Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: My PhD thesis: Algorithmic Bayesian Epistemology, published by Eric Neyman on March 17, 2024 on LessWrong.

In January, I defended my PhD thesis, which I called Algorithmic Bayesian Epistemology. From the preface:

For me as for most students, college was a time of exploration. I took many classes, read many academic and non-academic works, and tried my hand at a few research projects. Early in graduate school, I noticed a strong commonality among the questions that I had found particularly fascinating: most of them involved reasoning about knowledge, information, or uncertainty under constraints. I decided that this cluster of problems would be my primary academic focus.

I settled on calling the cluster algorithmic Bayesian epistemology: all of the questions I was thinking about involved applying the "algorithmic lens" of theoretical computer science to problems of Bayesian epistemology.

Although my interest in mathematical reasoning about uncertainty dates back to before I had heard of the rationalist community, the community has no doubt influenced and strengthened this interest.

The most striking example of this influence is Scott Aaronson's blog post Common Knowledge and Aumann's Agreement Theorem, which I ran into during my freshman year of college.[1] The post made things click together for me in a way that made me more intellectually honest and humble, and generally a better person. I also found the post incredibly intellectually interesting -- and indeed, Chapter 8 of my thesis is a follow-up to Scott Aaronson's academic paper on Aumann's agreement theorem.

My interest in forecast elicitation and aggregation, while pre-existing, was no doubt influenced by the EA/rationalist-adjacent forecasting community.

And Chapter 9 of the thesis (work I did at the Alignment Research Center) is no doubt causally downstream of the rationalist community.

Which is all to say: thank you! Y'all have had a substantial positive impact on my intellectual journey.

Chapter descriptions

The thesis contains two background chapters followed by seven technical chapters (Chapters 3-9).

In Chapter 1 (Introduction), I try to convey what exactly I mean by "algorithmic Bayesian epistemology" and why I'm excited about it.

In Chapter 2 (Preliminaries), I give some technical background that's necessary for understanding the subsequent technical chapters. It's intended to be accessible to readers with a general college-level math background. While the nominal purpose of Chapter 2 is to introduce the mathematical tools used in later chapters, the topics covered there are interesting in their own right.

Different readers will of course have different opinions about which technical chapters are the most interesting. Naturally, I have my own opinions: I think the most interesting chapters are Chapters 5, 7, and 9, so if you are looking for direction, you may want to tiebreak toward reading those. Here are some brief summaries:

Chapter 3: Incentivizing precise forecasts. You might be familiar with proper scoring rules, which are mechanisms for paying experts for forecasts in a way that incentivizes the experts to report their true beliefs.

But there are many proper scoring rules (most famously, the quadratic score and the log score), so which one should you use? There are many perspectives on this question, but the one I take in this chapter is: which proper scoring rule most incentivizes experts to do the most research before reporting their forecast? (See also this blog post I wrote explaining the research.)

Chapter 4: Arbitrage-free contract functions. Now, what if you're trying to elicit forecasts from multiple experts? If you're worried about the experts colluding, your problem is now harder. It turns out that if you use the same proper scoring rule to pay every expert, then the experts can collu...