Thread by @KevinZollman

This week in my Network Epistemology class, we looked at models of search in uncertain environments. (In particular, looking at bandit problems.) The basic question: when people are trying to find the best from among a few uncertain options, how should they communicate?

Bandit problems are named in an analogy with slot machines: you face two (or more) different slot machines, each which pays off at different rates. You will choose one, observe its results, and then repeat. What's the best way to choose?

There is a large literature in stats and ML about these types of problems. They are used as analogies for medical research, choice of technologies, scientific methods, policy interventions, etc. They provide a good analogy for learning when the environment is stochastic.

For this class, we looked at a collection of models where people are playing "myopically" -- they are only thinking about the next play. We then ask, how should they communicate their results to one another?

The earliest paper I know about bandits in a social network is due to Bala and Goyal. They prove that in some contexts a less connected group is better than a more connected group because misleading information can be better contained.

academic.oup.com/restud/article…

There are some ways that this result is limited, because they focus on what can be proven in the infinite limit (as the population grows to infinity and as time also goes to infinity). So, more systematic analyses often uses simulation.

We looked at an old paper of mine, where I investigated a similar situation. I show that in finite groups and finite time, connectivity is bad. Groups who don't communicate very much outperform groups who are connected more.

link.springer.com/article/10.100…

I attribute this to the presence of "transient diversity." Groups that don't communicate much diversify their behavior more than groups that communicate more. As a result, misleading information is contained and there is more time for "the truth to win out."

Most of these results only hold for setting where the underlying learning problem is "hard" in a certain sense. A paper by Rosenstock, Bruner, and @cailinmeister considers whether the results hold true when the learning problem gets easier.

journals.uchicago.edu/doi/abs/10.108…

While they never find a setting where more connected groups do better they find that the benefit from being less connected shrinks as the learning problem gets easier.

Transient diversity (of this sort) is most beneficial when learning problems are hard.

The type of diversity discussed both my paper and Rosenstock, Bruner, and @cailinmeister is "behavioral" or "cognitive" -- its about choosing different actions to pursue. That might be connected to demographic diversity (like race, sex, etc.) But it might not be.

So, we also read very nice new draft paper by Dan Steele and @sinafazelpour. They apply some of the research on how in-group and out-group people interact to settings like those analyzed by me and Rosenstock, Bruner, and @cailinmeister.

In particular, Steele and @sinafazelpour consider phenomena where in-group members discount the contribution of out-group members. They find that this also helps performance because this bias translates the demographic diversity into behavioral or cognitive diversity.

They are clear they are not NOT saying that racism is good or anything like that. (For obvious reasons.) But, what they do show is that demographically diverse teams can endogenously generate behavioral or cognitive diversity -- *even if the people are otherwise the same*.

This later insight is really interesting because it represents a novel way of connecting cognitive diversity to demographic diversity. It might be that demographic diversity can generate new types of cognitive diversity. Keep your eyes pealed for this paper when it comes out!

The class discussion centered around a couple of different threads. Like every week we focused on what the model includes and what it leaves out. This week we asked to what extent its appropriate to think that learning problems have "fixed" and exogeneous payoff distributions.

In science, for instance, how good a choice is depends on what other have done before you and what they do after you. Its best to adopt a method before others do, but also only good if others eventually follow your lead. These models don't have that.

We also talked about the relationship between "group rationality" and "individual rationality" and what to make of that difference. That is, how shall we interpret a model that shows that a group can be made smarter by making individuals dumber?

On this latter topic, we didn't come to a conclusion, but thought it a very interesting topic for further investigation.