Truth-seekers and ideologues

People learn socially: they get information from their friends. Research on social learning takes as given that people want to learn the truth.¹ This assumption motivates worries about online misinformation: if your friends see something wrong and share it with you, then you might believe it and be wrong too.

But people share for more reasons than learning. Sometimes we share to feel connected: to let each other know we’re not alone in what we see. We enjoy having like-minded friends who have relatable experiences and validate ours. But if we only talk to like-minded friends then it’s hard to learn the truth because no one challenges our subjective experiences of objective reality.

Thus, when forming social networks, we face a trade-off. We want friends with similar experiences because they help us feel connected. But we also want friends with different experiences because they help us learn the truth. How we resolve this trade-off depends on how much we care about the truth. If we care a lot then we should choose friends with unbiased experiences; if we don’t care at all then we should choose friends who share our biases.

Here’s a basic model to illustrate. Imagine reality is chosen by a coin toss: Heads or Tails, each with probability 0.5. There are two types of people:

“Truth-seekers” try to see the world for what it is. But they do so noisily: their experience matches reality with probability $a>0.5$.
“Ideologues” always see the world the same way: they always experience Heads.

These types represent two extremes: truth-seekers have unbiased but noisy experiences, whereas ideologues have biased but precise experiences. I choose a friend to help me win one of two games:

In the “learning” game, I win if my friend’s experience matches reality.
In the “connecting” game, I win if my friend shares my experience.

I want to maximize my chance of winning the game we play. But I don’t know which we’ll play until I’ve chosen my friend. Which type should I choose?

If I’m a truth-seeker then I’m better off choosing a truth-seeking friend.² They’re better in the learning game because they’re more likely than ideologues to experience reality. They’re also better in the connecting game because we both tend to experience reality. Our pursuit for truth makes our experiences correlated. In contrast, ideologues’ indifference to the truth makes their experience uncorrelated with mine.

Things are different if I’m an ideologue. Then my best choice depends on how likely I am to play each game. Let $p$ be the probability I play the learning game. I’m better off choosing a truth-seeking friend if and only if $p$ exceeds³ $$\overline{p}\equiv \frac{1}{2a}.$$ Intuitively, I face a trade-off: Truth-seekers are better in the learning game for the same reason as above. But now ideologues are better in the connecting game because they always share my ideological experience. This trade-off tilts in favor of truth-seekers as their accuracy $a$ rises, lowering the threshold probability $\overline{p}$.

Now suppose I can choose my own type. Should I be a truth-seeker or an ideologue? Again, my choice depends on the probability $p$ that I play the learning game. It turns out I’m better off seeking truth if and only if $p$ exceeds another threshold $\underline{p}$ that depends on $a$.⁴ This threshold has two interesting properties:

It’s positive, so if $p$ is small enough then I’m better off being an ideologue.
It’s smaller than $\overline{p}$, so if I’m better off being an ideologue then I’m also better off choosing an ideologue as my friend.

Intuitively, if the truth doesn’t matter then there’s no point seeking it. I might as well be an ideologue and choose ideological friends who always share my experience.

One can extend this model to choosing many friends with a range of accuracies and biases. Some people might be more truth-seeking than others. Some people might have correlated experiences because they get information from the same like-minded sources. These correlations determine the “experience portfolio” my friends can provide. But the goal of this portfolio—whether I want it to provide truth or connection—still depends on how much I care about learning the truth.

Indeed this assumption motivates the extensive literature on social learning “failures.” These failures arise from, e.g., unequal influence (Acemoglu et al., 2011; Golub and Jackson, 2010), network structure (Chandrasekhar et al., 2020; Dasaratha and He, 2021), herding (Banerjee, 1992; Bikhchandani et al., 1992; Smith and Sørensen, 2000), conformity (Mohseni and Williams, 2021), misinformation (Mostagir and Siderius, 2022), and misinterpretation (Frick et al., 2020). ↩︎
Choosing another truth-seeker makes me win the learning game with probability $a$ and the connecting game with probability $a^2+(1-a)^2$. Both of these probabilities exceed 0.5, the probability of winning either game if I choose an ideologue. ↩︎
If I’m an ideologue, then my ex ante chance of winning is $pa+0.5(1-p)$ if I choose a truth-seeking friend and $0.5p+(1-p)$ if I choose another ideologue. ↩︎
The exact probability is $$\underline{p}\equiv \frac{4a(1-a)}{2a-1+4a(1-a)}.$$ It comes from comparing the truth-seeker’s indirect objective $$pa+(1-p)(a^2+(1-a)^2)$$ and the ideologue’s indirect objective $$\begin{cases}pa+0.5(1-p)&\text{if}\ p\ge\overline{p}\\0.5p+(1-p)&\text{otherwise}.\end{cases}$$ These functions coincide when $p\in\{\underline{p},1\}$. ↩︎