Thread by @ben_golub

Excited to watch this talk by @renee_bowen_lyn : a model of echo chambers in social networks and how they take way less "behavioral error" than you might have thought to get started.

Paper here if you want to follow along

…9-a-62cb3a1a-s-sites.googlegroups.com/site/tamararen…

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Behind the scenes there's a sort of puzzle based on a "naive martingale intuition": if there's abundant data and you understand the information process you're seeing, then a Bayesian should converge to accurate beliefs.

Well, information is abundant so.... what gives?

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To put the focus on kind of intuition and why it may fail, the model is a pure learning model. Renee says: "There's NO game, there's no optimization," etc. Which I like! Pure learning forces are interesting/challenging enough.

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Here are some key motivating empirical facts.

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Here's a summary of what the theory will deliver about how these forces matter.

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And here's the preview of results on polarization. Note that polarization and different groups "different sets of facts" is an important and old observation in political science, and one that has been very motivating to theorists

Big literature on this! Typically quite difficult to model network communication "well": realistically and tractably..... :)

The information model is totally canonical: common priors about a binary state, independent binary signals ("pieces of news") about it. Quality of news is q, probability that a piece of news is accurate.

A key aspect of their model which is a departure from a totally canonical setup is that some people are dogmatic, and only share news from one side. These are the "crazy uncles," political partisans, whatever you want to call them.

More detail: there's a network communication model, and people hear things from their friends. Some friends share everything they know, others share selectively. Of course, the martingale intuition applies! If I have correct beliefs about how my friends communicate, ...

even if some of them only share the right-leaning signal, my beliefs will be correct on average and, under abundant information, will converge to the truth.

These observations are independent of the details of how network communication works. In this paper, info flow is modeled very simply: you can just share the signal you got with your friends, and info doesn't flow farther than that. So it's one-step hard information.

The first set of results is essentially this: if people do not have accurate beliefs about how much information their friends have (the probability gamma they have signals), then learning can be wrong.

Here's something weird/cool -- out of a very simple (essentially single-agent) model of information processing you get this funky curve of how expected posterior beliefs depend on the quality of signals. (In a Bayesian model this curve should be flat at 1!)

Here d_A is the number of A-partisans (people who share only A news) and d_B the number of B-partisans (people who share only B news). I think n is the number of normal agents who share whatever they hear but have to check this.

Yep, that's what it is. The authors ask next - is this about small neighborhoods (i.e. small number of signals?)

Nope - with as many signals as you want, long-run beliefs can be messed up in the long run.

"Long run" = signals keep coming and people keep communicating this way.

Intermission: plug for a related very active social literature focusing on the effects of misspecification on learning outcomes. This paper develops some techniques based on KL divergence etc., an important set of tools for general misspec models

personal.psu.edu/yxi5014/papers…

Intermission over! "Now we get to the fun results on polarization, what we were interested in from the get go"

One basic polarization result: restrict attention to the normal agents (non-dogmatic) and consider the difference in long run beliefs.

Polarization is positive and in fact some normal agents are sure of the correct state of the world while others are sure of the opposite

This is a set of essentially independent single-agent learning problems, and just because of somewhat different learning environments (and some misspecification, meaning perceived gamma is not true gamma) you end up with extremely different long run beliefs.

They study how the situation can be remedied by introducing public information aggregators that publish summaries of MANY signals.

NERD TIME! They use Hoeffding's inequality (I think) for binomial signals to bound how much this helps and whether it can overpower polarization

The model so far has been driven, at a technical level, by wrong beliefs of gamma (probability that your friends have signals). The authors show that misperception of other aspects of your informational environment can also lead to similar forces - e.g. wrong beliefs about

quality of your friends' information.

Ok, that's a wrap! Super interesting paper. A few quick, personal reflections.

In 2012 Matt Jackson and I used the "different sets of facts" that different political sides had about the Iraq war (even 10 years after it was over) to motivate a related study.

Today, different communities having different realities is, if possible, even more salient and troubling. It's exciting to see different theoretical efforts that shed light on this.

This paper focuses on the ways that this arises simply due to different people being exposed to different streams of (social) information, which they don't understand perfectly.

One-step "hard information" sharing still results in big polarization.

... at least in the long run. To learn correctly from your imperfect friends, you need to understand them perfectly, even if everything else is in your favor. That is a powerful point, and establishes a benchmark for other studies of polarization.

END :)