Comparing attribute-based and memory-based preferential choice

Jarecki, Jana B.; Rieskamp, Jörg

doi:10.1007/s40622-021-00302-9

Comparing attribute-based and memory-based preferential choice

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Published: 24 March 2022

Volume 49, pages 65–90, (2022)
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Comparing attribute-based and memory-based preferential choice

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Abstract

Common theories of multiattribute preferential choice predict that people choose options that have on average better attribute values than alternative options. However, following an alternative memory-based view on preferences people might sometimes prefer options that are more similar to memorized options that were experienced positively in the past. In two incentivized preferential choice experiments (N = 32, N = 28), we empirically compare these theoretical accounts, finding support for the memory-based value theory. Computational modeling using predictive model comparison showed that only a few participants could be described by a model that uses sums of subjectively weighted attribute values when experience was available. Most participants’ choices resembled the predictions of the memory-based model, according to which preferences are based on the similarity between novel and old memorized options. Further, people whose experience consisted of direct sensory exposure, like tasting a portion of food, were also those with higher likelihoods of a memory-based process, compared to people whose exposure was indirect. These results highlight the central role of memory and experience in preferential choices and add to the growing evidence for memory and similarity-based processes in the domain of human preferences.

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Introduction

Imagine a person selecting a lightweight but expensive pair of running shoes. How do they arrive at this preference? A common psychological theory of preferences is multi-attribute value or multi-attribute utility theory (e.g. Keeney and Raiffa 1976). It explains preferences by a trade-off between attribute values; for example, a lighter weight of a shoe justifies a higher price (e.g. Dyer and Sarin, 1979; Keeney and Raiffa 1976; Krantz and Tversky 1971). People are assumed to have different preferences because of inter-individual differences in the importance of attributes (if the shoes’ weight is unimportant, it will not justify a high price) and the utility given to different attribute values. This account of human preferences is highly prominent and generally well supported (e.g. Galotti 1999; Ikemi 2005; Poortinga et al. 2003; Van Oel and Van den Berkhof 2013; Wu et al. 1988). We will empirically test this attribute-based approach against an alternative memory-based view on human preferences.

Memory-based approaches represent another family of multiattribute preference theories, which need not be inconsistent with multi-attribute value theory (Payne, Bettman, Schkade, Schwarz, and Gregory 1999; Slovic 1995). Memory-based approaches include attribute value updating with experience (Müller-Trede et al. 2015; range frequency theory, Parducci 1965; options as information theory, Sher and McKenzie 2014) or extrapolating from the evaluations or from value anchors in memory (Barkan et al. 2016). These memory-based approaches stress that experience and memory will systematically affect preferential evaluations. The present work focuses on memory-based preference theories that explain preferences based on a combination of the memorized attribute values and the subjective overall evaluation of previous options in memory (Gilboa and Schmeidler 1995, 1997, 2001; Gonzalez et al. 2003; Scheibehenne et al. 2015). These memory-based value theories suggest that people use a current option’s attribute values in combination with the attribute values and evaluation of options in memory and make a choice based on similarity. People should, for instance, prefer a new lightweight shoe over a heavyweight shoe after they have had good experiences with lightweight shoes, because the new shoe’s attribute values are similar to the experienced attribute values. Conversely, if people had memorized bad experiences with lightweight shoes, they would dislike a lightweight new shoe. The preferences regarding a new option that is very similar to a previous option’s attribute values should resemble the previous option’s good or bad subjective evaluation. Conversely, if new options are dissimilar to previously experienced options, the subjective evaluations of the options in memory should have little influence on the preference for the new option. This theory, which we will label memory-based value theory of multiattribute preferences, suggests that preferences are a function of the similarity to and the experienced subjective evaluations of memorized previous options.

The present article aims to test one instantiation of a memory-based value theory against the classic multi-attribute value theory. In the classic multi-attribute value theory, preferences are a function of the current option’s attribute values. In memory-based value theory, preferences depend on the attribute values and the overall evaluation of memorized options compared to the current option’s attribute values. The classic multi-attribute value theory, the associated psychological processes, and the elicitation of the subjective importance weights (Fischer 1995) have been studied extensively in psychology, marketing, and consumer research (for a review in marketing, Van Ittersum et al. 2007). However, comparably little attention has been devoted to the family of memory-based value theories (as already remarked by Weber and Johnson 2011). Therefore, we report two empirical tests of one specific instantiation of memory-based value theory in different consumer domains.

Similarity as a fundamental cognitive mechanism of decision-making

The similarity to memorized options, which is a key component of the memory-based value theory of preferences that we investigate, has received support across many psychological domains. Most of this work focusses on inferences, meaning situations in which decision makers receive external feedback, such as learning skills (Gonzalez et al. 2003), learning judgments (Juslin et al. 2008), or learning categorizations (Medin and Schaffer 1978; Nosofsky 1992; Nosofsky et al. 2014; Smith 2014). For example, the well-supported instance-based learning theory posits that the similarity to past action-situation pairs determines the next actions’ perceived utility (Gonzalez et al. 2003). Despite the empirical support for similarity-based processes in inferences, in the domain of preferences, in which due to the subjective nature of the decision no external feedback about performance exists, the application of similarity-based theories seems underrepresented compared to their prominent role in the domain of inferences.

Mechanisms underlying memory-based and multi-attribute value theory

The psychological mechanisms in multi-attribute value theory differ from those in memory-based value theory (see Table 1). One difference concerns the role of current versus memorized information. In multi-attribute value theory, the current options’ attribute values are what drives preferences without necessarily accessing experiences from memory. By contrast, in memory-based value theory, previously experienced options influence preferences. As such, memory-based value theory is path-dependent, meaning that if two people have experienced different options, their preference for the same new option may differ; and the theory consequently allows that the order in which options are experienced can change preferences for subsequent options. Memory-based value theory also requires the processing of not only the attribute values but also of the overall evaluation of memorized options, such as “how did I like past running shoes and how lightweight were these shoes?” In multi-attribute value theory, by contrast, people need to access the subjective importance of attributes “how important is the weight of running shoes?” Lastly, in memory-based value theory, the information is integrated into a psychological similarity by computing distances, whereas in multi-attribute value theory, information is integrated by a linear additive summation.

Table 1 Main differences between the multi-attribute value theory and memory-based value theory

Full size table

Memory-based and multi-attribute value theory’s predictions differ regarding attribute interactions and the complexity of the cognitive process. When preferences are an interaction-free linear function of attributes such as in Fig. 1a, both theories can explain such preferences (Fig. 1a, small panel “MAV” and “MEM”, the formal models used for the prediction are described in the next section). Multi-attribute value theory traditionally does not describe interactions between attributes (Keeney and Raiffa 1993; Keeny and Raiffa 1976). Memory-based value theory describes such interaction-free preferences if people have seen all options, and this principle extends beyond the shown example with two attributes. However, when the true preferences are not interaction-free, as in Fig. 1b, memory-based and multi-attribute value theory’s predictions differ unless the latter theory’s complexity is increased by accounting for interactions. In Fig. 1b, options are preferred for which either both attributes take low or both take high values, and the options with intermediate attribute values are less preferred. The classic multi-attribute value theory cannot explain these preferences unless explicit attribute interactions are added. Therefore, when fitted to the data, it predicts similar preferences across all attribute value combinations (Fig. 1b, small panel “MAV”). Memory-based value theory, by contrast, can explain these preferences well, given the decision-maker has experienced the attribute combinations (Fig. 1b, small panel “MEM”). This is because the memory-based theory determines preferences from the similarity between an option and the other options’ overall subjective evaluation, that is the preference. A memory-based value theory can thus explain many preferential patterns that multi-attribute value theory explains and above this can describe additional data patterns in the presence of attribute interactions without increasing the theory’s complexity.

In the current work, we empirically compare memory-based value theory to multi-attribute value theory. We will use existing cognitive model implementations of the theories and test them in a preferential domain, adding to the growing evidence for memory’s central role in preference formation (e.g., Gluth et al. 2015; Mechera-Ostrovsky and Gluth 2018; Sher and McKenzie 2014). To this end, we conducted two multi-attribute choice experiments and used computational modeling to assess the theories’ predictive validity. The experimental task design reported here goes beyond earlier work (Bettman and Zins 1977; Scheibehenne et al. 2015), because several past experimental designs fully controlled the options’ attribute values but needed to use hypothetical rather than real choice options without the possibility to incentivize participants (e.g. Gershman et al. 2017; Sher and McKenzie 2014). Other designs used real consumer products with incentives, but without fully controlling the options’ attributes (e.g. Gluth et al. 2015). Both of the experimental designs used in our tests have the advantage of providing full control of the attribute values and simultaneously using real products that allow incentivizing participants.

Empirical evidence for similarity-based processes in the preferential domain

There are some results supporting similarity to memorized options as a cognitive mechanism in preferential choices. Early exploratory results have found indicative evidence for similarity to previous choices in consumer decisions (Bettman and Zins 1977). Huber (1975) received mixed results when formally testing a multi-attribute value theory against a specific version of a memory-based preference theory, testing if the psychological similarity to a prototypical previous experience influences preferences for new options. Scheibehenne et al. (2015) have reported support for memory-similarity processes in consumer choice. Participants were trained in an environment in which the true relationship between wine attributes and prices was similarity-based, and most participants inferred prices for new wines from the similarity between the new and past wines in memory. However, since participants received external feedback about the actual wine prices in this study, the study design resembled an inferential learning task rather than a pure preferential task. Overall, these empirical results indicate that similarity to options in memory constitutes a promising cognitive process underlying not only inferential but also preferential choices.

Cognitive models instantiating memory-based and multi-attribute value theory

The next paragraphs present the computational cognitive preference models that we used to formalize the theoretical accounts. Both these models are deliberately not new models, rather we focus on comparing two established models in the domain of preferences.

Multi-attribute value model

The multi-attribute value model we use is the classic additive multi-attribute value model without interactions (Keeny and Raiffa 1976), which calculates a subjective value for an object i characterized by attributes a_i by

$$\begin{array}{*{20}c} {v_{i} = b + \mathop \sum \limits_{d} w_{d} \times a_{id} } \\ \end{array}$$

(1)

where a_id denotes the d^th attribute value of the i^th object. The weights w_d are free parameters, interpreted as subjective importance of attributes, which allow to model individual heterogeneity in the attribute value trade-offs; further, b is a free parameter mathematically corresponding to the intercept in a regression, which is interpreted as individual evaluative bias toward objects.

For decisions between purchasing an object i or keeping m dollars, the model additionally calculates a subjective value of money by

$$\begin{array}{*{20}c} {v_{m_i} = w_{m} \times m_{i} } \\ \end{array}$$

(2)

where m_i is the monetary loss if buying object i and w_m is a free model parameter, that we do not interpret here (because it mainly rescales the monetary range to fit the attribute range). In this case, the decision-maker’s net value of an option i equals the subjective value difference between the object and its price, v_i – v_mi. In case of a choice between an option and a monetary amount (as implemented in the experiment), the choice probability of choosing the option o_i over the monetary amount m_i can be determined with a logit choice rule: $\Pr \left({ \text{prefer } o_{i} } \right) = \frac{1}{{1 + \exp \left( { v_{i} - v_{{m_{i} }} } \right)}}.$

Memory-based value model

We implemented memory-based value theory using a classic multiple-cue judgment model which is commonly used to explain inferential choice (Juslin et al. 2008; Scheibehenne et al. 2015) and extends Nosofsky’s (1986) exemplar model suggested by the generalized context model (GCM). The model assumes that the similarity to options in memory determines preferences. Psychological similarity is computed by a similarity function, and the similarity s_ie between an object i and an object e in memory is given by the inversely scaled distance between the objects’ attribute values:

$$\begin{array}{*{20}c} {s_{ie} = \exp \left[ { - \lambda \left( {\mathop \sum \limits_{d = 1}^{D} w_{d} \left| {a_{id} - a_{ed} } \right|} \right)} \right] } \\ \end{array}$$

(3)

Where a_id and a_ed are the attribute values of the d^th attribute of objects i and e, respectively. Parameters, w_d and $\lambda$, are free model parameters, with $0\le {w}_{d}\le 1; {\sum }_{d}{w}_{d}=1,$ and $\lambda$ > 0. The parameter w_d is interpreted as the proportion of attention to the d^th attribute, and $\lambda$ is the discriminability between objects. These parameters allow to model inter-individual differences. The model here uses a city-block (Manhattan) distance metric (other metrics are possible, Goldstone and Son 2005), which is the recommended metric for separable attributes as we will use (Nosofsky 1992). The distance is rescaled to a similarity measure by an exponential decay function that allows to model individual discriminability of objects in psychological space.

The subjective overall evaluation of option i is a weighted sum of the memorized qualities of the previous options, weighted by the standardized similarity between the current and previously seen options:

$$\begin{array}{*{20}c} {v_{i} = \mathop \sum \limits_{e} v_{e} \times \frac{{s_{ie} }}{{ \mathop \sum \nolimits_{e}^{{}} s_{ie} }}} \\ \end{array}$$

(4)

where s_ie is the similarity between the current object i and a past object e, and v_e is the quality value of an object in memory, e indexes the options experienced until and excluding the current trial.

When responses are binary (select the option or the money), we use softmax choice rule (Sutton and Barto 1998), which is the equivalent of the logit choice rule in the multi-attribute value model, to arrive at the predicted probability to prefer an option over the monetary value: $\Pr\left( {\text{prefer } o_{i} } \right) = \frac{1}{{1 + \exp \left( { - \tau \left( {v_{i} - m_{i} } \right)} \right)}} ,$ where m_i is the price of option i, the parameter $\tau$ is a temperature parameter and a free model parameter ($\tau >0)$ with higher values leading to more random choice.

Relation of the memory-based preference model to other models

Our implementation of the memory-based model resembles Juslin’s (2003) extension of Nosofsky’s (1986) model (GCM) with an added softmax choice rule. Our model also relates to instance-based learning (IBL, Gonzalez et al. 2003) and the microeconomic case-based decision theory (case-based decision theory, Gilboa and Schmeidler 1995). The latter has been formally studied but not yet empirically tested (Gilboa and Schmeidler 1995, 1997, 2001; Gilboa et al. 2002). The GCM and IBL share with our model that psychological similarity to options in memory forms the basis of evaluations (Gonzalez et al. 2003; Juslin et al. 2008; Medin and Schaffer 1978; Nosofsky 1986). Unlike these models, our model does not rely on external feedback but uses the decision-maker’s subjective past estimations. Thus, our model relies on an internal evaluation criterion.

Experiment 1: preferences between writing pens

The goal of Experiment 1 was to empirically test the memory-based value theory against multi-attribute value theory. We used a multi-attribute preferential choice task about writing pens, described by four binary attributes. Figure 3 shows the materials. In an initial phase, participants formed subjective preferences for half of the available pens, after which they indicated preferences for eight old and eight new pens with novel attribute value combinations.

Methods

Participants

In total, 33 participants recruited from the University of Basel subject pool completed an online study, one was excluded (for evaluating the eight pens in the BDM auction with only two distinct values), leaving a final sample of N = 32; 29 females and 3 males (91% and 9%, respectively), mean age 25 years (Mdn = 22, SD = 6, range 19–50 years), mean remuneration was 2.6 CHF (Mdn = 2.7, SD = 0.8, range 1.2–3.9 CHF; n = 18 received a pen, see below for the incentives), the study was approved by the institutional review board of the Department of Psychology of the University of Basel.

Task

An incentivized multi-attribute choice task was used, as illustrated in Fig. 2. The task was to choose a writing pen shown image on the screen which had four attributes, see Fig. 3. Participants initially saw only 8 of the 16 pen attribute combinations (stimulus 1–8 in Table 2). For each of the 8 pens, participants first stated their willingness to pay as a value between 0.00 and 4.00 with two-digit precision, which was incentivized using a Becker–Degroot–Marschak auction, hereafter BDM auction^{Footnote 1} (for details, see Becker et al. 1964); which was repeated once; the first BDM auction served as familiarization. The elicitation of the willingness to pay allowed us to, by design, account for inter-individual differences in how much the participants generally valued pens to avoid assuming that everybody liked pens equally.

Table 2 Attribute value combinations used in the experiments

Full size table

After the BDM evaluation, participants completed a two-alternative choice task in which they repeatedly chose between one of the eight pens they had already seen and a monetary value. The monetary value was the individual’s BDM value, because it adapts the choice task to individual differences in liking pens. Participants made the choices for 8 pens in random order, repeated for 10 blocks (yielding 80 choices). Each block contained the same set of choice pairs in a different order. The pens were repeated to allow for valid estimations of the decision models. Participants could choose freely between the pen or money; no feedback was given, and the task was incentivized (see below). Our design involved choosing between a pen and money, rather than between two pens, to keep the task relatively short.^{Footnote 2} The learning phase served to stabilize preferences, accounting for the fact that BDM values represent true subjective values imperfectly (Noussair et al. 2004), and different response formats (pricing or choice) can produce inconsistent preferences (Lichtenstein and Slovic 1971). Because we model choices in our analysis, this design kept response modalities for old (learning) and novel (test) options identical.

Next and without announcement, participants entered a test phase. The task did not change, participants selected between a pen and money, but they also saw 8 new pens with new attribute combinations. Participants decided between pens and the BDM value, and for the pens they had not seen before the average BDM value of the evaluation phase for the other pens was presented as the second monetary option. In within-block randomized order, choices were repeated for all pens for 5 blocks (80 trials in total).

The task was designed such that every value of each attribute appeared during the learning phase, but not all possible attribute value combinations were shown, ensuring that all participants experienced the attribute values and to avoid that differences in experienced attribute ranges would influence the new attributes’ perception (Sher and McKenzie 2014). Further, participants were familiarized with the attribute value ranges before the evaluation phase. Table 2 shows the attribute value combinations during learning and test, with values 0 and 1 representing the pens’ two attribute values. Attributes were binary to simplify the task. The mean similarity between the options in the test phase and the learning phase was kept relatively equal (see Supplement A, Table s1); additionally, the design ensured that each new option had a high similarity to some old options and had a low similarity to other old options.

Materials and procedure

Figure 3 shows the material: writing pens differing in tint color, case color, the color of an ornament, and case shape, resulting in 16 possible attribute combinations. The pens were manufactured for this experiment (to incentivize participants) such that pens differed in only the four attributes and no other aspects. After the experiment, one random trial of the BDM auction or the choice phase was realized as bonus payment in form of a real pen or money. BDM trials were paid according to the BDM mechanism (see footnote 1), choice trials were paid according to the participant’s choice. The instructions informed participants about the bonus payment procedure.

Results

The analyses were conducted in the statistical environment R v3.6.0 (R Core Team 2019), the cognitive models were estimated using the glm native R function and the cognitive models package v1.0.2 (Jarecki & Seitz, 2019). The analysis code is available at https://osf.io/bn53z/.

Descriptive similarity analysis

Qualitative tests of predictions from memory-based value theory will be reported first followed by cognitive modeling results. If preferences involve similarity to memorized options, then the new options that a person likes should be more similar to the old options in memory that the person has liked compared to the disliked old options in memory. Conversely, new options that a person disliked should be more similar to old disliked options than old liked options in memory. The theory thus predicts that the similarity between new and old pens determines how much a person likes the new pens. To test these hypotheses, we defined the old pens in memory as pens seen during the learning phase and defined liking a pen as choosing it more often than the pen chosen with median frequency^{Footnote 3} (disliking otherwise) at the individual level, because participants had their own preferences.^{Footnote 4} Similarity was measured as Manhattan (city-block) distance^{Footnote 5} between each new pen in the test phase and the old learning-phase pens, averaged across the old pens. We tested if the liked new pens were more similar to the liked old pens than to the disliked old pens, which was supported: Fig. 4a shows that the pens that were liked in both the learning and test phase were more similar to each other (similarity M = 2.20), compared to the pens that were liked in the learning but disliked in the test phase (M = 1.53). These effects are based on the new pens; the mean similarity difference was MΔ = 0.67 and significantly greater than zero, 95% CI [0.53, 0.81], t(31) = 9.94, p < .001, Cohen’s d = 1.757. Considering the similarity to the disliked old pens, the opposite pattern emerges, as hypothesized: Pens that were disliked during both the test and learning phases were more similar to each other (M = 2.02) compared to pens disliked during the learning but liked during the test phase (M = 1.54), with a significant difference, MΔ −0.47, 95% CI [–0.66, –0.29], t(31) = –5.20, p < .001, Cohen’s d = 0.920. These analyses used only the new pens, the effects from computing the similarity between learning phase and test phase using old and new pens are even stronger; see Supplement B, Table s3.

Memory-based value theory further suggests that when new pens are more similar to an old pen that a person preferred very much, the person should choose the new pens more often. Conversely, the more similar a new pen is to a consistently disliked old pen, the less it should be chosen. Figure 4b shows that the relative pen choice frequency during the test phase—i.e., preferring pens over money—correlates positively with the test-phase pens’ similarity to the most-liked past pen from the learning phase. Conversely, choice frequencies correlate negatively with similarity to the least-liked past pen, at the aggregate level. Most-liked (least-liked) pens were defined as the pen with the maximum (minimum) choice frequencies during learning, and similarity was defined as described above. If multiple pens were most-liked during learning, the mean similarity between pens in the test set and the most-liked learning set pens was used. The resulting data pattern does not change when computing correlations for each different pen separately, suggesting that the correlation is not an aggregation artifact (Supplement B, Figs. 1 and 2). Participants were 3.4 times more likely to select the pen over money if the pen increased in similarity to the pens they liked most in the learning phase, which was reliable in a generalized mixed logit (GLM) regression taking the repeated measures into account (random participant intercept and correlated slope, pooled across pens), $O{R}_{sim(most)}$ = 3.45, b = 1.24, 95%CI [0.94,1.57], p < .001. Participants were less likely to prefer a pen over money when the pen increased in similarity to the least-liked pen from the learning phase, $O{R}_{sim\left(least\right)}$ = 0.23, b = –1.48, 95%CI [–1.98,– 1.04], p < .001. GLMs were fit in R by maximum likelihood with the lme4 package version 1.1 (Bates et al. 2015), here and below. These analyses are based on the new and old pens shown in the test phase.

Because in certain cases, the predictions of memory-based value theory resemble those of multi-attribute value theory, the just-shown qualitative findings could also be the result of a decision process following multi-attribute value theory. To directly pinpoint the two theories’ processes against each other, computational model comparisons were employed.

Model-based analysis

Modeling Procedure

The models were compared to a baseline random choice model with constant Pr(prefer o_i) = 0.50 for all trials. Sensible models are expected to outperform the baseline model. An additional simplified version of the multi-attribute value model was tested to control for effects of overfitting, because the multi-attribute value model might overfit the data and therefore perform badly in predicting choices for an hold-out sample (Dawes 1979; Geman et al. 1992). The additional model was constructed by constraining all parameters of the multi-attribute value model to unit weights (+ 1 or −1), with the sign being based on the sign of the estimated weights from the unconstrained multi-attribute value model.^{Footnote 6} We call this model the unit-weights multi-attribute value model (hereafter MAV-UNI).

The memory-based model’s attention weight parameters were restricted to equal-weighting (see also Persson and Rieskamp 2009), which means that only its memory-similarity mechanism, rather than an attention mechanism, is left to account for data. The memory-based model requires as input the subjective overall evaluations of objects in memory (v_e in Eq. 4), which is a latent value that we approximated by increasing the BDM value for a chosen learning-phase pen decreasing the BDM value for rejected pens.^{Footnote 7} All free model parameters (ws in the multi-attribute value model; $\lambda , \tau$ in the memory-based model) were estimated at the individual level to the data from the first 80 trials in which only 8 of the 16 pens appeared using maximum likelihood.^{Footnote 8}

Parameter estimates

Table 3 shows summary statistics of the resulting estimated parameter values after classifying participants as best described by each model. The most important attribute, for the participants best described by a multi-attribute value theory, was the color of the pen.

Table 3 Model parameter estimates for experiment 1

Full size table

The models’ parameters were fixed to each participants’ maximum-likelihood estimates to generate the model predictions for the hold-out data in the last 80 trials (the data not used for parameter estimation). Predictive model comparisons were used to account for differences in model complexity, since a priori it is not clear which model is more complex because although the multi-attribute-value model has more parameter, the memory-based model uses the trial order as input.

Model comparison at the aggregate level

The mean log likelihoods of the data given the models, aggregated over participants and trials, showed that the memory-based model (MEM) predicted participants’ test-phase choices best. The rank order of log likelihoods was MEM > MAV > RAND > MAV-UNI with respective mean log likelihoods equal to –40, –55, –80, –114 (log likelihood values of 0 indicate perfect predictions). The multi-attribute value (MAV) model and the equal-weights version of it (MAV-UNI) were even outperformed by the random model, in the aggregate. This is, in part, driven by the sensitivity of log likelihood to outliers since some individuals are particularly poorly predicted by the MAV model (Fig. 5a shows four outliers). When changing the scoring rule to a less outlier-sensitive one, the random choice model performs worst in the aggregate, as expected: scored by predictive accuracy (meaning proportion correct predictions with an arg max choice rule with Pr > 0.50 = 1, Pr < 0.50 = 0, Pr = 0.50 = 0.50), the models are ordered as MEM > MAV > MAV-UNI > RAND, with respective mean accuracies of 78%, 76%, 53%, and 50% predicted choices. Figure 5a and b also show that compared to the memory-based model, the multi-attribute value model with equal weights performs poorly when measured by mean-squared error, indicating that although the multi-attribute value model seems to correctly capture the direction of preferences, it mostly fails to predict the degree of preference strengths. Taken together, at the aggregate level, the memory-based model performs better than the additive multi-attribute value models. Because the aggregate level analysis averages out individual heterogeneity, we report an individual strategy classification next.

Model comparison at the individual level

Individuals were classified as described by a model based on the log likelihood of their responses in the last 80 trials given the model predictions. The results shown in Fig. 5c reveal that the memory-based value model predicts more than half of the participants best (n = 18 of 32, or 56%), followed by the multi-attribute value model (n = 11; 38%). The unit-weights and random model predicted two participants best (6%). Figure 5c also shows that the relative evidence strength (Wagenmakers and Farrell 2004) for the models is strong or very strong for most participants. Taken together, the individual-level analysis corroborates the aggregate-level results, suggesting that similarity to evaluations from memory play a vital role in preference formation for the majority of participants. The results also show that a substantial proportion of participants follow a decision process as explained by the multi-attribute value model, a finding that was not transparent at the aggregate level.

Illustration of model differences

The differences in model predictions will be briefly illustrated next. A situation where memory-based and multi-attribute value construction differ strongly is when one attribute seems most relevant for preferences given previous experience. Figure 6 illustrates a participant (S7, Exp. 1) who during the 80 learning trials prefers options for which the second attribute value is 1, mostly preferring options x1xx over x0xx. Multi-attribute value theory explains this behavior by a high importance of a value of 1 on the second attribute, as shown in the MAV importance weight estimates in the bottom-right of Fig. 6. Accordingly, multi-attribute value theory predicts the participant to like the novel option “0110,” but the participant never choses this option in the test trials. The memory-based value theory can capture this behavior. It compares the novel option “0110” to the learning-phase options and realizes that the novel option is rather dissimilar to the liked old options.

Extrapolation analysis

Next, we analyze why the additive multi-attribute value model failed to predict choices compared to the memory-based model. We investigate, how well a memory-based versus a multi-attribute-based process extrapolates to preferences for in the test phase. We selected the trials in which the models made very different predictions about the eight novel options that appeared in the test phase, across participants. Figure 7 compares the preference strength predicted by the models to the mean observed choice proportion for each novel option in the test phase. The figure shows that when the memory-based (MEM) model predicts higher preference strength compared to the multi-attribute value-based models (MAV), the MAV model underestimates the observed preference (left panel).

When the MEM model predicts a lower preference strength than MAV, the MAV model tends to overestimate the observed preferences for the pens. Only in the trials where MAV and MEM make roughly equal predictions does the MAV model capture observed choices well (middle panel). These results indicate that a multi-attribute value preference model fails in extrapolation because this process exaggerates preferences in the wrong direction, on average, compared to the memory-based model.

Temporal change analyses

Temporal changes in preferences offer a different way to compare assumptions underlying multi-attribute value theory and memory-based value theory. Because the classic multi-attribute-based theory suggests that decision-makers’ importance weights do not change over time, it assumes stable preferences unless one adds an additional importance learning process that learns importance weights to the model, which is possible but not part of the original model. By contrast, memory-based value theory can suggest that preferences change in a systematic way because decision-makers’ values and preferences develop dynamically with the incoming experience.

Figure 8a and b illustrate the preference development according to the models across the experimental trials 1 through 80. The figure also highlights two participants’ preferences; one participant with stable preferences and one with changes across the encounters of the pens. Note that memory-based value theory can model changing and stable preferences (e.g., Fig. 8a, stimulus “1011”). Figure 8c shows that participants changed their preferences by 17 percentage points, on average; where preference change was measured as the change in choices between the first half and the second half of the trials (M = 0.18, Mdn = 0.18, SD = 0.07, range = 0.05–0.32), which is greater than zero, 95% CI [0.15, 0.20], t(31) = 14.97, p < .001, d = 2.64. As robustness check, we excluded the first block—in which participants may explore the task-and re-tested for preference changes between trials 9–48 and 49–80; the preference changes remained (M = 0.19, 95% CI [0.16, 0.22], t(31) = 14.29, p < .001, d = 2.52). This means that many participants’ preference changed over time, which is not in line with the assumption of preference stability in multi-attribute value theory. Also, an extension of the multi-attribute value model that includes attribute interactions cannot model the observed changes over time.^{Footnote 9} Thus, it appears as if the mulit-attribute value model needs to be extended with a dynamic learning component that allows to explain changes of the importance of attributes.

To assess the models’ performance with respect to the preference changes over time, we compared the observed and predicted preference changes by the MAV and MEM model (given their estimated parameters). To this end, we calculated the just-described measure of preference change based on the predictions by the MEM model and separately for the MAV model, the latter of which predicts zero change. The performance was scored by the individual mean-squared error (MSE) between the predicted change and the observed change. It turned out that the MEM model outperformed the MAV model for n = 17 participants, whereas the MAV model scored better for n = 15 participants; the mean MSE was MSE_MEM = 5.8% (SD = 3%), and MSE_MAV = 6.5% (SD = 3.8%; median: MSE_MEM = 5.3%, and MSE_MAV = 6.0%).

Discussion

Experiment 1 used a preferential choice task to compare memory-based to additive multi-attribute value theories. The results of the first experiment suggest that memory and similarity to past experiences may be determinants of preferential choices. Both at the aggregate and individual level, a model with a memory-based comparison process performed at least as well as the standard additive interaction-free multi-attribute valuation model in predicting preferential choices; however, a substantial minority of participants was best described by models representing multi-attribute theories of preferential choices. This shows heterogeneity in human preference formation.

Experiment 2: tasting cereal bars

The pens in Experiment 1 were presented visually. Although visual presentation is common in situations such as internet purchases, many real-world preferential choices are more experiential. That is, individuals can touch, taste, or smell the goods before a purchase in situations such as food tastings, in clothes stores, or by test-driving cars. To avoid limiting our results’ generalizability to visual presentation formats, we extended the experimental paradigm by adding experience. Further, we adjusted the presentation on the screen to control for bottom-up visual saliency effects and slightly modified the learning phase to account for individual differences in the time needed to form preferences (please see the procedure section).