Children’s Utilization of Stated Probabilistic Information in Decision Making

In a variety of paradigms, children are confronted with stated probabilistic information in child-friendly formats, such as relative frequencies of options’ wins and losses, which they can subsequently utilize in choices. According to the classical Piagetian view, children up to 8 years of age completely lack an understanding of probability and thus the ability to properly utilize such probabilistic information (Piaget and Inhelder, 1951). However, more recent research has documented sensitivity for probabilistic information in 8-months-old infants who distinguished probable from less probable samples based on statistical properties of their environment (Xu and Garcia, 2008). Preschool-aged children are able to utilize stated probabilistic information for decisions in social contexts when choosing whom to trust or imitate (Pasquini et al., 2007; Zmyj et al., 2010); and to judge gambles with different expected values: children as young as 5 years consider winning probabilities and values and even integrate these variables in a multiplicative fashion (Schlottmann, 2001; Schlottmann and Tring, 2005).

When it is required to not only judge but to choose between two or more risky options, the findings have been strikingly different. Employing an information-board paradigm, Betsch and co-workers (Betsch and Lang, 2013; Betsch et al., 2014, 2016) assessed probabilistic inference decisions in preschoolers (6-year-olds) and elementary schoolers (9-year-olds). Preschoolers were not able to systematically use stated probabilistic information as decision weights. Moreover, only about one third of elementary schoolers was able to do so. This is consistent with studies that have shown that children up to 8 years of age do not systematically consider stated probabilistic information when choosing between lotteries (Levin and Hart, 2003; Levin et al., 2007b, but see Levin et al., 2007a). Thus, the evidence on children’s abilities to utilize stated probabilistic information for decision making is mixed. Judgment tasks so far suggest that children at preschool age consider such information (Acredolo et al., 1989; Anderson and Schlottmann, 1991; Schlottmann, 2001; Schlottmann and Tring, 2005); results in choice tasks are rather inconclusive with some demonstrating its utilization prior to school age (Levin et al., 2007a; Pasquini et al., 2007; Zmyj et al., 2010), while others do not (Levin and Hart, 2003; Levin et al., 2007b; Betsch and Lang, 2013; Betsch et al., 2014, 2016).

Children’s Utilization of Feedback in Decision Making

Children’s ability to improve their decisions through feedback has been studied with gambling tasks in which participants repeatedly choose between options of different expected value (e.g., decks of cards), and only learn about frequencies and magnitudes of associated gains and losses through experiencing outcomes. Children up to 13 years of age typically fail to properly learn from feedback to avoid inferior options when multiple pieces of information such as gains and losses for different options have to be considered to make a choice (for a review see Cassotti et al., 2014; Defoe et al., 2014). The high complexity of this type of game presumably accounts for the poor performance (but cf. Crone et al., 2005). In simpler versions, children at preschool age learn to choose the advantageous option more frequently (Kerr and Zelazo, 2004; Boyer, 2007). When options only differ on one dimension (e.g., only gains) even 3-year-olds can adapt their choices and improve their decisions over time (Bunch et al., 2007).

Further, children’s deficits in feedback processing are, at least partly, caused by their over-responsiveness to negative outcomes. When choosing between options, children are highly sensitive toward negative feedback (Crone et al., 2005; Huizenga et al., 2007; Eppinger et al., 2009) and tend to switch behavioral responses after experiencing failure (Cassotti et al., 2011; Van Duijvenvoorde et al., 2012). In a probabilistic environment where even the best performing behavior sometimes provides negative outcomes, this tendency leads children to abandon the superior response and thus prevents optimal choice performance (see Brehmer, 1980 for similar findings in adults).

Mixed-Information Paradigms

Studies that provide children with both stated information about probabilistic relations between choices and outcomes and self-sampled experience are rare. Mata et al. (2011) demonstrated that 9-year-olds can adapt their decision strategies to feedback in an information-board paradigm, when probabilistic information is provided before choices. Van Duijvenvoorde et al. (2012) observed children’s abilities to identify the advantageous option in a gambling task to be much improved when outcome probabilities and values were made explicit. However, even then children up to 13 years could not overcome the tendency to switch options after experiencing failure.

While these findings show that decisions can improve when the probabilistic properties of the environment are stated, research in child decision making provides little insight into how feedback influences choices that should be based on stated probabilistic information. Importantly, even in adults, feedback does not always improve decision making (see Karelaia and Hogarth, 2008 for a review) and can increase deviations from normative models (Barron and Erev, 2003; Newell and Rakow, 2007). Betsch and co-workers (Betsch and Lang, 2013; Betsch et al., 2014, 2016) found that 6-year-old preschoolers fully neglected stated probabilistic information, available as validities of different cues, and 9-year-old elementary schoolers partly did so when feedback could also be used for subsequent choices. Especially preschoolers switched between options in line with the last experienced outcome (Betsch and Lang, 2013). This leads to the question whether children’s neglect of such probabilistic information is due to the presence of feedback. As a second source of information, feedback can be used mal-adaptively by children and decrease the reliance on stated probabilistic information. If this is the case, children’s utilization of stated probabilistic information should be increased when no feedback is available. On the other hand, if feedback does not contribute to children’s probability neglect, it should be observed with and without feedback.

Results

Choices

We first analyzed choices on the aggregate level with our focus on over-responsiveness to recent outcomes in feedback conditions and an increased use of stated probabilistic information, that is, cue validities, in conditions without feedback. Secondly, we analyzed individual choice patterns, expecting children to use the feedback-based choices rule WSLS with feedback and to use probability-based choice rules substantially more frequently without feedback.

Over-responsiveness to negative outcomes in choices

To test whether children tended to stay with an option and switch between options based on recent feedback, we compared the percentage of option switches after a negative outcome to option switches after a positive outcome (OR = percentage of switches after losses/percentage of switches after gains). Over-responsiveness is reflected in increased switching after losses in feedback conditions (OR > 1). In adults, switches were equally likely following positive and negative outcomes, OR = 0.96, 95% Bootstrap CI [0.87, 1.04]. Likewise, in elementary schoolers, switches were equally frequent, OR = 1.11, CI [0.92, 1.38]. In contrast, preschoolers switched significantly more often after losses than after gains, OR = 1.31, CI [1.11, 1.52]. To ensure that this was indeed a result of the experienced outcomes and not due to a strategy independent of feedback, preschoolers’ option switching without feedback served as a standard of comparison, OR = 1.10, CI [0.98, 1.25], t(54) = 1.61, p = 0.017, d = 0.5. Thus, only preschoolers’ choices were over-responsive to negative outcomes indicating a bias by feedback that was absent in elementary schoolers.

Choices following the high valid cue (HVC)

Normatively, in this environment participants should always follow the HVC. Figure ​Figure33 depicts the mean frequencies of choices following the HVC’s prediction for each age group, separated for feedback conditions and prediction patterns. A GLM analysis of variance with the frequency of following the HVC as dependent variable, and age group, feedback condition (between) and pattern (within) as factors revealed large age and pattern effects as well as an age-pattern interaction, Age, F(2,160) = 57.46, p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.22; Pattern, Huynh–Feldt F(1.79,289.38) = 67.89, p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.20; Age × Pattern, Huynh–Feldt F(3.58,288.48) = 18.65, p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.12; all other ps ≥ 0.400.

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FIGURE 3

Mean frequencies of choices in line with the high valid cue’s predictions for each pattern type and feedback condition in Study 1. Chance level is four out of eight choices. Bars represent 95% bootstrap confidence intervals.

Adults approximated normative decision making in Types 1 and 2 prediction patterns with choices following the HVC’s predictions in 7 out of 8 cases. However, when both other cues contradicted the HVC this rate dropped to about half the cases. Similarly, elementary schoolers followed the HVC’s prediction less often in Type 3 patterns and chose generally less systematically than adults but still above chance level in the first two prediction patterns. Preschoolers, in contrast, performed at chance level in each prediction pattern.

Crucially, children without feedback did not follow the HVC’s prediction more often, neither in any of the prediction patterns nor when analyzed over all 24 choices, preschoolers, M_{No feedback} = 10.74, SD = 2.68, M_Feedback = 10.96, SD = 3.11; elementary schoolers, M_{No feedback} = 12.34, SD = 3.88, M_Feedback = 11.86, SD = 3.09; adults, M_{No feedback} = 17.89, SD = 4.05, M_Feedback = 17.11, SD = 4.02; all ps ≥ 0.83. Thus, the assumption that feedback prevented children from choosing in line with normative expectations was not supported.

Individual choice strategies

To account for individual differences, we classified participants according to their choice behavior over all patterns using an outcome based strategy classification method (Bröder and Schiffer, 2003). Predictions were derived from five different choice models (LEX; WADD; WSLS; SW; LVC, see section “Choice Strategies in Children”). For each individual, we calculated the likelihood of the observed choice pattern under each of these models, assuming that strategies are not applied flawlessly but with a constant error maximizing the likelihood. Individuals were classified to a choice model, if their choices fitted the model predictions perfectly or if (a) the likelihood for the classified strategy was higher than for any other strategy and at least twice as high as for a Random Model (OR > 2), and (b) at least 66% of choices were successfully predicted by the model. Otherwise participants were classified to the Random Model. Individuals with equal likelihoods for two strategies remained unclassified. Error rates were allowed to vary over participants. Table ​Table11 shows the results of the classification and the mean error rates for each age group and strategy.

Table 1

Strategy classification in Study 1.

	No feedback		Feedback		Overall
Preschoolers	n = 27		n = 29		n = 56
	n	%	n	%	n	%	Error
LEX	-	-	-	-	-	-
WADD	-	-	-	-	-	-
LVC	-	-	2	6.9	2	3.6	0.29
SW	3	11.1	3	10.3	6	10.7	0.18
WSLS			1	3.4	1	1.8	0.21
Random	15	55.6	20	69.0	35	62.5
Unclassified	9	33.3	3	10.3	12	21.4
Elementary schoolers	n = 26		n = 28		n = 54
	n	%	n	%	n	%	Error
LEX	1	3.8	1	3.6	2	3.7	0.15
WADD	2	7.7	3	10.7	5	9.3	0.21
LVC	1	3.8	–	–	1	1.9	0.21
SW	4	15.4	3	10.7	7	13	0.15
WSLS			1	3.6	1	1.9	0.25
Random	15	57.5	12	42.9	27	50.0
Unclassified	3	11.5	8	28.6	11	20.4
Adults	n = 28		n = 28		n = 56
	n	%	n	%	n	%	Error
LEX	7	25.0	7	25.0	14	25.0	0.08
WADD	10	35.7	10	35.7	20	35.7	0.07
LVC	–	–	1	3.6	1	1.8	0.25
SW	–	–	1	3.6	1	1.8	0.17
WSLS			–	–	–	–
Random	8	28.6	9	32.1	17	30.4
Unclassified	3	10.7	–	–	3	5.4

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Unclassified, individuals who could not be classified in one of the considered strategies; Random, random choice; probability-based choice rules; LEX, Lexicographic Rule; WADD, weighted additive rule, invalid choice rules, LVC, following low valid cue; SW, switching rule, feedback-based choice rule, only applicable in feedback conditions; WSLS, Win-Stay-Lose-Shift Rule; Error, mean error rate, that is, the mean proportion of trials in which strategy inconsistent choices were observed for the corresponding strategy and age group. For example, the error rate of 0.08 in adults being classified as LEX users means that on average strategy-incongruent choices were observed in 8%, that is, in less than two out of 24 choices. In case of n = 1, absolute values are displayed.

The individual strategy classification largely confirmed aggregate findings. Contrary to our expectations, WSLS was not a common choice rule in either child age group, and application of probability-based strategies was not more prevalent without feedback. Most children’s choices were captured best by the Random Model (63% in preschoolers, 50% in elementary schoolers), only a minor percentage of children applied a choice rule systematically (16% in preschoolers, 30% in elementary schoolers). Intriguingly, all preschoolers that followed any strategy at all relied on invalid information with a simple switching rule being most common (11%). Elementary schoolers, on the other hand, while employing invalid strategies as often as preschoolers (17%), also and almost as often applied probability-based strategies (13%).

While the majority of adults were classified as users of probability-based strategies, 30% were classified to the Random Model. This was mainly due to inconsistent behavior by these adults in decisions with the Type 3 pattern². Nonetheless, the prevalence of probability-based decision strategies was strongly determined by age, χ²(2, N = 166) = 61.42, p < 0.001, Cramer’s V = 0.61. Probability-based strategies were mainly used by adults (61%), rarely by elementary schoolers (13%), and not found in preschoolers. Complementary, invalid choice rules were not found in adults and were observed equally often in preschoolers (16%) and elementary schoolers (17%), χ²(1, N = 110) = 0.007, p = 0.93.

Method

The design, stimulus material, and procedure were identical to Study 1, with the exception that the information-board matrix in the choice phase was open so that all predictions could be inspected at once for every decision (see Figure ​Figure2C2C). Search data are therefore not available.

Results

Choices Following the High Valid Cue (HVC)

Figure ​Figure44 depicts the mean frequencies of following the HVC’s predictions for every age group, feedback condition and prediction pattern. The results largely matched those in Study 1. Again, feedback did not affect choices in any age: not in any of the patterns nor when analyzed over all 24 choices, preschoolers, M_{No feedback} = 10.09, SD = 4.63, M_Feedback = 10.78, SD = 4.42; elementary schoolers, M_{No feedback} = 13.50, SD = 5.02, M_Feedback = 14.21, SD = 4.35; and adults, M_{No feedback} = 18.52, SD = 2.58, M_Feedback = 18.70, SD = 3.65; all ps ≥ 0.40. A GLM ANOVA resulted in similarly large age and pattern effects, and a pattern-age interaction as in Study 1, Age, F(2,177) = 54.65 p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.26; Pattern, Huyn–Feldt F(1.59,281.64) = 93,24, p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.19; Age × Pattern, Huyn–Feldt F(3.81,281.64) = 42.79, p < 0.001, ${\mathrm{\eta }}_{\mathrm{G}}^{\mathrm{2}}$ = 0.18, all other ps ≥ 0.170. Adults followed the HVC’s prediction except when both other cues contradicted its prediction. The same pattern effect was observed in elementary schoolers, who followed the HVC’s prediction less systematically but above chance level in the first two prediction patterns. Preschoolers performed at chance level, regardless of the prediction pattern.

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FIGURE 4

Mean frequencies of choices in line with predictions of the high valid cue for each pattern type and feedback condition in Study 2. Chance level is four out of eight choices. Error bars represent 95% bootstrap confidence intervals.

Over-Responsiveness to Negative Outcomes But No Systematic Use of Feedback-Based Strategies

Children overreact to negative feedback and tend to switch responses. This behavior has been attributed to deficits in inhibitory control (Crone and van der Molen, 2007; Van Duijvenvoorde et al., 2012); and linked to the assumption, that negative consequences lead to an affective reaction to avoid this option, which must be actively overruled (Damasio, 1994, but see Brehmer, 1980). At the age of nine, children in our studies no longer showed over-responsiveness. This contrasts prior findings of over-responsiveness to negative outcomes until late school age (Cassotti et al., 2011), even when winning probabilities of options are stated explicitly (Van Duijvenvoorde et al., 2012).

Importantly, although over-responsiveness biased preschool-aged children’s search and choice behavior, they did not strategically utilize recent outcomes and consistently rely on an option-based Win-Stay-Lose-Shift rule for choices, which solely considers recent feedback. On individual level Win-Stay-Lose-Shift did not fit children’s choice patterns when compared to other plausible models of choice. This apparent contradiction underlines the important distinction between data analysis at the aggregate and the individual level. It is still possible, that children applied a more sophisticated form of Win-Stay-Lose-Shift as a feedback-based strategy, for example switch and stay in relation to the option’s expected value calculated over several trials (e.g., Worthy and Maddox, 2014). However, application of such a strategy is inconsistent with the overall lack of differences between feedback conditions on both aggregated and individual level.

Robustness of Probability Neglect

In line with previous findings, we observed large differences between age groups in the utilization of stated probabilistic information for choices in both studies. The majority of adults used strategies based on stated probabilistic information such as the Lexicographic or Weighted Additive Rule consistently while only few elementary schoolers and only one preschooler did so. Previous studies with the same paradigm have found that such probability neglect is only marginally affected by variations of the decision environment such as information search constraint (Betsch et al., 2016) or lure information (Betsch and Lang, 2013). The present findings further underline the robustness of probability neglect in children’s risky decision making. Across two decision environments—one requiring an active search for cue predictions, the other displaying all cue predictions without search—preschool-aged children at the age of six were unable to utilize stated probabilistic information to adapt choices, whereas 9-year-old elementary schoolers were partly able to do so. Further, withholding feedback had no facilitating effect on the utilization of stated probabilistic information at the aggregate or the individual level. Thus, probability neglect is not a consequence of the mixed-source paradigm which offers feedback as a second and possibly preferred source of information.

Our findings contribute to the complex picture of children’s ability to utilize stated probabilistic information for decisions and are in line with findings from gambling studies that highlight children’s deficits until late school age (Levin and Hart, 2003; Levin et al., 2007b). However, there is also contradicting evidence stemming from selective trust tasks (Pasquini et al., 2007), judgments tasks (Schlottmann, 2001), and low-complex experienced-based gambling tasks (Bunch et al., 2007), in which utilization at preschool age was observed. Although these paradigms differ much in terms of information presentation and complexity, they all share that probabilities are directly assigned to options. The challenge for children is to make advantageous choices between these options. In a probabilistic inference task, however, the relations between options and outcomes are moderated by cues, to which these probabilities are assigned. Therefore, they pose a greater challenge to children’s conceptual understanding of probabilities, which might overburden them and explain the contradictory results. Probability neglect in children might therefore strongly depend on specifics of the probabilistic environment created by the research paradigm.

Development of Decision Strategies

Our results corroborate prior findings regarding the prevalence of probability-based strategies in individuals of different age groups (e.g., Mata et al., 2011; Betsch et al., 2014). At the age of six, children do not rely on probability-based choice rules, at the age of nine this ability is still emerging. This is in line with research from other areas that suggests a strong developmental improvement in cognitive strategy use during that period (see Björklund and Causey, 2018 for an overview). Yet, while most children neglected both sources of potentially valid information—stated probabilistic information and feedback—many nonetheless did not chose randomly between options. Instead, they systematically relied on invalid information, that is, information that was not useful to maximize choice outcomes, such as, which cue was liked the most and which option had been chosen in the preceding decision. This is not only interesting from a theoretical point of view, but holds important implications for the improvement of decision quality in children. Rather than just introducing or teaching appropriate strategies, children’s current strategies must be directly addressed and revealed as inappropriate.

Implications of Individual Strategy Classification

In each age group we observed rather large proportions of individuals that could not be classified to a decision strategy (i.e., Random). This finding has two important implications. First, it shows that adults’ decision behavior is a more appropriate benchmark for children’s decisions than normative standards, that is, ideal choices under all circumstances. Second, though, it points to a limitation of our strategy classification method. Many adults remained unclassified because they choose indifferently in Type 3 prediction patterns. We cannot rule out, however, that these participants used different strategies for different prediction patterns, which the applied method cannot detect, or might have used decision strategies not considered a priori. For example, participants might have applied an Equal-Weight Rule (e.g., Payne et al., 1988), which prescribes to follow the majority of predictions and, in case of a tie, to guess between options. This would lead to guessing in two thirds of the investigated choices and choices in line with the majority in Type 3 prediction patterns. We cannot rule out that single participants might have used this strategy; however, choices in Type 3 prediction patterns are not in line with this model.⁴ It is therefore unlikely, that it was widely used in any age group.

Further, it is conceivable, that participants classified to WADD instead used a compound-strategy that favors the option with more positive predictions and only in case of indifferences considers cue validities. Although, this strategy would lead to exactly the same choices as WADD, the underlying cognitive steps are quite different. Nonetheless, it would still rely on the probabilistic cues. As our main focus was to differentiate choice rules based on which kind of information was used—probabilities, feedback, or invalid information—the possibility of a compound-strategy does not alter our interpretation of the results.