[1,2,3]Axel Abels [1,2,3,4]Tom Lenaerts

1]Machine Learning Group, Université Libre de Bruxelles, Boulevard du
Triomphe, CP 212, Brussels, 1050, Belgium 2]AI Lab, Vrije Universiteit
Brussel, Pleinlaan 2, Brussels, 1050, Belgium 3]FARI Institute, Université
Libre de Bruxelles - Vrije Universiteit Brussel, Brussels, 1000, Belgium
4]Center for Human-Compatible AI, UC Berkeley, 2121 Berkeley Way, 94720
Berkeley, CA, USA

# Mitigating Biases in Collective Decision-Making: Enhancing Performance in
the Face of Fake News

<EMAIL_ADDRESS>Elias Fernandez Domingos<EMAIL_ADDRESS>Ann Nowé<EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  [  [

###### Abstract

Individual and social biases undermine the effectiveness of human advisers by
inducing judgment errors which can disadvantage protected groups. In this
paper, we study the influence these biases can have in the pervasive problem
of fake news by evaluating human participants’ capacity to identify false
headlines. By focusing on headlines involving sensitive characteristics, we
gather a comprehensive dataset to explore how human responses are shaped by
their biases. Our analysis reveals recurring individual biases and their
permeation into collective decisions. We show that demographic factors,
headline categories, and the manner in which information is presented
significantly influence errors in human judgment. We then use our collected
data as a benchmark problem on which we evaluate the efficacy of adaptive
aggregation algorithms. In addition to their improved accuracy, our results
highlight the interactions between the emergence of collective intelligence
and the mitigation of participant biases.

###### keywords:

Bias, Collective Intelligence, Fake News, Crowdsourcing

Cognitive biases are systematic errors in judgment and decision-making
resulting from cognitive limitations, individual preferences, and/or
inappropriate heuristics [1]. When human groups deliberate, individuals tend
to transmit these biases to others, which may lead the group as a whole to
make sub-optimal choices [2]. Such biases can pose a significant threat to
accurate and fair decision-making, especially in situations that involve
sensitive attributes. In settings wherein group decisions play a pivotal role
— from medical diagnostics to crowdsourcing — an understanding of these
biases, how they affect the integrity and efficiency of collective decisions,
and how they can be countered is paramount.

Existing literature underscores the profound influence of stereotypes, biases,
and decision-making across multiple facets of life, from choices in
recruitment [3] to judiciary decisions [4, 5]. While tools and studies like
the Stereotype Content Model [6, 7], Implicit Association Tests [8, 9] offer
crucial insights into measures of biases, there remains a considerable scope
for further exploration. This includes the understanding of interactions
between bias mitigation and the emergence of collective intelligence.

Figure 1: Overview of the Collective Decision-Making problem studied in this
work. Participants (identified here by the colors green, red and blue) in the
experiment were presented with a sequence of headlines and were asked to
estimate the likelihood that they were true. These diverging opinions are then
aggregated to reach a collective decision. The aggregation is iteratively
optimized by comparing it to a ground truth. Different aggregations weigh
opinions differently, see Appendix A for algorithmic details. Example weights
for the three participants are given for each approach. A majority vote values
all experts uniformly, resulting in even bars. EXP4 [10] selects a single
participant (i.e., weight is concentrated on a single participant) whose
opinion is followed. MetaCMAB [11] distributes weights more evenly,
correlating them with performance to enhance the collective decision-making
process. ExpertiseTree [12] similarly distributes weights, but will learn
distinct models for each headline category if this proves beneficial.

Pooling human expertise through a centralized platform may mitigate biases
(e.g., confidence bias [13], biases with temporal effects [14, 15], or
illusory correlations [16]) that affect the judgment of participants in a
collective decision-making task. Works such as those of de Condorcet [17],
Rawles [18], and Surowiecki [19] have provided a theoretical understanding of
how collective decisions can bring about improvements over individuals. Modern
algorithms (e.g., [20, 11, 12]), while drawing inspiration from those seminal
works, address the complexities of aggregating possibly dissenting opinions by
dynamically adapting to varying levels expertise. While those works provide a
theoretical analysis of the performance of these algorithms, empirical
performance has so far been primarily established on synthetic experts [21,
22, 11, 12]. It is therefore not obvious that the assumptions they rely on
hold for human experts, and thus, how these methods perform in a real
situation.

The primary purpose of this study is to address this gap by experimentally
evaluating the performance of both static (e.g., majority voting) and adaptive
(EXP4 [10], MetaCMAB [11], and ExpertiseTree [12]) aggregation algorithms in
settings involving human advisers. Specifically, we evaluate their capacity to
mitigate biases and enhance the efficacy of collective decision-making.

Our experimental design111This experiment has been preregistered [23],
inspired by crowdsourced fact checking [24, 25, 26], involves human
participants tasked with discerning the authenticity of news headlines,
particularly those that involve sensitive groups (see Fig. 1). In the
experiment, participants encountered a sequence of headlines, half of which
were authentic and half of which were altered by switching the sensitive
groups involved. Without being informed of the proportion of authentic
headlines, they were asked to rate the likelihood of each headline being
genuine. By contrasting the true outcome with opinions provided by
participants, adaptive algorithms can optimize the aggregation of human
opinions, possibly conditioned on the problem category.

This setup enabled us to not only identify potential bias patterns in
participant responses but also to assess the effectiveness of various
collective decision-making algorithms in real-world scenarios. Crucially, our
study demonstrates the potential of state-of-the-art machine learning
algorithms to tailor aggregations in a way that mitigates biases and enhances
collective intelligence.

To summarize, our contributions are

  * •

A dataset containing participant responses to a collection of news headlines
involving sensitive characteristics, providing a rich source for analyzing
human biases in decision-making.

  * •

A comprehensive exploration of these responses, focusing on potential biases
and the presence of stereotyping.

  * •

An analysis of the performance of collective decision-making algorithms, with
an emphasis on the interaction between bias mitigation and the emergence of
collective intelligence.

##  1 Overview

We designed an online experiment (see Methods for more information) which
emulates the use of human fact checkers as a tool to combat the spread of fake
news on social media. Participants were presented with a sequence of headlines
for which they were asked to rate the likelihood of the headline being real.
In order to elicit bias, we focused on headlines which involved sensitive
groups.

In particular, we curated headlines from [27, 28, 29] based on the following
criteria:

  * •

The headline (implicitly or explicitly) contrasts two sensitive groups (e.g.,
“Men more likely than women to say they are financially better off since last
year”)

  * •

The headline should present a clear negative or positive outcome. For example,
it is not clear whether “Poll: Kanye more popular with whites than nonwhites”
is positive or negative, but “African-Americans, Hispanics, dying at faster
rate of fentanyl overdoses than whites: analysis” is clearly a negative
outcome for African-Americans and Hispanics.

Each headline was characterized by a sensitive group (thus whether it
concerned a gender group, an ethnic group, or an age group), by a sentiment
(positive or negative), and by a truth value (whether the headline was real or
altered). For details, see Methods.

We sequentially presented one of $5$ distinct sets of headlines to each
participant and asked them to assess the likelihood of each being real using a
discrete score: For each headline, participants were asked “How likely is it
that this headline is real?” and given $5$ choices (see Fig. 1): {“very
unlikely”, “unlikely”, “undecided”, “likely”, “very likely”}.

Once collection of all participant responses was completed, these responses
were used in simulated collective decision-making tasks (see Section 5.4). For
each simulation, we sampled uniformly $N\in\\{2,4,6,...,36\\}$ participants
who answered the same set of headlines. Their answers to each headline were
iteratively fed into the studied aggregation algorithms. These algorithms then
aggregated the responses from this subset to reach a collective decision.
Following each decision, the algorithms were presented with the actual type of
the headlines (i.e., genuine or altered). This feedback loop (see Fig. 1)
allows the algorithms to adapt and refine the decision-making processes to
improve accuracy in subsequent iterations on novel headlines222Headlines are
not repeated within a simulation. Any decision made is therefore the result of
training on a history that does not include the headlines on which the
decision-making quality is estimated. Specifically, at time $t$ we evaluate
the quality of a decision made by a model trained on the data experienced at
times $1$ to $t-1$. This allows us to test the effectiveness of models on data
they have not encountered before, analogously to training and test sets which
are more typical of a supervised learning setting. .

Crucially, the manner in which the various algorithms studied here assimilate
experiences varies. For instance, the weighted majority vote (WMV) algorithm
is static and does not adapt based on past outcomes. Considering the sensitive
attributes involved in this setting, our intent is to counteract biases. This
is achieved through:

  1. 1.

A collective approach: Rather than pinpointing the single best participant, we
optimize a weighted average of expertise. Intuitively, using a weighted
average —–instead of singling out one participant —– may ensure that
individual errors offset each other.

  2. 2.

An active bias counteraction method: Recognizing that biases may cause varying
expertise levels dependent on the sensitive group, we suggest learning
aggregates tailored to the sensitive groups we encounter. This can be realized
by implementing an ExpertiseTree [12]. Essentially, this decision tree’s
leaves contain an aggregator optimized for a subset of sensitive groups. For
example, if headlines related to gender benefit from a distinct aggregate, the
ExpertiseTree algorithm provides an adapted aggregator to handle that need.

Our data analysis led to several significant findings:

  * •

Algorithms accounting for participant bias (like ExpertiseTree) consistently
achieve collective intelligence, in doing so these algorithms significantly
mitigate the biases present in individual participants.

  * •

Participants tend to be less skeptical towards headlines involving age and
more skeptical towards headlines involving ethnicity.

  * •

When performance differences between groups occur, they tend to occur on
headlines involving those groups. For example, men and women perform
comparably on ethnic or age-related headlines, but differ on gender headlines.

These findings not only contribute to our understanding of bias in human
decision-making but also underscore the potential of advanced algorithms to
foster collective intelligence from human inputs and mitigate bias. The
following sections provide a detailed examination of these results,
highlighting the role machine intelligence can play in enhancing decision-
making processes.

##  2 Results

###  2.1 Influence of Aggregation Algorithms on Collective Decision-Making
Processes

Here we compare the performance of various aggregation algorithms: selecting a
participant at random (random expert), a Weighted Majority Vote (WMV), EXP4
[10], MetaCMAB [11], and ExpertiseTree [12]. Each approach is included in the
study for its unique contribution to understanding and improving collective
decision-making. We provide a description of these algorithms, as well as a
more detailed justification for their inclusion in the methods section. We
focus first on how these algorithms influence the overall decision quality
compared to individual participants.

##### Accuracy

Figure 2: Performance as a function of the number of participants. Shaded
areas around the lines in panels a-d represent $95\%$ confidence intervals. a,
displays the accuracy (i.e., the proportion of correctly identified headlines,
see Methods) of each algorithm for each group size. b, shows, for each group
size, the terminal instantaneous regret (see Methods): the difference in
performance between the best group member and the algorithm for the final
decision. Negative values in b show when the collective outperforms the single
best group member. Panels c and d, depict for, respectively, groups of size
$4$ and $36$ the instantaneous regret as learning progresses — the difference
in performance between the best group member and the algorithm for the
decision at that time (see Methods). These two plots show at which point
algorithms surpass the single best group member. e, presents the algorithmic
improvement on expertise for different algorithms and different group sizes
($N$). Within each heatmap, group members are ranked by accuracy, and the
x-axis indicates the member’s performance quantiles. In particular, the lower
the quantile, the more accurate the group member. For each row within a
heatmap, each cell represents the proportion of cases for which the respective
algorithm surpasses the corresponding group member’s performance. In
particular, the left-most cell in each diagram corresponds to the best group
member. Non-zero values for this cell suggest the emergence of collective
intelligence.

Fig. 2a shows overall accuracy as a function of group size for these
algorithms and compares it to the best group member (identified in hindsight).
Fig. 2b gives terminal regret values, i.e., the difference in performance with
the best expert for the last round. Based on Wilcoxon tests (see Methods) with
an $\alpha=0.05$ significance threshold, the performance of all methods is
significantly different, except for the terminal regret of EXP4 and the WMV.

##### Round-by-Round Analysis of Instantaneous Regret

To further analyze these dynamics, we analyzed the round-by-round performance
for group sizes of 4 and 36 participants, specifically focusing on
instantaneous regret (Fig. 2c-d). This metric measures the performance gap
between each algorithm and the best performing group member at specific time
steps. In particular, a negative regret indicates performance surpassing the
single best group member, indicative of the emergence of collective
intelligence. As it collects more experiences, ExpertiseTree approaches this
threshold, and ultimately surpasses it for larger groups (compare $N=4$ and
$N=36$, Fig. 2c-d).

##### Win Percentage

An alternative way of evaluating the prevalence of collective intelligence is
by measuring how often collective decision-making algorithms surpass the
performance of the single best group member. Fig. 2e provides this
comprehensive view of how different algorithms fare against individual
participants. While all methods tend to outperform a majority of group
members, MetaCMAB and the ExpertiseTree approach consistently outperform all
but 2 (for MetaCMAB) or 1 (for ExpertiseTree) group members. For example, for
group size $N=36$, ExpertiseTree exceeds the performance of the top group
member in $45\%$ of cases (as shown in the bottom left cell of the relevant
heatmap), and surpasses the second-best member in $56\%$ of simulations
(second leftmost cell). On the other hand, MetaCMAB generally matches the
performance of the second-best member (with a win ratio of $0.40$) and less
often outperforms the top member, achieving a win ratio of $0.3$.

###  2.2 Dissecting Participant Biases

This section explores the biases exhibited by participants within our
collective decision-making framework. Through this analysis, we aim to provide
a foundation for understanding to what extent collective decision-making
systems, as discussed in Section 2.3, can mitigate biases.

##### Demographic Differences in Performance

We first investigate whether the participants’ demographics correlate with
differences in performance across headline categories and find the following,
as illustrated by Fig. 3:

Figure 3: Participants’ accuracy as a function of their demographic
information and the type of headline they respond to. The figures, from left
to right, depict the accuracy in responding to each headline category in
function of three demographic variables: age group (threshold at the median
participant age of $35$), ethnicity (partitioned into majority and minority
ethnicities, see Fig. 7), and gender. The GEEs fitting reveals statistically
significant differences (Bonferroni adjusted p-values $p^{\prime}<0.05$) in
age and gender related questions. Specifically, older participants showed
slightly lower accuracy in responding to age-related questions, and male
participants exhibited lower accuracy in responding to questions related to
gender.

  * •

There is a significant difference in accuracy between men and women,
especially when responding to gender-related headlines. Men exhibited a lower
average accuracy ($0.524$) compared to women ($0.554$), with a statistically
significant difference ($\beta=0.0303,p=0.01,ci=[-0.053,-0.007]$).

  * •

Participants’ performance varied significantly with age, particularly when
interpreting headlines about different age groups. Individuals younger than 35
years were more accurate in identifying altered headlines about age ($0.535$
accuracy) compared to those older than 35 years ($0.511$ accuracy), with a
significant difference ($\beta=0.024,p=0.013,ci=[0.005,0.043]$).

  * •

Unlike gender and age, we did not observe significant differences in accuracy
based on participants’ ethnic backgrounds. Both majority and minority ethnic
groups performed similarly across various headline types ($|\beta|\leq
0.013,p\geq 0.384$).

##### Framing Effect

We next investigated the framing effect — how the presentation of information
shapes responses [30] — by comparing participant reactions to original versus
altered headlines. We hypothesize that, in the absence of framing effects, if
a headline is believed to be true, its altered version would likely be deemed
false, and vice versa. Deviations from this expectation indicate a framing
effect, suggesting that people respond to more than just the headline’s
content.

Using the Mann-Whitney U test, we tested whether the response distribution for
a real headline differed from its altered counterpart. A total of $44\%$ of
headlines were found to induce a framing effect ($p<0.05$). To further dissect
this phenomenon, Fig. 4 illustrates the relationship between average responses
to original and altered headlines.

Figure 4: Effects of framing in participants’ responses. a-c, the quadrants
represent false stereotypes (Q1), positive framing effects (Q2), common
knowledge (Q3), and negative framing effects (Q4). a, Each point represents a
distinct headline; the x-coordinate displays the average response to its
original form, and the y-coordinate shows the average response to its altered
form. b, The x and y coordinates indicate MetaCMAB’s model predictions for the
original and altered headlines, respectively. c, In a similar manner, x and y
coordinates reveal the predictions of ExpertiseTree’s model for the original
and altered headlines, respectively. d, Response distributions for highlighted
points (i), (ii), (iii) and (iv) in panels a-c are given as histograms. Each
point’s headline and response distribution are given in its original (orange),
and [altered] (blue) form.

##### Group Biases

Next, we contrasted responses between groups within the same category. For
example, are responses to headlines reporting positive outcomes for men
different from those reporting positive outcomes for women?333In our
experimental design, any negative outcome for one group was implicitly a
positive outcome for the complementary group. Thus, a positive outcome for men
is implicitly a negative outcome for women, and conversely, a positive outcome
for women is implicitly a negative outcome for men

(a) Headlines involving ethnicity

(b) Headlines involving age

(c) Headlines involving gender

Figure 5: Error rates categorized by sensitive attributes in headlines.
Brackets indicate that there are significant differences (*, **, and ***
indicating respectively p-values below $0.05$,$0.01$, and $0.001$) between
pairs of boxplots as identified by Kruskal-Wallis H-tests (ethnicity:
$H=33.995$, $p<0.001$, $df=3$, $\eta^{2}=0.408$, age: $H=34.167$, $p<0.001$,
$df=3$, $\eta^{2}=0.410$ gender: $H=10.421$, $p=0.0153$, $df=3$,
$\eta^{2}=0.098$) followed by Dunn’s tests (see Methods).

5(a) shows that participants are more prone to errors when evaluating altered
headlines which report positive outcomes for white people, and real headlines
which report negative outcomes for white people.

A similar analysis as a function of age, shown in 5(b) reveals that the
disparity in error between real and altered headlines is consistent across
sentiments. In particular, it shows that participants are strong at
identifying real headlines, but weak at identifying altered headlines.

Finally, the analysis by gender, given in 5(c) reveals that errors are
relatively consistent across all but one group; headlines altered to be
negative for Males.

###  2.3 Collective Decision-Making Models Mitigate Biases

In this section we compare and contrast the prevalence of biases in
aggregations through either an average or adaptive methods MetaCMAB and
ExpertiseTree. We restrict the analysis of EXP4 to the Supplementary Appendix
B as we found it did not improve over the performance of a simple average.

##### Reduced Framing Effects

Our hypothesis posits that advanced collective decision-making algorithms,
such as MetaCMAB and ExpertiseTree, should show a notable reduction in framing
effects. This would manifest as decreased densities in Quadrants Q1 (False
Stereotypes), Q2 (Positive Framing Effect), and Q4 (Negative Framing Effect)
of the framing effect analysis.

We evaluated this hypothesis by analyzing the aggregated predictions of these
models (see Fig. 4b for MetaCMAB and Fig. 4c for ExpertiseTree). These plots
indicate a reduced proportion of headlines in Q1 ($19\rightarrow 8$) and an
increased proportion of headlines in Q4 ($15\rightarrow 25$) for MetaCMAB, as
well as a reduced proportion of headlines in Q1 ($19\rightarrow 4$) and Q2
($34\rightarrow 11$) and an increased proportion in Q3 ($52\rightarrow 97$)
for ExpertiseTree.

##### Reduced Group Biases

We now evaluate whether different algorithms are predictive of different error
rates conditioned on the category. This evaluation involves comparing error
rates from three sources: average participant predictions, MetaCMAB
predictions, and ExpertiseTree predictions. We summarize here the results and
provide full GEE tables in the Supplementary Information.

The GEE analysis for averaged responses highlights significant interactions
across all variables with respect to prediction error. The baseline error
(intercept) was estimated at $\beta=0.579$ ($p<0.001$, $ci=[0.536,0.623]$).
Negative effects were observed for headlines classified by ethnicity
($\beta=-0.135$, $p<0.001$, $ci=[-0.204,-0.067]$) and gender ($\beta=-0.093$,
$p=0.049$, $ci=[-0.186,-0.001]$), with significant interactions noted between
headline class and alteration status for both categories.

For MetaCMAB’s predictions, the extent of bias was reduced. The baseline error
was lower ($\beta=0.431$, $p<0.001$, $ci=[0.377509,0.484283]$), and while the
ethnicity headline class maintained a significant effect ($\beta=-0.087$,
$p=0.021$, $ci=[-0.160649,-0.012963]$), the gender effect was not significant.
MetaCMAB’s error is however significantly worse for genuine headlines than for
altered headlines ($\beta=-0.079$, $p=0.023$, $ci=[-0.148,-0.011]$). The
interaction effect of genuine headlines also remained significant in relation
to ethnicity ($\beta=0.132$, $p<0.001$, $ci=[0.088,0.179]$).

In contrast, the GEE analysis for ExpertiseTree’s predictions showed that none
of the variables had a significant effect on the prediction errors. The
intercept was $\beta=0.319$ ($p<0.001$, $ci=[0.287,0.351]$), and all other
parameters concerning headline classes (both ethnicity and gender) and their
interaction with altered status were non-significant (e.g., ethnicity headline
class: $\beta=-0.053$, $p=0.108$, $ci=[-0.118,0.0117]$).

Figure 6: Prevalence of splits learned by ExpertiseTree as a function of the
number of members in a group. ExpertiseTree can learn to either i) not split,
ii) split off the ethnicity category, iii) split off the gender category, iv)
split off the age category, v) split all categories. For (ii) — and
analogously for (iii) and (iv) — this implies that one model is learned for
all headlines relating to ethnicity, while another model is learned for both
the gender and age category.

A comparison of the splits learned by ExpertiseTree (see Fig. 6) shows its
trees grow deeper as the group size increases. In particular, for large group
sizes the ExpertiseTree learns distinct models for all headline categories.

##  3 Discussion

Our investigation into collective decision-making, biases, and the
effectiveness of adaptive methods, reveals several key insights with
implications for the field of machine intelligence.

##### Collective Intelligence through Online Machine Learning

With no prior knowledge of the expertise of the group members, efficient
collective decision-making systems need to learn to surpass the performance of
the single best group member. When group members provide honest confidence
estimates, these can be used to weigh their input. In our experiment,
participants were given the option to express strong confidence (e.g., ’very
likely’), weak confidence (e.g., ’likely’), or a lack of knowledge
(’undecided’). If participant responses were properly calibrated, i.e., their
expressed confidence aligned with their expected accuracy, previous work
indicates that the resulting confidence-weighted majority vote (WMV) would
consistently outperform the single best group member [31]. As Fig. 2a
illustrates, however, this is not the case: the WMV consistently performs
worse than the single best group member.

To tackle this confidence bias, various online machine learning approaches
have been proposed to supplement participants’ self-reported confidence with
algorithmically determined weights. These weights are iteratively refined as
more information regarding the participants’ accuracy is gathered, thereby
enhancing the system’s ability to adjust its aggregation over time.

We compared here three different approaches: EXP4, MetaCMAB, and
ExpertiseTree. We find that MetaCMAB and ExpertiseTree, which act on an
aggregate over all group members, perform significantly better than EXP4,
which is designed to select the single best decision-maker in a group. In
fact, as the group sizes increase, their accuracy converges towards the level
achieved by the best-performing group member.

While ExpertiseTree typically does not outperform the top individual
participant overall, its potential becomes more evident in later stages of the
decision-making process. As shown in Fig. 2b, this algorithm ultimately
surpass the best participant’s performance in larger groups ($N\geq 8$).
Therefore, although initial uncertainty limits overall performance, these
results suggest that this algorithm eventually facilitate the emergence of
collective intelligence. In contrast, while a WMV can achieve collective
intelligence in specific scenarios (homogeneous performance levels and low
correlation between group members, or properly calibrated confidence, see
[11]), participant responses in this context do not satisfy these necessary
conditions.

Results in terms of win percentages (Fig. 2e) confirm that the WMV and EXP4
algorithms consistently underperform in comparison with the top-performing
group member. In contrast, algorithms emphasizing collective intelligence
(MetaCMAB and ExpertiseTree) frequently outperform the single best group
member.

Overall, our findings align with prior results on the performance of these
algorithms established on synthetic expertise: the use of adaptive algorithms
enables a dynamic and responsive collective decision-making process. Although
they initially are on par with a WMV, MetaCMAB and ExpertiseTree quickly
improve their performance by adjusting the importance assigned to group
members. Notably, for groups of 36, MetaCMAB and ExpertiseTree begin to
surpass the best expert after 42 and 24 headlines, respectively. This
demonstrates that these algorithms quickly adapt to the collective pool of
knowledge, often surpassing the performance of the most skilled individual in
larger groups. This collective intelligence is achieved by leveraging diverse
inputs without prior knowledge about participants’ expertise.

##### Headline Categories and Implicit Biases

Based on prior research [9, 32], we expected to observe differences in
participants’ responses to various headline categories, such as gender,
ethnicity, or age. For instance, individuals might be less inclined to
question stereotypes concerning age groups but more cautious when it comes to
stereotypes associated with ethnic groups. Our analysis of how participants
respond to different headline categories yielded notable trends in skepticism.
In particular, the quadrants of Fig. 4a align with four types of beliefs:

  * •

(Q1, False Stereotypes) Stereotypes skew judgment, leading to consistent
misjudgment of these headlines that align with preconceived notions.

  * •

(Q2, Positive Framing Effect) Headlines are perceived as true regardless of
alterations, indicating a lower skepticism induced by their phrasing or
content.

  * •

(Q3, Common Knowledge) Headlines matching widespread beliefs are accurately
judged, irrespective of their alteration.

  * •

(Q4, Negative Framing Effect) Converse of Q2; these headlines are consistently
deemed false, pointing towards inherent skepticism or bias in their
presentation.

Interestingly, headlines related to age were predominantly found in Q2 and
rarely in Q4. On the contrary, ethnicity-related headlines were absent from
Q2. This suggests participants generally exhibited reduced skepticism towards
age-related headlines, contrasting with a heightened skepticism towards ethnic
headlines. This pattern persisted even when headlines were altered to focus on
different sensitive groups (see Supplementary Information); responses for a
headline whose subject is changed from an ethnic group to an age group will be
less skeptical. This suggests that this skepticism (or lack thereof) is not a
feature of the specific headlines, but rather of the sensitive group it
contains. This finding aligns with research by [33], suggesting that people
are more inclined to associate age with positive or negative concepts than
ethnicity. This could explain the greater likelihood of believing age-related
headlines.

When detailed by subcategory, our results (in particular 5(a)) suggest that
participants in the experiments were more skeptical of headlines which report
negative outcomes for white people.

These patterns can also be understood in terms of confirmation bias, the
tendency for people to favor information that confirms their pre-existing
beliefs or biases [34]. This phenomenon, notably discussed in studies of
crowdsourcing [35, 36], offers further insights into participants’ responses.
For example, if individuals hold implicit biases that view certain groups in a
specific light, they are more likely to believe headlines that confirm these
biases, and dismiss those that challenge them.

##### Demographic Differences in Performance

Results on the Implicit Association Test (IAT) [9] suggest that most groups,
with the exception of African-Americans, displayed an implicit bias against
African-Americans. Similarly, [32] found stigmatized groups can form
coalitions, in the sense that members of a stigmatized group might be more
sensitive to the discrimination of other stigmatized groups. We found that
performance disparities between demographic groups predominantly appeared in
dimensions relevant to those groups (see Fig. 3). For instance, differences in
gender or age influenced the accuracy of responses to headlines pertaining to
those specific categories. This suggests that personal identity factors play a
crucial role in shaping perceptions and biases.

##### Mitigating Bias in Collective Decision-Making through Machine
Intelligence

Considering the enhancements in performance shown by MetaCMAB and
ExpertiseTree compared to individual expert predictions, we investigated if
these improvements also indicate a reduction in group bias, i.e., whether the
group (e.g., gender, ethnicity, or age) for which a prediction is given
impacts the predictor’s error.

Our analysis reveals that individuals often display biased performance. When
individual responses are pooled through an average, these biases tend to
permeate, resulting in biased aggregations. In contrast, adaptive aggregations
acquired through for example MetaCMAB or ExpertiseTree should mitigate these
biases.

We found that, unlike other methods, ExpertiseTree’s performance remained was
not significantly affected by changes in headline categories, suggesting
individual biases were effectively mitigated.

What is more, the distribution of points in Fig. 4b suggests a decrease in
false stereotypes and a reduced positive bias for MetaCMAB, but a similar
prevalence of negative framing effects. In contrast, we found less populated
biased quadrants for ExpertiseTree. This supports its robustness in mitigating
false stereotypes and framing effects, making it a valuable tool in creating
unbiased, balanced decision-making processes.

Finally, the prevalence of fully grown trees for larger group sizes (see Fig.
6) suggests that when there are more group members available, the
ExpertiseTree algorithm is more likely to find a subset of members which is
stronger for a given headline category.

##  4 Conclusion

In this study, we explored the impact of individual and group biases in
collective decision-making, particularly in the context of identifying the
authenticity of news headlines. Our findings underscore the potential of
adaptive aggregation algorithms, such as MetaCMAB and ExpertiseTree, in
enhancing collective intelligence and mitigating biases.

We demonstrated that while individual responses are prone to various biases,
including those related to demographic factors, adaptive algorithms can
effectively counteract these biases. The ExpertiseTree algorithm, in
particular, showed a significant reduction in framing effects and group biases
compared to individual responses or simple aggregation methods like the
weighted majority vote.

Those findings contribute to the understanding of how machine learning
algorithms can be utilized to improve the quality of collective decisions. By
integrating a diverse set of individual opinions and dynamically adjusting to
the varying levels of expertise, these algorithms enable the emergence of
collective intelligence, which is crucial in contexts where decision-making
involves complex, sensitive issues.

In summary, our research underscores the importance of understanding and
addressing biases in human advice to enhance the performance of collective
decision-making. The use of advanced machine learning algorithms, such as
MetaCMAB and ExpertiseTree, offers a promising avenue for achieving this goal.
By effectively aggregating diverse human opinions and dynamically adjusting to
various levels of expertise and bias, these algorithms pave the way for
collectively intelligent, fair, and effective decision-making processes.

Finally, it is worth noting that complementing the online learning method we
propose with proactive bias reduction strategies could further enhance overall
bias mitigation. In contrast to our approach, various studies have proposed to
mitigate biases by promoting deeper analytical thinking [37, 38, 39, 40, 41].
Techniques such as prompting participants to justify their decisions or
encouraging them to reconsider their initial responses have been effective in
reducing biases [42, 43, 44, 45]. Although our primary goal was to optimize
the extraction of knowledge from collected responses, future work could study
how well these additional approaches synergize with ours.

##  5 Methods

We developed an online experiment aimed at gathering human decisions regarding
fake news444This experiment has been preregistered [23], we compare this paper
to the preregistration in “Preregistration Discussion” section below..

To focus on individual biases, we designed our experiment without any
interaction between participants, ensuring that the collected responses were
independent. Following this, we sampled subgroups from the participant pool to
evaluate the performance of the different online learning algorithms.

###  5.1 Questionnaire

In order to ground our results in a realistic problem, we presented
participants with a fake news problem. In doing so, we are emulating the use
of human fact checkers as a tool to combat the spread of fake news on social
media. Our aim is thus to evaluate how laypeople perform at this task, what
factors influence their choices, and how they could be enhanced by a
collective decision-making system. Participants were presented with a series
of headlines for which they were asked to express a likelihood of the headline
being real. In order to elicit possibly biased responses, we focused on
headlines which involved sensitive groups.

In particular, we collected headlines from [27, 28, 29] based on the following
criteria:

  * •

The headline (implicitly or explicitly) contrasts two sensitive groups (e.g.,
“Men more likely than women to say they are financially better off since last
year”)

  * •

The headline should present a clear negative or positive outcome. For example,
it is not clear whether “Poll: Kanye more popular with whites than nonwhites”
is positive or negative, but “African-Americans, Hispanics, dying at faster
rate of fentanyl overdoses than whites: analysis” is clearly a negative
outcome for African-Americans and Hispanics.

Participants were presented with a mix of such headlines: $50\%$ were
unaltered, while the other $50\%$ had their sensitive group swapped.

Alterations were made by swapping sensitive groups with their complementary
group. For example, “Men” $\leftrightarrow$ “Women”, “Older people”
$\leftrightarrow$ “Younger people”, or “African-Americans” $\leftrightarrow$
“White Americans”.

Each headline was characterized by a sensitive group (thus whether it
concerned a gender group, an ethnic group, or an age group), by a sentiment
(positive or negative), and by a truth value (whether the headline was real or
altered).

Headlines for each participant were selected to represent a balanced mix of
these features. The number of headlines required to achieve this balance can
be computed as:

$(\text{\\# of sensitive groups}\times\text{\\# of sentiments})\\\
\times(\text{\\# of outcomes}\times\text{\\# of truth values})\\\ =(3\times
2)\times(2\times 2)=24.$

Each treatment, or set of questions, should therefore contain a multiple of
$24$ headlines.

Moreover, to understand the influence of presentation, every headline was
included in both its real and altered versions, distributed across different
treatments.

Consequently, our finalized dataset encompasses $5$ sets of questions
(=treatments), with each set containing $48$ headlines. These $240$ headlines
contain $40$ instances for each of the 6 sensitive groups. By distributing
these over $5$ treatments, we ensured each participant saw $8$ real and $8$
altered headlines for every sensitive group. Note that a positive sentiment
towards one group implies a negative sentiment towards its complementary
group. For example, “Across Age Groups, Whites Fared Worse in Employment
Rates” is both negative for whites and implicitly positive for African-
Americans. We thus have $16$ real ($8$ positive and $8$ negative) and $16$
altered (again $8$ positive and $8$ negative) headlines per group.

We sequentially presented the headlines to participants and asked them to
assess the likelihood of each being real. For each headline, participants were
given $5$ choices; {“very unlikely”, “unlikely”, “undecided”, “likely”, “very
likely”}.

###  5.2 Participants and Data Collection

Figure 7: Demographic distribution of participants. Age categories are
established by splitting participants according to the median age of $35$.
Ethnicity categories, Majority and Minority, are assigned according to whether
participants belong to the most frequent group (i.e., White). NA = Not
Available

We recruited 200555Additionally, 26 participants who did not complete the
questionnaire were excluded from this analysis. participants via the Prolific
crowdsourcing platform [46]. While the distribution of participants by gender
was balanced, balancing participants by ethnicity or by age is more
challenging through Prolific. We therefore did not impose restrictions on
participation by ethnicity or by age, except that all participants are $\geq
18$ years old. As a result, participants were predominantly white
($N_{\text{white}}=122$, $N_{\text{non-white}}=78$, see Fig. 7), reflecting
demographics of the sampled population.

Participants were paid a flat sum for participation at a rate of 6£ an hour.
Median completion time was $8$ minutes $58$ seconds. Participants were
uniformly assigned to one of the 5 treatments (=set of $48$ headlines). Only
participants who completed the questionnaire were included in our analysis.
Consequently, our dataset contains a total of $5\times 40\times 48=9600$
responses.

Along with responses, we captured the following metrics: the headline’s
sensitive group, the order in which responses were given, participants’
demographic data (age, gender, and ethnicity), headline sentiment (positive or
not), its authenticity (altered or not), and response time.

###  5.3 Evaluating Performance

To assess the quality of participants, we gauge the accuracy of their
estimates against actual outcomes. Define $p_{n}(h)$ as participant $n$’s
response for headline $h$. Following experimental evidence on how humans
interpret these categories [47], we map the responses to numerical quantities
as follows:

$p_{n}(h)=\begin{cases}0&\text{if ``very unlikely"}\\\ 0.25&\text{if
``unlikely"}\\\ 0.5&\text{if ``undecided"}\\\ 0.75&\text{if ``likely"}\\\
1&\text{if ``very likely"}\end{cases}$

The true value of $h$ is denoted as $y(h)$, with $y(h)=0$ for altered
headlines and $1$ otherwise. Participant error is then quantified in terms of
absolute difference: $\epsilon(h,n)=|p_{n}(h)-y(h)|$. Conversely, the accuracy
is the complement of the error: $a(h,n)=1-\epsilon(h,n)$, and takes as value
$1$ if participant $n$ predicts the headline’s class with high confidence.

In this setting, bias can be assessed by observing whether participants are
more likely to associate specific outcomes (either negative or positive) with
certain groups. Additionally, differences in accuracy or error rates based on
the sensitive group featured in the headline can also serve as indicators of
bias. For example, participant errors for headlines reporting positive
outcomes for white people could be significantly larger than those same
participants’ errors for headlines reporting negative outcomes for white
people. Such differences are explored in Fig. 5 and its related discussion.

###  5.4 Collective Decision-Making Process

While it is typically hard to properly estimate the performance of
participants a priori, online learning algorithms allow us to learn how to
aggregate expertise as we encounter new cases. We outline this decision-making
setting in Algorithm 1.

Algorithm 1 Collective Decision-Making for Headline Selection

1:Initialize learner (e.g., EXP4 [10], MetaCMAB [11], or ExpertiseTree [12])
with initial aggregation policy

2:for $t=1,2,...,T$ do

3: Participants observe the set of headlines for round $t$

4: Each participant rates a headline on how likely it is to be real

5: Aggregate their ratings to select a headline

6: Collect reward of $r_{t}=0$ if chosen headline was altered, $1$ otherwise

7: Use collected penalty to update aggregation policy for $t+1$

8:end for

In practice, we bootstrap, for every group size $N$ and for each treatment
(set of headlines), $1000$ subsets of $N$ participants with which we simulate
this collective decision-making process for each of the methods we now
describe.

##### Chosen Methods

Several methods have been developed to improve decision-making with expert
advice. Among them, we select four pivotal approaches that span from
fundamental to state-of-the-art, providing a comprehensive view of online
learning algorithms for collective decision-making. These approaches include:
a simple majority vote serving as a baseline for comparison; EXP4 [10], which
uses observed performance to gradually pinpoint the single best participant;
MetaCMAB [11], an online learning approach that enables more collective
decisions by integrating diverse opinions; and ExpertiseTree [12], which
tailors aggregation strategies to specific contexts.

As illustrated in Fig. 1, a key differentiator among these methods is their
strategy for assigning weight to participants’ opinions, ranging from equal
weighting to complex, performance- and context-based adjustments. Crucially,
the more advanced approaches (MetaCMAB and ExpertiseTree) learn to weight
participants based on their responses, not only relative to the truth, but
also relative to each other. These methods not only prioritize contributions
from the highest performers, resembling strategies that rely on the collective
input of empirically proven subsets of participants [48], but they also
incorporate mechanisms to offset the influence of highly polarized groups of
experts. By recognizing and adjusting for common errors among participants,
these approaches can reduce the negative effects of polarized groups, whose
insights, though potentially insightful, overlap significantly with those of
others [11]. Accounting for correlation among participants in this way is
somewhat similar to approaches which explicitly contrast individual’s
contributions with that of the group [49]. The main distinction between those
alternative approaches and the ones we test in this study is the inclusion of
exploration techniques which prevent premature reliance on a limited group of
experts.

This selection of approaches is intentionally diverse, covering both
traditional and state-of-the-art methods to highlight the spectrum of
possibilities for aggregating advice. From the benchmark simplicity of
majority voting to the nuanced, context-sensitive aggregation offered by
ExpertiseTree, each method contributes uniquely to our understanding of
effective decision-making in varied scenarios. A more detailed description of
these chosen methods and the rationale behind their selection is provided in
Appendix A.

##### Measures of Collective Decision-Making Performance

Because we consider an online learning setting, we evaluate the performance on
two metrics. First, on overall accuracy, i.e., the proportion of rounds for
which an optimal decision was made. And secondly, on final performance, i.e.,
the expected performance at the end of training. In addition, we can analyze
how performance changes as a function of the number of participants.

Given our objective of enhancing the probability of choosing authentic
headlines, our goal becomes maximizing the _average reward_ defined as
$\bar{\mathcal{R}}_{T}=\frac{1}{T}\sum_{t=1}^{T}r_{t}$, where $r_{t}=1$ if the
chosen headline is genuine and $0$ otherwise.

We denote by $\bar{\mathcal{R}}_{T}^{n}$ the average reward we would obtain if
we were to select participant $n$ and choose at each round the headline which
they rate highest. Maximizing over the set of participants, we can in
hindsight select the optimal participant as being
$n^{*}=argmax_{n=1}^{N}\bar{\mathcal{R}}_{T}^{n}$.

To facilitate comparison to the single best participant, we can juxtapose an
algorithm’s performance against the best participant’s performance.
Specifically, for each round, we compute the instantaneous regret:

$R_{t}=r^{n^{*}}_{t}-r_{t}$ (1)

Of particular interest is the instantaneous regret at time $t=T$, i.e.,
$R_{T}$, which we refer to in the main text as terminal instantaneous regret.

If our performance is lower than the best participant, this metric averages
out positively; otherwise, it is negative. Thus, observing negative regret
suggests the presence of collective intelligence.

###  5.5 Establishing Significance

####  5.5.1 Confidence Intervals

In Fig. 2, the confidence intervals for the means are determined using a
bootstrapping method [50]. For each data point, we perform the following
steps: We draw $1,000$ separate samples from the original set of $5,000$
simulation results. Each of these samples is of size $1,000$ and is drawn with
replacement. For each of these $1,000$ samples, we calculate its average.
These $1,000$ averages are then used to form the distribution of means. The
95% confidence intervals are then established by identifying the values at the
2.5th and 97.5th percentiles of this distribution, corresponding to the lower
and upper limits of the interval.

To more rigorously evaluate the significance of our results, we make use of
the following two-sided tests.

####  5.5.2 Wilcoxon Tests

The Wilcoxon test is a non-parametric test used to compare two paired groups
[51]. It is suitable for data that is not normally distributed and assesses
whether the differences between paired observations are symmetric about zero.
In our study, we applied the Wilcoxon test to evaluate the differences between
algorithms ran on the same sets of participants. For example, we might compare
the performance of EXP4 on participant groups $P_{1},P_{2},P_{3}$ to that of
MetaCMAB on those same participant groups. The performance of both algorithms
on any of those participant groups is therefore paired.

####  5.5.3 Generalized Estimating Equations

Generalized Estimating Equations (GEE, [52]) are an extension of the
generalized linear model framework, designed to address the presence of
correlated observations. GEEs are particularly useful for handling data
characterized by repeated measures or clustered data, as it provides robust
parameter estimates even when the correlation structure is misspecified.

For instance, the significance of the results on demographic differences in
performance (Section 2.2) is determined by GEE models with the dependent
variable being the accuracy, the primary predictor being the participant’s
concerned sensitive attribute, e.g., their gender, and by clustering by
participant groups.

####  5.5.4 Mann-Whitney U Tests

The Mann-Whitney U test is a non-parametric test used to compare the
distributions of two independent samples [53]. It is based on the ranks of the
data rather than their actual values and is especially useful when the
assumptions of the t-test (like normality) are not met. In our research, we
utilized the Mann-Whitney U test to compare the distributions of two groups
when no pairing was present. For example, we use it to compare the
distribution of responses between headlines. This should provide a robust
assessment of the differences between them without making stringent
assumptions about the underlying data distribution.

####  5.5.5 Kruskal-Wallis H-test

The Kruskal-Wallis H-test is a non-parametric method used to compare three or
more independent samples [54]. It is an extension of the Mann-Whitney U test
to multiple groups and tests the null hypothesis that all groups come from the
same distribution. In our study, we employed the Kruskal-Wallis H-test when
comparing the distributions of more than two independent groups. For instance,
we might use it to assess the distribution of responses across multiple
headline categories, aiming to determine if at least one headline category
differs significantly from the others in terms of response distribution.

####  5.5.6 Dunn’s Test

Following a significant Kruskal-Wallis H-test result, post-hoc pairwise
comparisons are necessary to determine which groups differ from each other.
Dunn’s test is a non-parametric post-hoc method used to conduct these pairwise
comparisons while adjusting for multiple comparisons [55]. It compares the
differences in the sum of ranks between groups, similar to the Mann-Whitney U
test but with a correction for multiple tests. In this paper, after finding a
significant Kruskal-Wallis result, we applied Dunn’s test to pinpoint which
specific groups had significantly different distributions. For example, if we
found a difference in response distributions across multiple headline
categories, Dunn’s test would help identify which specific headline categories
were significantly different from each other.

##  6 Limitations

###  6.1 Sampling Bias

Participants recruited through Prolific might not be a representative sample
of the general population, leading to potential sampling bias. The results
might be more reflective of individuals familiar with online tasks and surveys
rather than a broader demographic. While we would therefore be hesitant to
claim biases observed in our results are held by the general population, the
participant’s profiles likely align with those typically crowdsourced for
identifying fake news in real-world applications. In particular, not all
participants may exhibit the same level of conscientiousness as an experienced
fact checker. Therefore, their inclusion in our results highlights the
importance of algorithms that can handle such outliers.

Similarly, our recruitment of participants within the Anglosphere limits our
ability to generalize to the whole world. We believe this to be mainly
limiting when it comes to the observed biases, as it is likely that other
populations hold other beliefs.

###  6.2 Problem Selection

Due to our desire to analyze the impact of biases and their mitigation, the
headlines we selected focus on a subset of headlines which involve contrasting
sensitive groups. Response patterns might differ when faced with broader sets
of headlines wherein stereotypes do not play as strong of a role.

###  6.3 Lack of Interaction

The design choice to have participants operate in isolation, while
intentional, means our study does not capture the potential influence of group
dynamics, discussions, or peer pressure on decision-making. It should however
be noted that commonly held stereotypes likely arise from group dynamics and
discussions which occurred before participants completed our experiment. We
leave to future work the exploration of explicit information exchange and how
it should be managed.

##  7 Preregistration Comparison

We now compare and contrast this paper with the preregistered experimental
design. While the objectives and experimental design we describe in this paper
are in line with the preregistration, differences are essentially constrained
to the language used to describe biases. The following compares and contrasts
this paper with the preregistration in more detail.

###  7.1 Research Questions

Our preregistration outlined several primary and secondary research questions.
Below, we detail how we addressed each question in this paper, referring to
specific sections for in-depth analysis.

does the within-factor algorithm have an effect on the accuracy for a subject
group (i.e., is one algorithm better)? We provide relevant results in Section
2.1 and discuss them in section Collective Intelligence through Online Machine
Learning, .

does the within-factor sensitive group have an effect on the advice or error
of a subject individual (i.e., is an expert biased)? We provide the relevant
results in Section 2.2, and discuss them in Headline Categories and Implicit
Biases. Note that ’Sensitive group’ and ’Headline Category’ are used
interchangeably to refer to the same feature.

In addition, we considered the following secondary questions:
do people consistently misevaluate some headlines (either individual headlines
or headlines pertaining to a particular protected group)? In other words, does
the headline or sensitive group have an effect on the error and/or advice?
These results can also be further evaluated in terms of participant
demographics This question is addressed through our results and discussions on
the framing effect.

do people tend to be more conservative/assertive in their answers? That is,
are they more likely to select the ’very’ option? Again, results between
demographic groups can be contrasted In the main text, we discuss (a lack of)
skepticism as a function of the headline category. In addition, we provide an
answer to this question in the supplementary material.

do demographically diverse groups enhance the wisdom of the crowd? I.e., is
the performance of heterogeneous groups better than that of homogeneous
groups. We provide a discussion in the supplementary material.

Is response time a predictor of advice quality or bias? We provide a
discussion in the supplementary material.

##  8 Code availability

Code necessary to reproduce our results is available at
https://github.com/axelabels/fakenews.

##  9 Data availability

Data necessary for reproducing our results, including participant responses,
is available at https://doi.org/10.5281/zenodo.10794209.

##  10 Ethics considerations

Due to the sensitive nature of the questions, participants were informed ahead
of the questionnaire that “Some of the questions presented in this study
involve sensitive characteristics such as gender and ethnicity. Please be
advised that exposure to scenarios involving these characteristics may
potentially make you feel discomfort.”. In addition, ethical approval was
granted on February 16th 2023 by the host institution’s ethics board before
data collection. To ensure ethical compliance, informed consent was obtained
from all participants. This consent process involved clearly explaining the
purpose of the study, the types of data that would be collected, how the data
would be used, and the participants’ rights.

##  11 Acknowledgements

A.A. was supported by a FRIA grant (nr. 5200122F) by the National Fund for
Scientific Research (F.N.R.S.) of Belgium. T.L. is supported by the F.N.R.S.
project with grant number 40007793, the Service Public de Wallonie Recherche
under grant n°2010235–ARIAC by DigitalWallonia4.ai. A.A., T.L. and A.N.
benefit from the support of the Flemish Government through the AI Research
Program. T.L. and A.N. acknowledge the support by TAILOR, a project funded by
EU Horizon 2020 research and innovation program under GA No 952215. E.F.D. is
supported by an F.N.R.S Chargé de Recherche position, grant number 40005955.

##  12 Competing Interests

The authors declare no competing interests.

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##  Appendix A Algorithms

The problem we study in this work can be formalized as a problem of bandits
with expert advice [10].

A straightforward approach in this setting is to perform static aggregation of
participant opinions. In particular, decisions can be made by acting on an
arithmetic mean of all opinions, resulting in a majority vote. Such votes are
most effective when expertise is homogeneous and participants’ errors are
uncorrelated [56, 31]. Participants however often differ in their performance,
and can show varying degrees of correlation due to shared experiences or
stereotypes. Both factors degrade the performance of the simple average. By
giving all group members an equal amount of influence, we dilute the knowledge
of more accurate experts. The majority vote serves as a fundamental baseline
for evaluating more sophisticated algorithms. Its simplicity and widespread
use in decision-making scenarios make it a valuable point of comparison.

If information about the experts’ expected performance is available, votes can
instead be weighted as a function of this performance estimate. The
exponential weighting method EXP4 [10] for example, maintains weights over the
experts, which are updated to favor participants with higher performance. For
each decision, it selects one of the participants according to its current
probability distribution. This single participant’s opinion is then acted
upon. In this sense, the decisions made by EXP4 are not collective, as a
single participant is decisive. However, among algorithms that select a single
participant, EXP4 has optimal theoretical guarantees and is straightforward to
implement, leading to its inclusion in this study.

The reliance on a single expert by EXP4 underscores a significant limitation:
the lack of collective decision-making. Recent advancements have introduced
algorithms like MetaCMAB [11], which, by employing a regression across all
participant opinions, enables a more nuanced combination of expert advice. In
doing so, MetaCMAB can optimally combine the opinions of diverse groups in
order to enable better decisions. This approach allows MetaCMAB to outperform
even the best individual participant, showcasing the potential of collective
intelligence.

Nonetheless, MetaCMAB and similar algorithms assume uniform performance across
different contexts (here, headline categories), an assumption rarely met in
practice. Performance can vary significantly with the context, influenced by
factors like prior experience and cognitive biases. Such heterogeneous
performance permeates into collective decisions, meaning the optimal weighting
of opinions also is a function of the headline category. To tackle such
heterogeneity, the ExpertiseTree [12] learns to split the context space
(consisting here of the headline categories) and then fits distinct models to
each region. Note that regions are only split if it induces a better estimated
performance. In theory, this allows ExpertiseTree to adapt the granularity of
its models to the available expertise.

##  Appendix B Framing Effect for EXP4

Figure 8: Effects of framing in participants’ responses for EXP4. This plot is
analogous to those in Fig. 4; the quadrants represent false stereotypes (Q1),
positive framing effects (Q2), common knowledge (Q3), and negative framing
effects (Q4). Each point represents a distinct headline; the x-coordinate
displays the expected response to its original form, and the y-coordinate
shows the expected response to its altered form.

We provide in Fig. 8 the framing effects for EXP4 (analogously to those in
Fig. 4). EXP4 tends to concentrate its weights on a single group member,
resulting in predictions which are often aligned with that group member’s
advice (and are thus close to $0,0.25,0.5,0.75,\text{or }1$). In terms of
shifts from the simple average, we find the following: Q1: $19\rightarrow 16$,
Q2: $34\rightarrow 41$, Q3: $52\rightarrow 49$, and Q4: $15\rightarrow 14$.
While there are slight shifts from Q3 to Q2, overall these framing effects are
comparable to the average.

In terms of group biases, captured by the GEE summary in Table 2, none of the
features seem to have a significant impact, however the intercept indicates
the model’s error is generally large.

##  Appendix C Transposed Categories

Our results in the main text suggest that headline categories induce different
biases. For example, we found that age-related headlines gave rise to low
skepticism, whereas headlines related to ethnicity gave rise to high
skepticism. To eliminate the hypothesis that this is not due to the categories
but instead is a result of the specific headlines presented in each category,
we ran a secondary experiment wherein the sensitive groups were swapped. For
example, we swapped a headline’s age group by a gender group. If our
hypothesis that the biased responses are due to the groups themselves, rather
than to the specific headlines, is true, we would expect to find the same
patterns of (lack of) skepticism in these altered headlines. In contrast, if
the (lack of) skepticism was a result of the headlines themselves, we would
find that when permuting categories, the categories susceptible to skepticism
would also change.

Our results suggest that our hypothesis holds, as we find that the number of
age headlines in Q4 is low both when generating age headlines from gender
headlines (2/80 headlines in Q4), and when generating age headlines from
ethnicity headlines (3/80 headlines in Q4).

In contrast, ethnicity headlines are absent from Q2 when generated from age
headlines (0/80 headlines in Q2) or from gender headlines (again 0/80
headlines in Q2).

##  Appendix D GEE tables

Tables 1 to 4 summarize the GEE analyses in support of the group bias
discussion of Section 2.3. These tables analyze the effects of headline class
(gender, ethnicity, age) and alteration status (genuine vs. altered) on error.
Headline class variables indicate the headline’s focus, with the baseline
being age. “Genuine” takes as value $1$ when the headline is unaltered.
Interaction terms (e.g., Gender+Genuine) explore the combined effect of
headline class and authenticity.

Reference characteristics are age and altered. Therefore, for example, an
estimate of $0.579$ for the intercept in Table 1 indicates that for an altered
headline conveying an outcome about age groups, the expected error is $0.579$.
Other estimates are coefficients, such that, for example, a value of $-0.093$
for the “Headline Class: Gender” parameter indicates that the expected error
for altered headlines about gender is $0.579-0.093=0.486$. In addition, the
associated $p$-value indicates that this difference is significant. We
therefore conclude that, when using an average to aggregate, there is a
significant difference in error between genuine and altered headlines.
Conversely, for MetaCMAB for example (Table 3), the same parameter’s estimate
is $-0.036$, but with a $p$-value of $0.660$, suggesting this feature no
longer has a significant effect.

Parameter | Estimate | Std. Error | t-value |  $p$-value
---|---|---|---|---
Intercept | 0.579 | 0.022 | 26.085 |  $<$ 0.001
Headline Class: Ethnicity | -0.135 | 0.035 | -3.866 |  $<$ 0.001
Headline Class: Gender | -0.093 | 0.047 | -1.972 | 0.049
Genuine | -0.204 | 0.040 | -5.045 |  $<$ 0.001
Headline Class: Ethnicity:Genuine | 0.219 | 0.058 | 3.782 |  $<$ 0.001
Headline Class: Gender:Genuine | 0.155 | 0.063 | 2.435 | 0.015
Table 1: GEE summary for the average, predicting the aggregate’s error as a function of headline characteristics. Parameter | Estimate | Std. Error | t-value |  $p$-value
---|---|---|---|---
Intercept | 0.537 | 0.046 | 11.712 |  $<$ 0.001
Headline Class: Ethnicity | -0.088 | 0.057 | -1.553 | 0.120
Headline Class: Gender | -0.036 | 0.081 | -0.440 | 0.660
Genuine | -0.126 | 0.110 | -1.144 | 0.253
Headline Class: Ethnicity:Genuine | 0.034 | 0.118 | 0.285 | 0.776
Headline Class: Gender:Genuine | -0.084 | 0.170 | -0.492 | 0.622
Table 2: GEE summary for EXP4, predicting the aggregate’s error as a function of headline characteristics. Parameter | Estimate | Std. Error | t-value |  $p$-value
---|---|---|---|---
Intercept | 0.431 | 0.027 | 15.819 |  $<$ 0.001
Headline Class: Ethnicity | -0.087 | 0.038 | -2.304 | 0.021
Headline Class: Gender | -0.056 | 0.039 | -1.417 | 0.156
Genuine | -0.079 | 0.035 | -2.274 | 0.023
Headline Class: Ethnicity:Genuine | 0.134 | 0.023 | 5.780 |  $<$ 0.001
Headline Class: Gender:Genuine | 0.110 | 0.068 | 1.610 | 0.107
Table 3: GEE summary for MetaCMAB, predicting the aggregate’s error as a function of headline characteristics. Parameter | Estimate | Std. Error | t-value |  $p$-value
---|---|---|---|---
Intercept | 0.319 | 0.017 | 19.326 |  $<$ 0.001
Headline Class: Ethnicity | -0.053 | 0.033 | -1.606 | 0.108
Headline Class: Gender | -0.043 | 0.037 | -1.154 | 0.249
Genuine | 0.003 | 0.024 | 0.136 | 0.892
Headline Class: Ethnicity:Genuine | -0.015 | 0.035 | -0.426 | 0.670
Headline Class: Gender:Genuine | 0.029 | 0.026 | 1.080 | 0.280
Table 4: GEE summary for ExpertiseTree, predicting the aggregate’s error as a
function of headline characteristics.

##  Appendix E Secondary Questions

###  E.1 Inclination Towards Conservative or Assertive Responses: Contrast by
Error and Demographic Group

(a) Distribution of confidence levels as a function of altered status.

(b) Distribution of accuracy as a function of confidence level.

Figure 9: Confidence histograms Figure 10: Proportion of confidence categories
displayed by participant demographic groups.

People tend to be conservative in their answers, being more likely to answer
(un)likely rather than very (un)likely (see Figure 9(a)).

Note that detailing by demographic groups (Figure 10) shows that in general,
all demographic groups tend to more low confidence than high confidence. One
exception to this observation is the group of black females which participated
in this study, as they tend to express low and high confidence in equal
measure. Furthermore, people do tend to answer more extremely when correct
than when incorrect, indicating that their confidence estimates are somewhat
calibrated. In particular, when maximally confident, participants have an
expected accuracy of 60.6%, while, when less confident, they have an expected
accuracy of 54.2%.

While the difference is small, it suggests that weighing the participants’
contribution by their own confidence is likely to be beneficial. Comparing the
accuracy of a majority vote with a confidence-weighted majority vote, we find
that the latter obtains an accuracy of $64.0\%$, while the former’s accuracy
is $54.8\%$. A Wilcoxon test suggests that this difference is significant
($p=0.0008$).

###  E.2 Response Time as an Indicator of Accuracy

Figure 11: Accuracy by response time. Responses are sorted by response time
and then aggregated through a moving average with a window of size $100$.
Shaded areas are the bootstrapped $95\%$ confidence intervals.

We observe two trends in Figure 11. First, the fastest response times induce
the lowest accuracy. This suggests that for those response times, users simply
provided answers without taking the prompts into account. Conversely, as
response time increases, the error rate also tends to increase. These slower
response time could be a sign of greater uncertainty, which correlates with
more mistakes. Finally, the rightmost points have a slightly higher
performance, however, given the large response times involved (over $5$ times
the standard deviation), these responses were likely given after participants
switched off the questionnaire.

###  E.3 Performance of Demographically Diverse Groups

While we found that women perform slightly better than men, this individual
improvement is not reflected in an improved performance of groups; we find
that acting on the average of all female responses is not superior to acting
on the average of all male responses (based on a Wilcoxon test). This is
likely because, while women tend to perform better on average, they are more
strongly correlated than men; men have an average Pearson correlation
coefficient of $0.178$, while women have an average correlation coefficient of
$0.220$. In practical terms, higher correlation within groups will result in
group members making more of the same errors, which are then reinforced by an
average aggregate. In contrast, lower correlation means individuals tend to
make errors on different instances, which are more easily subdued by an
average.

We might therefore wonder whether mixing demographic groups is a better
approach to maximizing group performance than selecting the group with the
best individuals. Unfortunately we found no significant improvement from mixed
groups. While we might hope that mixed groups would be less correlated than
the individual groups which compose them, we found that instead the
correlation of a mixed group was approximately equal to the average
correlation of the individual groups. In particular this means that a mixed
group is typically more correlated than the least correlated individual group.
For example, the correlation of a group with equal number of women and men is
$0.194$, approximately halfway the correlation values of the individual groups
given above.