Judgment of news veracity and success rate
We first confirmed that performance accuracy was at chance level when judging the veracity of news. Participants' average success (i.e., correctly judging a true news as true and correctly judging a false news as false) rate was of 51.6 ± 6.7% (Supplementary I.1, Fig. S1). A comparison of the performances with a random distribution within a Bayesian framework confirmed that performances were at chance level. Modelling random responses with a logistic function λ~logistic (λ0,rscale) with priors \({\lambda }_{0}\)= 0.5 and rscale = 1.5, the Bayes Factor (BF) favored the null hypothesis of chance-level by a factor of about 0.3. This factor is considered the low boundary of a moderate evidence37, however posteriors probabilities fell within the range of [49–53]% success, centered around 51.5%. (Supplementary I.1, Fig. S3 & Table S2).
Next, we examined in what conditions participants’ successes deviated from chance level. Although judgment of ambiguous news veracity was equivalent to chance, participants performed better with true news (64 ± 11.9%) than false news (39.1 ± 12%). Lowest accuracy was for democracy-related news (48.6 ± 11.5), with a slightly higher accuracy for news related to ecology (52.2 ± 11.3) and social justice (53.8 ± 11.8) (See Supplementary I.1, Table S3). Binomial Mixed Linear Models (MLMs) showed that participants predicted true news significantly more accurately than false news (odds-ratio = 2.77, p < 0.001), with the veracity of news interacting with its theme (p < 0.001). Democracy-related news had significantly lowest accuracy compared to ecology and social justice (odds-ratio respectively at 1.19 and 1.26, all p < 0.005) (see Fig. 2A). Effects remained highly significant (p < 0.005) after controlling for socio-demographics, veracity judgment, and confidence (Supplementary I.1, Table S4).
Such relatively higher ability to assess true news accurately can be explained by a general tendency to declare information as true (59.5 ± 10.6%), with slightly more true news declared as true (60.9 ± 12.7%) than false news (58.2 ± 13.1%) (See Supplementary I.1, Table S5). Modelling the success in estimating veracity confirmed that the veracity judgment was a highly significant explaining variable (p = 0.003), withstanding the inclusion of control variables (Supplementary I.1, Table S6). Interestingly, binomial MLMs of veracity judgment revealed that participants were especially more likely to judge as true ecology-related (prob. = 0.678 ± .02) and social justice-related news (prob. = 0.637 ± .02) than democracy-related news (odds-ratios 1.71 and 1.43, respectively; all p < 0.001) (see Fig. 2B).
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Our analysis of the relationship between accuracy in judging news veracity and confidence in this judgment showed that participants’ confidence did not significantly predict actual success nor veracity judgments (all p > .05).
Results instead demonstrated that individuals’ responses were primarily influenced by news ambiguity, specifically both the imprecision and the polarization of news content, potentially leading to a perception of falsity (Supplementary I.1, Fig. S4). We modelled success in veracity judgment with MLMs incorporating imprecision and polarization predictors in interaction with news veracity (Supplementary I.1, Table S7). Note that the news content imprecision and propensity to polarize (from 0 to 10) were obtained from ratings of a group of subjects (n = 55) independent from the actual participants in the experiment (see Methods). The interaction effect of each predictor had a highly significant effect on the success of veracity judgment likelihood (all p < 0.001, all odds-ratios < 0.76). Specifically, success in judging true news increased when their content imprecision and propensity to polarize were at their minimum (minimum/maximum, imprecision odds-ratio = 1.82; polarization odds-ratio = 2.17) Conversely, for false news, success increased with maximal imprecision (minimum/maximum odds-ratio = 0.53) and maximal propensity to polarize (minimum/maximum odds-ratio = 0.22) (all p < 0.001). Furthermore, MLMs of veracity judgments showed that the likelihood of judging news as true decreased with increased imprecision (p < 0.001, odds-ratio = 0.78) and the propensity to polarize (p < 0.001, odds-ratio = 0.64). The effects in all models withstood the inclusion of socio-demographics, veracity-theme interaction, and confidence (Supplementary I.1, Table S7).
Finally, we found that alignment of beliefs with news concerns, distrust in experts and socio-demographics had no significant effect on the accuracy of veracity judgments. Using MLMs (see Method; Supplementary I.1, Fig. S5, Table S8 & S9), response times showed a positive effect on judgment accuracy (p = .007, odds-ratio = 1.07), albeit not robust to the inclusion of other factors. We used Bayesian inference hypothesis testing to support these findings. Comparing Bayesian versions of the regression models (see Method, Supplementary I.2, Fig. S6-S9), the winning model featured interaction terms between news veracity and both news content imprecision and propensity to polarize (see Table 1). Overall, individuals’ accuracy deviated from chance level in reaction to variations in news ambiguity. Precision and apparent consensus about news content were interpreted as a signal of veracity, while imprecision and apparent polarization were seen as signals of falsity. Note that we found no significant difference between true and false news either in terms of imprecision (mean ± SD = 5.53 ± 1.24 vs. 5.17 ± 1.25, 𝑟𝑎𝑛𝑘𝑠𝑢𝑚, 𝑝=0.09), or in terms of polarization (mean ± SD = 6.61 ± 1.62 vs. 6.22 ± 1.62, 𝑟𝑎𝑛𝑘𝑠𝑢𝑚, 𝑝=0.3).
Uncalibrated metacognitive sense of confidence
To further investigate the relationship between confidence and accuracy in estimating veracity, we examined participants’ calibration, that is their ability to accurately estimate the chances that the news is true or false (see Supplementary I.3, Table S10). The confidence-accuracy calibration reflects, for given veracity judgments (the news is evaluated as true or false), the relationship between the continuous scale of confidence ([1,100]) and the binary outcome (true or false). This calibration indexes the extent to which confidence in one’s judgment predicts the accuracy of this judgment. A perfect calibration is characterized by a linear confidence-accuracy function with 100% accuracy for 100% confidence, 90% accuracy for 90% confidence, etc. We sorted the individual confidence-accuracy relationships into ten bins and represented an area of well-calibrated estimation that spanned 10% (see Fig. 3).
We expected that participants’ confidence would be non-calibrated and uncorrelated with actual success in estimating the veracity of uncertain news. As the plot shows, participants’ accuracy in estimating veracity was independent from their confidence in their estimation. Participants were neither well-calibrated, nor ill-calibrated for estimating probabilities. Values above the diagonal signal underconfidence (individuals have a higher proportion of correct guesses than their reported level of confidence) while values below the diagonal reveal overconfidence (individuals have a lower proportion of correct guesses than their reported level of confidence). Figure 3 shows that underconfidence dominates for degrees of confidence below 50% whereas overconfidence dominates for degrees of confidence above 50%. Underconfidence dominates for true news whereas overconfidence dominates for false news, while news veracity judgment did not affect the relationships between confidence and success levels (Supplementary I.3, Fig. S10).
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To understand the determinants of confidence during estimation of news veracity, we examined the sources of variability using MLMs of alignment of beliefs with concerns related to the news, socio-demographics and response times. Moreover, we examined models predicting effects of imprecision and polarization predictors on confidence in veracity judgments.
Alignment of beliefs with news concerns and socio-demographics showed no significant effects on confidence (Supplementary I.3, Table S11), while effects of response times were highly significant and negative (p < 0.001). Importantly, the interaction of both ambiguity predictors with the judgments of news as true decreased confidence (p < 0.001), even after including control variables (Supplementary I.3, Table S12). Sex also revealed higher confidence levels for males than females (p < 0.001).
Confidence ratings were reliably affected by news content ambiguity, reflecting higher confidence that a news is true under low ambiguity and higher confidence that a news is false under high ambiguity. Comparing confidence levels between judgments of true and false news across three different levels of content imprecision and propensity to polarize revealed a significant effect of these variables on confidence. Even after the inclusion of control variables, confidence was higher for judgments of the news as true when imprecision was lowest (t ratio = 3.85, p < .001) and median (t ratio = 2.60, p = .0092). In contrast, confidence was not significantly different for judgments of the news as false than for judgments of the news as true when imprecision was at its highest level (t ratio = -1.84, p = .065). Conversely, confidence was higher for judgments of the news as true when the news content propensity to polarize was at its lowest level (z ratio = 8.61, p < .001), but higher for judgment of the news as false when polarization was highest (z ratio = -8.34, p < .001). Finally, confidence was not significantly different between the two types of judgments for a median polarization level (p = .57). These findings support the use of imprecision and polarization as signals of falsity, influencing veracity estimation.
Demand and avoidance of extra information
Next, we analyzed the demand for or avoidance of extra information about news that might resolve uncertainty. We predicted that despite the lack of calibration (i.e., a low degree of fit between confidence in news veracity judgment and the actual accuracy), individuals would use their metacognitive sense of confidence to decide whether or not to demand extra information about the news. Hence, we expected confidence to primarily explain the demand for extra information, particularly when confidence was low. First, we present participants' reception choices and subsequent Willingness-To-Pay (WTP). Then, we explore linear relationships between confidence and reception choices/WTP. To test our hypothesis, we estimated separate MLMs with variables capturing main and interaction effects of participant confidence and news veracity judgment. The dependent variables were the binomial demand for more information or the continuous WTP. Post-hoc comparisons were conducted on estimated marginal means.
82.9% of participants demanded extra information at least once, with an average frequency of 42.29 ± 31.9%. Choice of extra information did not significantly differ between news themes (Kruskal Wallis Chi square = 4.39, p = .11, df = 2; democracy: 41.04 ± 33.16; ecology: 43.27 ± 33.67; social justice: 42.56 ± 33.09; see Supplementary I.4, Table S13). Participants chose to receive extra information 42.51 ± 32.44% of the time when news were judged as false and 42.07 ± 32.14% of the time when news were judged as true. Bayesian modeling of reception choices between judgments (Jeffreys priors: α = 0.5, β = 0.5) revealed a negligible difference (delta = 0.23, 95% Credible Interval [-0.008, 0.012]), indicating similar demand for extra information regardless of veracity judgments.
Participants exhibited a higher willingness-to-pay (WTP) for receiving extra information (mean: 7.07 ± 4.96 ECU) compared to not receiving it (mean: 5.75 ± 5.69 ECU) (see Fig. 4; see Supplementary I.4, Table S14). Bayesian models of WTP for receiving and not receiving extra information (Jeffreys priors: µ = 0, σ = 1 from half-Cauchy distribution) showed that participants were willing to pay more to receive it than to avoid it (delta = 1.327, 95% Credible Interval [-2.302, -0.344]).
As predicted, confidence explains the demand for extra information (p < 0.001, odds-ratio = 0.59), with a significant negative interaction with veracity judgment (p < 0.001). These effects remained significant even after incorporating controls such as the interaction of news veracity and theme and socio-demographics (Supplementary I.4, Table S15). The results show that the probability of demanding extra information is not affected by news content ambiguity (i.e., imprecision and propensity to polarize) (see Fig. 4A) while it decreases as confidence in one’s judgment increases. Specifically, the decrease is more pronounced when the news is judged as false (minimum/maximum confidence; judgment as false, odds-ratio = 6.41; judgment as true, odds-ratio = 2.59) (see Fig. 4B). A regression analysis of WTP further supported these findings, revealing a significant interaction between confidence and the demand for information (p < 0.001) (see Fig. 4C), holding up against the inclusion of control variables (Supplementary I.4, Table S16). According to this model, the effect size of confidence (minimum – maximum confidence levels) on the WTP when participants opted not to receive extra information was − 1.74 (p < 0.001), whereas the effect size for the WTP to receive extra information was only − 0.13 (p = 0.69) (see Fig. 4D).
The alignment of beliefs with news concerns from only two organizations predicted reception choices while we found no evidence for effects of sociodemographics, response times, distrust or ambiguity on decisions to seek information that might resolve uncertainty about our ambiguous news.
To sum up, there is a significant inverse relationship between the demand for extra information about the news and confidence in one’s judgment about news veracity. Moreover, this relationship is stronger for the news that participants judged as false. Supporting these findings, participants are also willing to pay more to not receive more information about what they think they already know.
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A moderated mediation analysis further extended the role of confidence in the estimation of ambiguous news veracity (Table 2, Fig. 5 ; Supplementary I.5, Fig. S11). Confidence had a unique direct effect on the outcome reception choice (standardized interaction β = -0.15, Z = -13.96, p < .001). Its effect was specifically a mediator effect, whereby the ambiguity of news, that is, news content imprecision and news content propensity to polarize, had an indirect effect on the reception choices through the confidence (imprecision: standardized interaction β = -0.06, Z = -3.93, p < .001; polarization: standardized interaction β = 0.11, Z = 6.32, p < .001). Veracity judgment played a role by moderating the effect on the news content imprecision to confidence path (standardized interaction β = 0.1, Z = 2.43, p = .015) as well as the effect on the news content propensity to polarize to confidence path (standardized interaction β = -0.36, Z = -8.34, p < .001). This analysis shows that the uncalibrated metacognition operating during the evaluation of true and false news induces a demand for disambiguating information that is increasingly ineffective as individuals are lured by the ambiguity of the news.
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