboratory, if search and thinking costs are minimized in an experiment or if we greatly enhance the relative rewards among brands, we might expect consumers to rely less on recognition.

4.2 In new situations consumers learn decision rules by self-reflection

Hauser, Dong, and Ding (Reference Hauser, Dong and Ding2011) sought to test three common methods of eliciting decision rules. Because they wanted to randomize over potential order effects (for within-subjects tests), they rotated the order of the tasks. Although one task was consistently better at predicting consideration in a delayed validation, they also found a large order effect, which persisted even when validation data were collected one-to-three weeks after the decision-rule-elicitation tasks.

Each of the three elicitation tasks were challenging to the subjects. For example, one task required that subjects evaluate 30 profiles on over 50 aspects. However, if the subject performed an elicitation task after another elicitation task, the subsequent task was a much better predictor of the delayed validation task. Qualitative data suggested strongly that the first task caused subjects to think deeply about the decision problem and, in doing so, think deeply about their decision rules. For example one subject volunteered “As I went through (the tasks) and studied some of the features and started doing comparisons I realized what I actually preferred.” When subjects got to the second and/or third elicitation tasks they used learned decision rules and continued to use the learned decision rules in the validation task one week later. The study was replicated with cellular telephones (with validation three weeks later), using a different experimental design. The cellular-telephone results also suggested that consumers learn by thinking deeply about their own preferences.

An hypothesis that consumers learn their decision rules through self-reflection is subtly different from an hypothesis that consumers’ decision rules are constructed in response to task characteristics and are easily influenced by manipulations (Payne, Bettman, & Johnson Reference Payne, Bettman and Johnson1992, 1993). Self-reflection learning suggests that naïve consumers do not carry around preferences (among aspects) or decision rules for categories in which they have not yet made a recent choice. Rather, when faced with a decision task in a new product category, consumers learn their own decision rules by attempting to use those decision rules in realistic choice situations. The hypothesis differs from the constructed-decision-rule hypothesis because, once the decision rules are learned, the decision rules are remarkably enduring. The learned decision rules become part of the adaptive toolbox.

The learning-by-self-reflection experiments also suggest an important methodological issue for experiments on consumer decision rules. Prior to the first elicitation task, all subjects completed an incentive-compatible warm-up task in which they evaluated ten realistic product profiles. This warm-up task was larger than the vast majority of warm-up tasks in the constructed-decision-rule literature. Perhaps key experimental outcomes in the constructed-decision-rule literature might be reversed if the experimenter first gave consumers warm-up tasks that are sufficient to enable self-reflection learning of preferences and decision rules.

Recognition-based heuristic experiments might also be sensitive to learning through self-reflection. It might turn out that recognition-based heuristics are used more often (or less often) when consumers are learning how to decide. Recognition-based heuristics might be used differently after consumers learn how to decide in a particular product category. For example, when a consumer first starts listening to a new genre of music, the consumer might purchase those songs which he or she most easily recognizes. However, as the consumer’s library of music increases and the consumer gains more experience with that genre of music, he or she might use a more sophisticated decision rule.

4.3 Recognition reduces risk

Roberts and Urban (Reference Roberts and Urban1988) study the process by which consumers learn about aspects of new products. They model explicitly how new information reduces risk and demonstrate that decision rules that take risk reduction into account explain consumer behavior better than decision rules that do not. To illustrate their model consider the well-known results for risk on a single product aspect. Assume for a moment that the consumer uses only one aspect in his or her decision rule. Anticipating a multi-aspect model and without loss of generality, we designate that aspect as the first aspect. Let be the uncertain value of that aspect for the j ^th brand. The tilde ( ˜ ) continues to denote a random variable. If we assume the consumer is risk averse with risk-aversion coefficient r and if we assume that is normally distributed with mean and variance then it is easy to show that the consumer will choose the brand with the largest “certainty equivalent (ce)”, where:Footnote ¹⁶

(5)

Equation 5 suggests that the consumer will discount risky brands, where risky has been defined by the fact that the consumer does not know for certain the level of the aspect that he or she will actually experience if he or she chooses (or at least considers) brand j.Footnote ¹⁷ To the extent that recognized brands have more certain aspects (lower ), Equation 5 provides one more argument why it may be rational to weigh more heavily recognized brands.

With the right technical assumptions we can extend Equation 5 to the multi-aspect case. Doing so leads us to use ce _kj rather than x _kj for the k ^th aspect when we describe how the consumer chooses among brands. If the decision rule is linear in the aspects, then risk implies that we discount those aspects about which the consumer is uncertain. If the consumer recognizes the brand (and there is no uncertainty in recognition), but the consumer is uncertain about all other aspects of the brand, then brand recognition will be relatively highly weighted in the linear rule. Risk reinforces the rationality arguments of Davis-Stober, Dana, and Budescu (Reference Davis-Stober, Dana and Budescu2010).

4.4 Consumer utility is not the same as a decision rule

Equation 5 establishes a case where the consumer’s utility is linear with one set of weights, but the consumer’s decision rule is linear with a different set of weights.Footnote ¹⁸ We use the results of Davis-Stober et al. (Reference Davis-Stober, Dana and Budescu2010) to establish another case with strong face validity. For most consumers, utility (net of price) for a new automobile is clearly decreasing in price. If a consumer could buy a 2011 Maybach 62S Landaulet for $10,000, he or she would surely consider it (assuming that the consumer recognized the Maybach brand and knew even a little about it). However, as much as we might like to dream, the Landaulet is reserved for “a select few customers with exceptionally deep pockets”.Footnote ¹⁹

Despite the fact that the consumer’s utility function is decreasing in price, it is still rational for the consumer to use price as a screening criterion. (I did so with the last vehicle I purchased.) It is rational because the desired tradeoffs in aspects in a vehicle are highly correlated with price. Price enters the decision rule differently than it enters the consumer’s utility function. By using price as a conjunctive criterion, the consumer can save the substantial search costs that might be incurred by test driving lower- and higher-priced vehicles. The lower- and higher-priced vehicles are not considered because there is little chance that the consumer would find the right aspects in a lower-priced vehicle and little chance that the consumer would maximize his or her utility by choosing a higher-priced vehicle. Brand names, or even aspects such as “coupe”, can easily enter a utility-maximizing consumer’s decision rule in ways that differ from the ways the same aspects enter the consumer’s utility function. This is particularly true of aspects that are negatively correlated with more-difficult-to-observe aspects that the consumer weighs heavily in his or her utility function.

My final observation is that some decision rules may be described by the researcher as heuristic simplifications but are actually optimal strategies by which the consumer can choose the product that maximizes utility. We have already seen that the value-priority algorithm for budget allocations and the more-time-for-higher-change-in-probability rule for information search are simple decision rules that might be described as heuristics but are, in fact, solution strategies that are near optimal. We expect to see such simple, but optimal, decision rules in other contexts.

For example, Gittins (Reference Gittins1979) established the surprising result that the optimal solution to extremely-difficult infinite-horizon highly-uncertain decision problems has a simple form. The problem is known as the “multi-armed bandit” problem because of an analogy to slot machines in a casino. (Slot machines are known colloquially as one-armed bandits.) Suppose we are faced with N slot machines and want to win the most money. Each machine pays off with some probability and the probabilities vary. However, you don’t know those probabilities. Each time you play a particular machine you learn something about its probability—you either win or not. The problem is to play the machines in some optimal manner trading off exploration (trying a new machine) with exploitation (playing the machine that you think has the highest probability of a payoff). This is an extremely difficult problem. Indeed, in an address to the Royal Statistical Society (February 14, 1979), the great statistician Peter Whittle opened: “[The bandit problem] was formulated during World War II, and efforts to solve it so sapped the energies and minds of Allied analysts that the suggestion was made that the problem be dropped [on their enemies], as the ultimate instrument of intellectual sabotage.” When Gittins proved that the problem had a simple solution, he opened up an entire literature. Gittins’ solutions now enable firms to solve all types of complicated choice problems including clinical trials, optimal experiments, job search, oil exploration, technology choice, and research & development project selection.

The proofs and the details are beyond the scope of this commentary. However, the basic form of the solution is to calculate an index for each choice object and, in every period, simply choose the object with the largest index. Subsequent research has shown that, while it may be difficult to compute the optimal index, indices can be approximated by simple functions. For example, consider Gittins’ index for the multi-armed bandit described above, but replace product experience with slot machines. For illustration, abstract the problem so that consumers observe only that a product is of high quality of low quality. If n is the number of times the consumer experiences the product i and G _i is the Gittins’ index, then G _i(n) smoothly decreases in n as shown in Figure 2 (adapted from Hauser, et al. Reference Hauser, Urban, Liberali and Braun2009, p. 221). In Gittins’ solution each product has an index and the consumer always chooses the product with the highest index.

Figure 2:

Gittins’ index as a function of the number of times the consumer tries a product.

It is not at all unreasonable that consumers might intuit the function form of G _i(n) and make close-to-optimal decisions with very simple rules. Consumers do not need to solve a complicated dynamic program to trade off learning about brands with consuming the highest-utility brand (Erdem & Keane Reference Erdem and Keane1996), but rather intuit a solution strategy that is somewhat similar to that described by an optimal Gittins’ index.

In mathematical programming and in machine learning there are many algorithms that achieve close to optimality with simple decision rules. We might expect consumers to learn these simple rules by experience or by observing others. Machine learning uses the concept of “complexity control” to improve the performance of algorithms (e.g., Vapnik, Reference Vapnik1998). The basic idea is to impose a constraint on the parameter space. This constraint, often arbitrary, prevents the algorithm from exploiting random error when choosing parameters. Subsequent predictions are more likely to be robust across situations that differ from the data on which they were calibrated. For example, Evgeniou, Pontil and Toubia (Reference Evgeniou, Pontil and Toubia2007) use complexity control to improve the predictive ability of linear models used to forecast consumer response to new products.

The analogy for consumer decision making is cognitive simplicity. When we constrained estimation methods to enforce cognitive simplicity in decision rules, we found that we were able to predict consumer consideration decisions much more accurately (Hauser, Toubia, Evgeniou, Dzyabura and Befurt Reference Hauser, Toubia, Evgeniou, Dzyabura and Befurt2010).