1. Introduction
Chaffee and McLeod (Reference Chaffee and McLeod1973) offered individuals a choice of pamphlets to read about upcoming elections. They found that individuals tended to choose those pamphlets that fit with their current preferences, rather than those that opposed them. Mynatt et al. (Reference Mynatt, Doherty and Tweney1978) presented subjects with a dynamic system on a computer and asked them to discover the laws governing this system. They found that once subjects generated hypotheses about the system they followed up with tests that would tend to confirm their hypotheses, rather than disconfirm them. Lord et al. (Reference Lord, Ross and Lepper1979) conducted an experiment on individuals with strong views on the death penalty. They found that when these subjects were offered new information regarding the deterrent effect of the death penalty they were very resistant to changing their opinions. Sweeney and Gruber (Reference Sweeney and Gruber1984) surveyed members of the public during the Watergate hearings and found that those who had voted for Nixon tended to ignore information about the hearings compared to those who had voted for McGovern.
These studies are just a few of those outlining the pervasive impact of confirmation bias on human learning. Confirmation bias refers to a cluster of related behaviors whereby individuals tend to seek out, to interpret, to favor, and to selectively recall information that confirms beliefs they already hold, while avoiding or ignoring information that disconfirms these beliefs. It has been widely implicated in the prevalence and persistence of false beliefs. Individuals exhibiting this bias often ignore information that might help them develop accurate beliefs about the world. Most notably, they are susceptible to holding on to false beliefs which have been discredited (Festinger et al. Reference Festinger, Riecken and Schachter2017; Anderson et al. Reference Anderson, Lepper and Ross1980; Johnson and Seifert Reference Johnson and Seifert1994; Lewandowsky et al. Reference Lewandowsky, Ecker, Seifert, Schwarz and Cook2012).
Confirmation bias has mostly been studied at the individual level—i.e., how does it influence individual beliefs and behaviors? Human knowledge and belief, though, are deeply social. Individuals influence the beliefs of those they interact with, and are influenced in turn. Ideas and evidence are shared via social networks in ways that impact further learning and exploration. This leads to a set of questions: How does confirmation bias influence learning and belief in human groups? Is it harmful to groups in the same way it seems to be harmful to individuals? A few authors have considered, in particular, whether confirmation bias might have unexpected or surprising benefits to group inquiry. Could confirmation bias actually be epistemically useful in the right contexts?
We use network models to study these questions. In particular, we draw on the network epistemology paradigm first developed in economics by Bala and Goyal (Reference Bala and Goyal1998) to study learning in groups. Subsequently, this framework has been widely employed in social epistemology and the philosophy of science to study related topics such as the emergence of consensus in scientific communities (Zollman Reference Zollman2007, Reference Zollman2010) and the impacts of social biases on group learning (O’Connor and Weatherall Reference O’Connor and Owen Weatherall2018). Unlike some other sorts of network models, in this paradigm agents gather and share data and evidence with each other. This is an important feature in studying confirmation bias since this bias impacts the way individuals deal with evidence they receive.
We find that in models incorporating moderate levels of confirmation bias groups do better than in models where individuals do not exhibit confirmation bias. Dogmatic individuals who do not easily change positions force the group to more extensively test their options, and thus avoid pre-emptively settling on a poor one. This result reflects claims from philosophers and psychologists who have argued that tendencies related to irrational stubbornness, such as confirmation bias, might benefit group learning in this way (Kuhn Reference Kuhn1977; Popper Reference Popper and Harré1975; Solomon Reference Solomon1992, Reference Solomon2007; Mercier and Sperber Reference Mercier and Sperber2017; Smart Reference Smart2018). Our results also echo modeling findings from Zollman (Reference Zollman2010), who shows that groups of stubborn individuals sometimes learn better than more individually rational learners. Footnote 1 In our case, confirmation bias functions as a sort of stubbornness. It leads individuals to keep exploring theories that might otherwise seem suboptimal, and, in doing so, to sometimes discover that these theories are actually worthwhile.
There is a downside to confirmation bias, though. While moderate levels can promote accurate group-level learning, we find that a more robust type of confirmation bias leads individuals to entirely ignore theories they do not currently favor. In such cases, communities can polarize, and epistemic progress is harmed. This suggests that while our models help confirm a useful function of confirmation bias, worries about its harms are still legitimate even when considered from the group perspective.
The paper will proceed as follows. In section 2 we describe relevant literature, first focusing on empirical work on confirmation bias. We then briefly survey related modeling work. Section 3 outlines our model, which incorporates a form of confirmation bias into epistemic network models. In section 4 we present two sets of results. The first considers models with a moderate level of confirmation bias, and shows how this bias can improve learning in a community. The second considers models where confirmation bias drives polarization, and prevents good group learning. In the conclusion we draw some more general lessons for social epistemology and philosophy of science. One relates to the independence thesis—that irrational individuals can form rational groups, and vice versa (Mayo-Wilson et al. Reference Mayo-Wilson, Zollman and Danks2011). Our models provide one more vein of support for this claim. Another relates to the rationality or irrationality of ignoring data as a Bayesian learner. And a last point regards what simple models of polarization can tell us.
2. Previous literature
2.1. Confirmation bias
As noted, confirmation bias is a blanket term for a set of behaviors where are unresponsive or resistant to evidence challenging their currently held beliefs (Klayman Reference Klayman1995; Nickerson Reference Nickerson1998; Mercier and Sperber Reference Mercier and Sperber2017). The models we present will not adequately track all forms of confirmation bias. They do, however, reflect behaviors seen by those engaging in what is called selective exposure bias, as well as those who selectively interpret evidence.
Selective exposure occurs when individuals tend to select or seek out information confirming their beliefs. This could involve avoidance of disconsonant information (Hart et al. Reference Hart, Albarracín, Eagly, Brechan, Lindberg and Merrill2009) or pursuit of consonant information (Garrett Reference Garrett2009; Stroud Reference Stroud and Kenski2017). The study by Chaffee and McLeod (Reference Chaffee and McLeod1973) where participants chose pamphlets to read about an upcoming election is an example of selective exposure bias. While selective exposure has been most frequently studied in the context of politicized information, it need not be. Johnston (Reference Johnston1996) observes it in participants seeking to confirm their stereotypes about doctors. Olson and Zanna (Reference Olson and Zanna1979) find selective exposure in participants’ art viewing preferences. Stroud (Reference Stroud and Kenski2017) gives a wider overview of these and related results.
As will become clear, our models can also represent confirmation bias that involves selective interpretation or rejection of evidence. Recall Lord et al. (Reference Lord, Ross and Lepper1979), where subjects received information both supporting and opposing the efficacy of the death penalty as a deterrent to crime. This information did little to change subjects’ opinions on the topic, suggesting they selectively rejected information opposing their view. Gadenne and Oswald (Reference Gadenne and Oswald1986) demonstrate a similar effect in subject ratings of the importance of information confirming vs. challenging their beliefs about a fictional crime. Taber and Lodge (Reference Taber and Lodge2006) gave participants pairs of equally strong arguments in favor of and against affirmative action and gun control, and found subjects shifted their beliefs in the direction they already leaned. In each of these cases, individuals seemed to selectively reject only the information challenging their views.
As noted, many previous authors have argued that confirmation bias may be epistemically harmful. Nickerson (Reference Nickerson1998) writes that “[m]ost commentators, by far, have seen the confirmation bias as a human failing, a tendency that is at once pervasive and irrational” (205). It has been argued that confirmation bias leads to irrational preferences for early information, which grounds or anchors opinions (Baron Reference Baron2000). In addition, confirmation bias can lead subjects to hold on to beliefs which have been discredited (Festinger et al. Reference Festinger, Riecken and Schachter2017; Anderson et al. Reference Anderson, Lepper and Ross1980; Johnson and Seifert Reference Johnson and Seifert1994; Nickerson Reference Nickerson1998; Lewandowsky et al. Reference Lewandowsky, Ecker, Seifert, Schwarz and Cook2012). Another worry has to do with “attitude polarization,” exhibited in Taber and Lodge (Reference Taber and Lodge2006), where individuals shift their beliefs in different directions when presented with the same evidence.
Further worries about confirmation bias have focused on communities of learners rather than individuals. Attitude polarization, for example, might drive wider societal polarization on important topics (Nickerson Reference Nickerson1998; Lilienfeld et al. Reference Lilienfeld, Ammirati and Landfield2009). For this reason, Lilienfeld et al. (Reference Lilienfeld, Ammirati and Landfield2009) describe confirmation bias as the bias “most pivotal to ideological extremism and inter- and intragroup conflict” (391).
Specific worries focus on both scientific communities and social media sites. Scientific researchers may be irrationally receptive to data consistent with their beliefs, and resistant to data that does not fit. Koehler (Reference Koehler1993) and Hergovich et al. (Reference Hergovich, Schott and Burger2010), for example, find that scientists rate studies as of higher quality when they confirm prior beliefs. If so, perhaps the scientific process is negatively impacted.
It has also been argued that confirmation bias may harm social media communities. Pariser (Reference Pariser2011) argues that “filter bubbles” occur when recommendation algorithms are sensitive to content that users prefer, including information that confirms already held views. “Echo chambers” occur when users seek out digital spaces—news platforms, followees, social media groups, etc.—that mostly confirm the beliefs they already hold. While there is debate about the impact of these effects, researchers have argued that they promote polarization (Conover et al. Reference Conover, Ratkiewicz, Francisco, Gonçalves, Menczer and Flammini2011; Sunstein Reference Sunstein2018; Chitra and Musco Reference Chitra and Musco2020), harm knowledge (Holone Reference Holone2016), and lead to worryingly uniform information streams (Sunstein Reference Sunstein2018; Nikolov et al. Reference Nikolov, Oliveira, Flammini and Menczer2015) (but see Flaxman et al. Reference Flaxman, Goel and Rao2016).
While most previous work has focused on harms, some authors argue for potential benefits from confirmation bias. Part of the thinking is that such a pervasive bias would not exist if it was entirely harmful (Evans Reference Evans1989; Mercier and Sperber Reference Mercier and Sperber2017; Butera et al. Reference Butera, Sommet and Toma2018). With respect to individual reasoning, some argue that testing the plausibility of a likely hypothesis is beneficial compared to searching out other, maybe less likely, hypotheses (Klayman and Ha Reference Klayman and Ha1987; Klayman Reference Klayman1995; Laughlin et al. Reference Laughlin, VanderStoep and Hollingshead1991; Oaksford and Chater Reference Oaksford and Chater2003). Lefebvre et al. (Reference Lefebvre, Summerfield and Bogacz2022) show how confirmation bias can lead agents to choose good options even when they are prone to noisy decision making. Footnote 2
Another line of thinking, more relevant to the current paper, suggests that confirmation bias, and other sorts of irrational stubbornness, may be beneficial in group settings. Footnote 3 The main idea is that stubborn individuals promote a wider exploration of ideas/options within a group, and prevent premature herding onto one consensus. Kuhn (Reference Kuhn1977) suggests that disagreement is crucial in science to promote exploration of a variety of promising theories. Some irrational stubbornness is acceptable in generating this disagreement. Popper (Reference Popper and Harré1975) is not too worried about confirmation bias because as, he argues, the critical aspect of science as practised in a group will eliminate poor theories. He argues that “… a limited amount of dogmatism is necessary for progress: without a serious struggle for survival in which the old theories are tenaciously defended, none of the competing theories can show their mettle” (98). Solomon (Reference Solomon1992) points out that in the debate over continental drift, tendencies like confirmation bias played a positive role in the persistence and spread of (ultimately correct) theories. (See also Solomon Reference Solomon2007.) All these accounts focus on how irrational intransigence can promote the exploration of diverse theories, and ultimately benefit group learning.
In addition, Mercier and Sperber (Reference Mercier and Sperber2017) argue that when peers disagree, confirmation bias allows them to divide labor by developing good arguments in favor of opposing positions. They are then jointly in a position to consider these arguments and come to a good conclusion. This fits with a larger picture where reasoning evolved in a social setting, and what look like detrimental biases actually have beneficial functions for groups. All these arguments fit with what Smart (Reference Smart2018) calls “Mandevillian Intelligence”—the idea that epistemic vices at the individual level can sometimes be virtues at the collective level. He identifies confirmation bias as such a vice (virtue) for the reasons listed above.
The results we will present are largely in keeping with these arguments for the group benefits of confirmation bias. Before presenting them, though, we take some time to address previous, relevant modeling work.
2.2. Previous models
To this point, there seem to be few models incorporating confirmation bias specifically to study its effects on epistemic groups. Geschke et al. (Reference Geschke, Lorenz and Holtz2019) present a “triple filter-bubble” model, where they consider impacts of (i) confirmation bias, (ii) homophilic friend networks, and (iii) filtering algorithms on attitudes of agents. They find that a combination of confirmation bias and filtering algorithms can lead to segmented “echo chambers” where small, isolated groups with similar attitudes share information. Their model, however, does not attempt to isolate confirmation bias as a causal factor in group learning. In addition, they focus on attitudes or opinions that shift as individuals average with those of others they trust. As will become clear, our model isolates the effects of confirmation bias, and also models learning as belief updating on evidence, thus providing better structure to track something like real-world confirmation bias.
There is a wider set of models originating from the work of Hegselmann and Krause (Reference Hegselmann and Krause2002), where agents have “opinions” represented by numbers in a space, such as the interval
$\left[ {0,{\rm{\;}}1} \right]$
. They update opinions by averaging with others they come in contact with. If agents only average with those in a close “neighborhood” of their beliefs they settle into distinct camps with different opinions. This could perhaps be taken as a representation of confirmation bias, since individuals are only sensitive to opinions near their own. But, again, there is no representation in these models of evidence or of belief revision based on evidence.
As noted, we draw on the network epistemology framework in building our model. While this framework has not been used to model confirmation bias, there have been some relevant previous models where actors devalue or ignore some data for reasons related to irrational biases. O’Connor and Weatherall (Reference O’Connor and Owen Weatherall2018) develop a model where agents update on evidence less strongly when it is shared by those with different beliefs. This devaluing focuses on the source of information, rather than its content (as occurs in confirmation bias). Reflecting some of our results, though, they find that devaluation at a low level is not harmful, but at a higher level eventually causes polarization. Wu (Reference Wu2023) presents models where a dominant group devalues or ignores information coming from a marginalized group. Wu’s model (again) can yield stable polarization under conditions in which this devaluation is very strong. Footnote 4 In both cases, and, as will become clear, in our models, polarization emerges only in those cases where agents begin to entirely ignore data coming from some peers.
There is another set of relevant results from epistemic network models. Zollman (Reference Zollman2007, Reference Zollman2010) shows that, counterintuitively, communities tend to reach accurate consensus more often when the individuals in them are less connected. In highly connected networks, early strings of misleading evidence can influence the entire group to preemptively reject potentially promising theories. Less-connected networks preserve a diversity of beliefs and practices longer, meaning there is more time to explore the benefits of different theories. A very similar dynamic explains why, in our model, moderate levels of confirmation bias actually benefit a group. Zollman (Reference Zollman2010) finds similar benefits to groups composed of “stubborn” individuals, i.e., ones who start with more extreme priors and thus learn less quickly. Frey and Šešelja (Reference Frey and Šešelja2018, Reference Frey and Šešelja2020) generate similar results for another operationalization of intransigence. And Xu et al. (Reference Xu, Liu and He2016) yield similar results for another type of model. In our model, confirmation bias creates a similar sort of stubbornness. Footnote 5
One last relevant set of models find related results using NK-landscape models, where actors search a problem landscape for solutions. March (Reference March1991), Lazer and Friedman (Reference Lazer and Friedman2007), and Fang et al. (Reference Fang, Lee and Schilling2010) show how less-connected groups of agents may be more successful at search because they search the space more widely and avoid getting stuck at local optima. Mason et al. (Reference Mason, Jones and Goldstone2008) and Derex and Boyd (Reference Derex and Boyd2016) confirm this empirically. And Boroomand and Smaldino (Reference Boroomand and Smaldino2023), in draft work, find that groups searching NK-landscapes adopt better solutions when individuals have preferences for their own, current solutions. This is arguably a form of irrational stubbornness that improves group outcomes. (Their models, though, do not involve actors with preferences for confirmatory data the way ours do.)
3. Model
3.1. Base model
As discussed, our model starts with the network epistemology framework (Bala and Goyal Reference Bala and Goyal1998), which has been widely used in recent work on social epistemology and the philosophy of science. Our version of the model builds off that presented in Zollman (Reference Zollman2010).
There are two key features of this framework: a decision problem and a network. The decision problem represents a situation where agents want to develop accurate, action-guiding beliefs about the world, but start off unsure about which actions are the best ones. In particular, we use a two-armed bandit problem, which is equivalent to a slot machine with two arms that pay out at different rates.
Footnote 6
The problem is then to figure out which arm is better. We call the two options A (or “all right”) and B (or “better”). For our version of the model, we let the probabilities that each arm pays off be
${p_{\rm{B}}} = 0.5$
and
${p_{\rm{A}}} = {p_{\rm{B}}} - \varepsilon $
. In other words, there is always a benefit to taking option B, with the difference between the arms determined by the value of
$\varepsilon $
.
Agents learn about the options by testing them, and then updating their beliefs on the basis of these tests. Simulations of the model start by randomly assigning beliefs to the agents about the two options. In particular, we use two beta distributions to model agent beliefs about the two arms. These are distributions from 0 to 1, tracking how much likelihood the agent assigns to each possible probability of the arm in question. The details of the distribution are not crucial to understand here.
Footnote 7
What is important is that there are two key parameters for each distribution,
$\alpha $
and
$\beta $
. These can be thought of as tracking a history of successes (
$\alpha $
) and failures (
$\beta $
) in tests of the arms. When new data is encountered, say
$n$
trials of an arm with
$s$
successes, posterior beliefs are then represented by a beta distribution with parameters
$\alpha + s$
and
$\beta + n - s$
. It is easy to calculate the expectation of this distribution, which is
$\alpha /\left( {\alpha + \beta } \right)$
.
Following Zollman (Reference Zollman2010), we initialize agents by randomly selecting
$\alpha $
and
$\beta $
from
$\left[ {0,4} \right]$
. The set-up means that at the beginning of a trial, the agents are fairly flexible since their distributions are based on relatively little data. As more trials are performed, expectation becomes more rigid. For example, if
$\alpha = \beta = 2$
, then the expectation is
$0.5$
. Expectation is flexible in that if the next three pulls are failures, then expectation drops to
$2/\left( {2 + 5} \right) \approx 0.286$
. However, if a thousand trials resulted in
$\alpha = \beta = 500$
, three repeated failures would result in an expectation
$500/\left( {500 + 503} \right) \approx 0.499$
(which is still close to
$0.5$
). In simulation, if the agents continue to observe data from the arms, their beta distributions tend to become more and more tightly peaked at the correct probability value, and harder to shift with small strings of data.
As a simulation progresses we assume that in each round agents select the option they think more promising, i.e., the one with a higher expectation given their beliefs. This assumption corresponds with a myopic focus on maximizing current expected payoff. While this will not always be a good representation of learning scenarios, it represents the idea that people tend to test those actions and theories they think are promising.
Footnote 8
Each agent gathers some number of data points,
$n$
, from their preferred arm. After doing so, they update their beliefs in light of the results they gather, but also in light of data gathered by neighbors. This is where the network aspect of the model becomes relevant. Agents are arrayed as nodes on a network, and it is assumed they see data from all those with whom they share a connection.
To summarize, this model represents a social learning scenario where members of a community (i) attempt to figure out which of two actions/options/beliefs is more successful, (ii) use their current beliefs to guide their data-gathering practices, and (iii) share data with each other. This is often taken as a good model of scientific theory development (Zollman Reference Zollman2010; Holman and Bruner Reference Holman and Bruner2015; Kummerfeld and Zollman Reference Kummerfeld and Zollman2015; Weatherall et al. Reference Weatherall, O’Connor and Bruner2020; Frey and Šešelja Reference Frey and Šešelja2020) or the emergence of social consensus/beliefs more broadly (Bala and Goyal Reference Bala and Goyal1998; O’Connor and Weatherall Reference O’Connor and Owen Weatherall2018; Wu Reference Wu2023; Fazelpour and Steel Reference Fazelpour and Steel2022).
In this base model, networks of agents eventually settle on consensus—either preferring the better option B, or the worse option A. If they settle on A, they stop exploring option B, and fail to learn that it is, in fact, better. This can happen if, for instance, misleading strings of data convince a wide swath of the group that B is worse than it really is.
3.2. Modeling confirmation bias
How do we incorporate confirmation bias into this framework? As noted, confirmation bias is varied and tracks multiple phenomena (Klayman Reference Klayman1995). For this reason, we develop a few basic models of confirmation bias that track the general trend of ignoring or rejecting evidence that does not accord with current beliefs. The goal is to study the ways such a trend may influence group learning in principle, rather than to exactly capture any particular version of confirmation bias.
For each round of simulation, after trial results are shared according to network connections, agents have some probability of accepting and updating their beliefs based on the shared results. This probability is based on how likely they believe those results are given their prior beliefs,
$\lambda $
. This likelihood is a function of the agent’s current beta distribution parameters,
$\alpha $
and
$\beta $
, as well as the details of the results, successes,
$s$
, per number of draws,
$n$
.
Footnote 9
An agent calculates
$\lambda $
separately for each set of results shared via a network connection. Examples of these probabilities as a function of an agent’s
$\alpha $
and
$\beta $
values are shown in figure 1.
Figure 1. The probability mass functions of beta-binomial distributions for different values of
$\alpha $
and
$\beta $
.
Additionally, the model includes an intolerance parameter,
$t$
, that impacts how likely agents are to accept or reject results for a given prior probability of those results occurring. The probability of an agent accepting a set of results is
${p_{{\rm{accept}}}} = {\lambda ^t}$
. When
$t$
is low, agents are more tolerant of results they consider unlikely, and when
$t$
is high they tend to reject such results. For example, suppose an agent thinks some shared results have a
$5{\rm{\% }}$
chance of occurring given their prior beliefs (i.e.,
$\lambda = 0.05$
). Then, for
$t = 1$
, the agent has a probability of accepting
${p_{{\rm{accept}}}} = 0.05$
. For
$t = 2$
, the agent is extremely intolerant with
${p_{{\rm{accept}}}} = {0.05^2} = 0.0025$
.
Footnote 10
For
$t = 0.5$
, the agent is more tolerant and
${p_{{\rm{accept}}}} = {0.05^{0.5}} = 0.22$
. And when
$t = 0$
the probability of acceptance is always 1, i.e., our model reverts to the base model with no confirmation bias. Whenever evidence is accepted, agents update their beliefs using Bayes’ rule as described. Agents never reject evidence they generated themselves.
Footnote 11
This feature mimics confirmation bias by representing either (i) a situation in which agents are selectively avoiding data that does not fit with their priors, or (ii) engaging with, but rejecting, this data and thus failing to update on it.
Notice that, for a given tolerance
$t$
, agents with the same expectation do not typically have the same probability of accepting evidence. For example,
$\alpha = \beta = 2$
gives the same 0.5 expectation as
$\alpha = \beta = 50$
, but for any
$t \ne 0$
, an agent with the former beliefs will be more likely to accept a 1000-test trial with 650 successes. The latter agent finds this data less likely because of the relative strength of their beliefs (see figure 1). In general, stronger beliefs in this model will be associated with a higher likelihood of rejecting disconsonant data. This aspect of the model neatly dovetails with empirical findings suggesting that confirmation bias is stronger for beliefs that individuals are more confident in (Rollwage et al. Reference Rollwage, Alisa Loosen, Hauser, Dolan and Fleming2020).
We consider several different simple network structures, including the cycle, wheel, and complete networks (see figure 2). We also consider Erdös–Rényi random networks, which are generated by taking some parameter
$b$
, and connecting any two nodes in the network with that probability (Erdős and Rényi Reference Erdös and Rényi1960). In general, we find qualitatively robust results across network structures. For each simulation run we initialize agents as described, and let them engage in learning until the community reaches a stable state.
Figure 2. Several network structures.
4. Results
4.1. Moderate confirmation bias
In the model just described, notice that actors can be very unlikely to update on some data sets. But the structure of the beta distribution and our rule for rejecting evidence means that they always accept data they encounter with some probability. Whenever agents continue to test different theories, their data continues to reach network neighbors and shape the beliefs of these neighbors. This mutual influence means that, as in previous versions of the model without confirmation bias, actors in our model always reach consensus eventually: either correct consensus that B is better, or incorrect consensus on A. The question is, how does the introduction of confirmation bias influence the frequency with which correct vs. incorrect consensus emerges?
Surprisingly, we find that confirmation bias improves the knowledge-producing capacity of epistemic networks, in that it increases the likelihood a particular network will reach correct consensus. This finding is robust across network structures, and variations in other parameters (network size, number of pulls per round
$n$
, difference between the arms
$\varepsilon $
).
Footnote 12
Figure 3 shows this result for the wheel network with different numbers of agents. The results are averages over 1000 runs of simulation for each parameter value. Each trace tracks a different amount of confirmation bias, as modulated by
$t$
. As is clear, the larger
$t$
is, i.e., the more confirmation bias, the more often the network of agents correctly concludes that B is the better option.
Footnote 13,Footnote 14
Figure 3. When agents use moderate levels of confirmation bias, groups tend to reach accurate consensus more often. This figure shows results for small wheel networks. Qualitative results are robust across parameter values.
$\varepsilon = 0.001$
,
$n = 1000$
.
As noted, this trend is robust across parameter values. In figure 4 we show similar results for larger graphs randomly generated using the Erdős–Rényi (ER) algorithm described above. Again, higher levels of confirmation bias correspond to better group learning.
Figure 4. When agents use moderate levels of confirmation bias, groups tend to reach accurate consensus more often. This figure shows results for moderate-sized ER random networks with the probability of connection between any two nodes
$b = 0.5$
. Qualitative results are robust across parameter values.
$\varepsilon = 0.001$
,
$n = 1000$
.
As previously mentioned, this finding relates to results from Zollman (Reference Zollman2007, Reference Zollman2010) showing that both lowering connectivity and increasing stubbornness can improve outcomes in this sort of model. This “Zollman effect” occurs because individuals can influence each other too strongly, and, as a result, incorrectly settle on option A as a result of early strings of misleading data. By making agents less willing to accept data that might change their mind, confirmation bias decreases social influence in a similar way to decreasing connectivity or stubbornness and leads to longer periods of exploration for both theories. This, in turn, increases the chances that the entire group selects the better option B in the end. While it is surprising that a reasoning bias which is usually treated as worrisome can actually improve the performance of a group, this result, as noted, reflects previous claims from philosophers and psychologists. The mechanism we identify—where confirmation bias leads to continued exploration and data gathering about multiple theories or actions—is very similar to that described by Kuhn (Reference Kuhn1977), Popper (Reference Popper and Harré1975), Solomon (Reference Solomon1992, Reference Solomon2007), and Smart (Reference Smart2018).
To test the robustness of our general finding, we implement another version of the model. Confirmation bias in the first version responds to the likelihood of some data set given current beliefs. But confirmation bias often occurs in the context of fairly coarse-grained information. What if we suppose individuals ignore details of the data and simply ask, which theory does this data support? And, do I think that theory is the better one? In deciding to accept or reject a set of data in this version of the model, the actor calculates their probability that B is better than A, or vice versa, and scales with an intolerance parameter as before.
Footnote 15
Actors accept any data set supporting B (or A) with probability
${P_{{\rm{accept}}}}$
.
The qualitative results of this “coarse-grained” model are similar to the previous one. Across parameters, increasing confirmation bias leads to improved group outcomes. Figure 5 shows results for ER random networks with different numbers of agents. As is clear, a higher value of
$t$
is again associated with a greater probability that the group adopts a consensus on the better option, B.
Figure 5. Moderate confirmation bias increases epistemic success under a different operationalization of confirmation bias. This figure shows results for moderate-sized ER random networks with the probability of connection between any two nodes
$b = 0.5$
. Qualitative results are robust across parameter values.
$\varepsilon = 0.001$
,
$n = 1000$
.
Our results to this point seem to suggest that confirmation bias is an unmitigated good in a group setting. It is true that the sort of confirmation bias modeled so far always improves group consensus formation in our models. There are a few caveats, though. First, for parameter settings where the decision problem is relatively easy—where the network (
$N$
) is large, agents draw more data (
$n$
is large), and/or the two arms are relatively easy to disambiguate (
$\varepsilon $
is large)—most groups successfully learn to choose the correct arm. In these cases confirmation bias does little to improve learning.
Footnote 16
On the other hand, confirmation bias as we model it always slows down consensus formation, sometimes very dramatically. This creates a trade-off between speed of learning and accuracy of consensus formation (Zollman Reference Zollman2007, Reference Zollman2010). In cases where it is important for a group to quickly reach consensus, then, confirmation bias might cause problems. Second, as will become clear in the next section, stronger assumptions about what confirmation bias entails will shift this narrative.
4.2. Strong confirmation bias
To this point, we have only considered models where agents always have some probability of updating on data they encounter, though this probability may be small. This means that all agents continue to exert influence on each other, regardless of what they believe and what sorts of data they gather. This influence might be small, but it ensures that, given enough time, the community will eventually reach consensus on one of the two options.
But what if agents sometimes entirely discount data that does not fit their prior beliefs? We now look at a much simpler version of confirmation bias. Agents calculate how likely some data set is given their current beliefs, as before. If that probability is below some threshold,
$h$
, they discard the data. If it is above that threshold, they update on it.
In this version of the model, we now observe outcomes where groups do not settle on consensus. It is possible for subgroups to emerge which favor different options, and where data supporting the alternative position is unpersuasive to each group. This can be understood as a form of polarization—agents within the same community settle on stable, mutually exclusive beliefs, and do not come to consensus even in the face of continued interaction and sharing of evidence. Footnote 17
Figure 6 shows results for Erdős–Rényi random networks with different thresholds for ignoring discordant data,
$h$
. As is clear, as the cutoff becomes more stringent, fewer simulations end up adopting an accurate consensus.
Figure 6. Strong confirmation bias hurts group learning. This figure shows results for moderate-sized ER random networks with the probability of connection between any two nodes
$b = 0.5$
. Qualitative results are robust across parameter values.
$\varepsilon = 0.001$
,
$n = 1000$
.
As noted, much of the reason that communities fail to reach accurate consensus in these models is because they polarize. When this happens, some actors adopt accurate beliefs, but others do not. Because actors with inaccurate beliefs develop credences where the accurate belief looks very unlikely to them, they become entirely insensitive to data that might improve their epistemic state. As figure 7 shows, polarization occurs more often the stronger the agents’ confirmation bias. Both accurate and inaccurate consensus become less common. For parameter values where only very likely data is accepted, polarization almost always emerges.
Figure 7. Strong confirmation bias leads to polarization. This figure shows results for ER random networks with the probability of connection between any two nodes
$b = 0.5$
. Qualitative results are robust across parameter values.
$N = 6$
,
$\varepsilon = 0.001$
,
$n = 1000$
.
Another question we might ask is: how does this stronger form of confirmation bias impact the general epistemic success of agents in the network? Note that since polarization occurs in these models this is a slightly different question than how strong confirmation bias impacts correct group consensus. Given that confirmation bias leads to an increase in polarization, and a decrease in both correct and incorrect consensus formation, it is not immediately clear whether it is epistemically harmful on average.
In general, we find that this stronger form of confirmation bias leads fewer individual actors, on average, to hold correct beliefs. As is evident in figure 8 for high levels of strong confirmation bias, fewer individuals hold true beliefs. In this figure notice that for lower levels of confirmation bias there is relatively little impact on average true belief. In fact, given details of network size, we find that there is often a slight advantage to a little confirmation bias for the reasons outlined in the last section—it prevents premature lock-in on false consensus. Footnote 18 This slight advantage is eventually outweighed by the negative impacts of too much distrust. As confirmation bias increases, eventually too many agents adopt false beliefs, and fail to engage with disconfirmatory evidence.
Figure 8. Avegerage correct beliefs under strong confirmation bias. This figure shows results for ER random networks of size 6 and 9, with the probability of connection between any two nodes
$b = 0.5$
. Qualitative results are robust across parameter values.
$\varepsilon = 0.001$
,
$n = 1000$
.
At this point, it may seem that small differences in how confirmation bias is modeled have large impacts on how it influences group learning. As long as agents continue to have some influence on each other, no matter how small, confirmation bias improves consensus formation (and thus average true beliefs). Once this is no longer true, it generally harms average true beliefs. This picture is not quite right. Recall from the previous section that moderate confirmation bias always slows consensus formation, sometimes dramatically. When this happens, a network can remain in a state of transient polarization for a long period of time. If we stopped our models at some arbitrary time period, rather than always running them to a stable state, the two sorts of confirmation bias would look more similar. In both cases confirmation bias leads to polarization, but in one case that polarization eventually resolves, and this process improves community learning. The take-away is thus a complex one—confirmation bias can have surprising benefits on group learning, and for the very reasons supposed by some previous authors, but these benefits are neither simple, nor unmitigated.
5. Conclusion
We find that confirmation bias, in a moderate form, improves the epistemic performance of agents in a networked community. This is perhaps surprising given that previous work mostly emphasizes epistemic harms of confirmation bias. By decreasing the chances that a group pre-emptively settles on a promising option, confirmation bias can improve the likelihood the group chooses optimal options in the long run. In this, it can play a similar role to decreased network connectivity or stubbornness (Zollman Reference Zollman2007, Reference Zollman2010; Xu et al. Reference Xu, Liu and He2016; Wu Reference Wu2023). The downside is that more robust confirmation bias, where agents entirely ignore data that is too disconsonant with their current beliefs, can lead to polarization, and harm the epistemic success of a community. Our modeling results thus provide potential support for arguments from previous scholars regarding the benefits of confirmation bias to groups, but also a caution. Too much confirmation bias does not provide such benefits.
There are several discussions in philosophy and social sciences where our results are relevant. Mayo-Wilson et al. (Reference Mayo-Wilson, Zollman and Danks2011) argue for the independence thesis—that rationality of individual agents and rationality of the groups they form sometimes come apart. Our results lend support to this claim. While there is a great deal of evidence suggesting that confirmation bias is not ideal for individual reasoners, our models suggest it can nonetheless improve group reasoning under the right conditions. This, as noted, relates to the notion of Mandevillian intelligence from Smart (Reference Smart2018).
This argument about the independence thesis connects up with debates about whether it is ever rational to ignore free evidence. Footnote 19 According to Good’s theorem, it is always rational to update in such cases (Good Reference Good1967). The proof relies on the idea that an individual who wishes to maximize their expected utility will not do worse, and will often do better, by updating on available, free information. But in our models agents sometimes choose to ignore evidence, and thus increase their chances of eventually holding true beliefs. Of course, in the meantime they ignore good evidence that should, on average, improve the success of their actions. Whether or not they “should” ignore evidence in this case arguably depends on what their goals are. But if the central goal is to eventually settle on the truth, we show that ignoring some data can help in a group learning setting.
As noted, our results are consonant with previous argumentation regarding the value of stubbornness or dogmatism to science. There is a question, though, about whether confirmation bias, or other forms of arguably irrational stubbornness, are the best mechanisms by which to improve group learning. Santana (Reference Santana2021) argues that stubbornness in science can have negative consequences, such as hurting public trust. Wu and O’Connor (Reference Wu and O’Connor2023) give an overview of the literature on transient diversity of beliefs in network models, and argue that in scientific communities there are better ways to ensure this diversity than to encourage actors to be stubborn. For example, centralized funding bodies can promote exploration across topics instead. By doing so, they allow scientists to learn about data rationally, but still prevent premature adoption of suboptimal theories. But Wu and O’Connor’s conclusions are specific to scientific disciplines where there are levers for coordinating exploration across a group. When it comes to more general epistemic groups, especially outside of science, such coordination may not be possible. If so, confirmation bias may provide benefits that are not available via more efficient routes.
One larger discussion this paper contributes to regards the mechanisms that can lead to polarization in real communities. Such mechanisms often include feedback loops wherein similarity of opinion/belief leads to increased influence between individuals, and vice versa. Individuals whose beliefs diverge end up failing to influence each other, and their divergent beliefs become stable. But under this general heading, theorists have identified a number of different such mechanisms. Hegselmann and Krause (Reference Hegselmann and Krause2002) show how this can happen if individuals fail to update on the opinions of those who do not share their opinions. Weatherall and O’Connor (Reference Weatherall and O’Connor2020) find polarization emerges when individuals conform with those in their social cliques, and thus ignore data from those outside. Pariser (Reference Pariser2011) argues that algorithms can drive polarization by supplying only information that users like in the face of confirmation bias. Echo chambers function when individuals seek out and connect to friends and peers who share their beliefs (see also modeling work by Baldassarri and Bearman Reference Baldassarri and Bearman2007). Wu (Reference Wu2023) finds polarization arises when entire groups mistrust other groups based on social identity. O’Connor and Weatherall (Reference O’Connor and Owen Weatherall2018) find that polarization emerges when actors do not trust data from peers who hold different beliefs. And in our models polarization can follow from confirmation bias because subgroups ignore different sets of disconfirmatory data.
This suggests that identifying sufficient causes of polarization is very different from identifying necessary, or even likely, causes of polarization. It also suggests that, in considering real instances of polarization, researchers should be sensitive to many possible causes. Thus, experimental/empirical research and modeling are both necessary in figuring out just what real causes are at work in producing social polarization.
As a last note before concluding, we would like to discuss limitations of our models. Of course, the models we present are highly simplified compared to real social networks. This means that the results should, of course, be taken with a grain of salt. In particular, we only consider one type of learning problem—the one-armed bandit model. The question remains whether and to what degree these results will be robust. We suspect that models with other problems might yield similar results. The general benefit of slowing group learning, and promoting a period of exploration, has been established across a number of models with different problems and mechanisms. We leave this for future research.
We conclude with one last note about why models are especially useful to this project. Psychological traits like confirmation bias are widespread and deeply ingrained. It is not easy to intervene on them in experimental settings. This means that it is hard to devise an experiment where one group learns with confirmation bias, and one without. Models allow us to gain causal control on the ways confirmation bias can impact group learning, even if we do so for a simplified system.
Acknowledgements
This material is based upon work supported by the National Science Foundation under Grant No. 1922424. Many thanks to the members of our NSF working group for discussion and feedback on drafts of this proposal—Clara Bradley, Matthew Coates, Carolina Flores, David Freeborn, Yu Fu, Ben Genta, Daniel Herrmann, Aydin Mohseni, Ainsley Pullen, Jim Weatherall, and Jingyi Wu. Thanks to the anonymous reviewers for comments. And thanks to members of the DFG Network for comments, especially Audrey Harnagel, Patrick Grim, Christoph Merdes, Matteo Michelini, and Dunja Seselja.
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