Older adults select different but not simpler strategies than younger adults in risky choice

Younger and older adults often differ in their risky choices. Theoretical frameworks on human aging point to various cognitive and motivational factors that might underlie these differences. Using a novel computational model based on the framework of resource rationality, we find that the two age groups rely on different strategies. Importantly, older adults did not use simpler strategies than younger adults, they did not select among fewer strategies, they did not make more errors, and they did not put more weight on cognitive costs. Instead, older adults selected strategies that had different risk propensities than those selected by younger adults. Our modeling approach suggests that age differences in risky choice are not necessarily a consequence of cognitive decline; instead, they may reflect motivational differences between age groups.


Application of the resource-rational strategy selection model to another dataset
To examine the generalizability of our conclusions for the dataset by Pachur, Mata, & Hertwig [1], we applied the resource-rational strategy selection model to the dataset collected by Horn, Schaltegger, Best, & Freund [2], who also examined risky choices in younger and older adults.To our knowledge, this is the only other dataset available for which there is a relatively large number of choices per participant, which is a prerequisite for reliably estimating the model parameters.It should be noted, however, that Horn et al. [2] did not find age differences in decision quality and risk aversion (a likely reason for this discrepancy with regard to the findings by Pachur et al. [1] is that their sample of older adults had considerably higher education levels).In that sense, the datasets by Horn et al. [2, ] and Pachur et al. [1, ] are somewhat difficult to compare.Still, given that similar decision behavior might be achieved by younger and older adults using different strategies (e.g., [3]), the dataset by Horn et al. [2] might still be an informative testbed for the current purposes.
Horn et al. [2] had collected risky choices from 147 younger adults (71 female, 68 male, 8 other, mean age: 25.4 years, range: 18-36 years) and 139 older adults (79 female, 60 male, mean age: 70.2 years, range: 60-89 years), recruited via Prolific Academic.Participants completed 78 risky choice problems, consisting of two gambles each with two outcomes and corresponding probabilities.Choice problems were evenly distributed across the gain, loss, and mixed domain.The type of incentivization was manipulated between participants; half of the participants received a financial bonus based on one randomly drawn choice and the other half received a financial bonus based on all their choices.Because there were no differences in decision quality and risk aversion between incentivization conditions, we collapsed both conditions for the purpose of our current analysis.

Posterior Predictive Checks
For each participant, we computed the proportion of trials in which the choice predicted by the model matched the empirically observed choice (averaging across 100 S3.2 Figure S3.1 shows the decision quality and risk aversion as empirically observed and as predicted by the resource-rational strategy selection model.Since in the Horn et al. [2] dataset the age differences in decision quality and risk aversion were not statistically significant, we did not conduct a statistical analysis of age differences in the model predictions.Note, however, that the model described the overall behavioral patterns in the data quite well. We also compared for each participant their empirically observed decision quality and risk aversion (pooled across all three problem domains) against the decision quality and risk aversion of the choices simulated with their best-fitting model parameters (Figure S3.2).The higher a participant's decision quality, the higher was the decision quality of their simulated choices (r = 0.94, BF 10 = 1.0 × 10 127 ).Moreover, the simulated levels of risk aversion were strongly correlated with the empirical ones S3.3

Comparison of simulated (based on the fitted resource-rational strategy selection model) and empirically observed levels of decision quality (left) and risk aversion (right) in the dataset by Horn et al. [2]. Each circle represents one participant (with the choices pooled across the three domains; i.e., gain, loss, mixed). The diagonal lines indicate identity (i.e., perfect fit).
(r = 0.69, BF 10 = 6.1 × 10 37 ).This analysis shows that similar as for the data by Pachur et al. [1] reported in the main text, the resource-rational strategy selection model captured the individual differences in choice behavior between participants rather well.

Age Differences in the Model Parameters
Although younger and older adults did not differ in decision quality and risk aversion, they might still rely on different strategies.A Bayesian contingency-table test showed that there was strong evidence that the distribution of strategies differed between age groups (BF 10 = 2.8 × 10 47 , Cramér's V = .11;Figure S3.3).The strategies with the more pronounced age differences in strategy use were the least-likely strategy (more often selected by older adults) and the equal-weight strategy (more often selected by younger adults).
To compare model parameters between younger and older adults, we conducted one-sided Bayesian t-tests.There was moderate evidence that older adults did not incur lower costs by the strategies used (BF 10 = 0.11), moderate evidence that older adults did not have smaller strategy toolboxes (BF 10 = 0.19), strong evidence that the S3.4  S3.5 cost-weighting parameter was not larger for older adults (BF 10 = 0.07), and inconclusive evidence that the trembling-hand error is higher for older adults (BF 10 = 2.3).Overall, these findings corroborate the conclusion from the main text that age differences in strategy selection are not predominantly driven by cognitive factors.

Parameter Recovery Analysis
We conducted a parameter recovery analysis similar to the analysis conducted for the choice problems from Pachur et al. [1] also for the Horn et al. [2] data.For the cost-weighting parameter delta, the recovered parameter values were correlated with the data-generating parameters at r = .35.For the trembling-hand error, the recovered parameter values were correlated with the data-generating parameter values at r = .90.
The recovered toolbox sizes were correlated with the data-generating toolbox sizes at r = .50.When computing the average strategy cost for each agent, we found a correlation of r = .47between the cost of the data-generating and the recovered strategies.On average, the data-generating strategy was recovered correctly in 53.7% of trials.For comparison, a model that guesses an agent's strategies would correctly recover the strategies in only 9.1% of trials.

Model Comparison
When comparing the model fit between the resource-rational strategy selection model and cumulative prospect theory, cumulative prospect theory captured the choice data better than the resource-rational strategy selection model for both younger and older adults (Table S3.1).

Table S3.1
Log-likelihoods of the resource-rational strategy selection model and cumulative prospect theory for the dataset by Horn et al. [2]

Figure S3. 1
Figure S3.1 Decision quality (left) and risk aversion (right) by problem domain and age group in the dataset by Horn et al. [2].Bars show the empirically observed behavior (error bars represent the standard error of the mean), red dots show the average predictions of the resource-rational strategy selection model.

Figure S3. 4
Figure S3.4Average strategy cost (A), toolbox size (B), cost-weighting parameter (C), and trembling-hand error (D) for younger and older adults in the dataset by Horn et al. [2].Bars indicate group means, with error bars representing the standard error of the mean.Points represent individual participants.
. Higher values indicate a better fit.