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: All the posts I will never write, published by Self-Embedded Agent on August 14, 2022 on LessWrong.
This post has been written for the first Refine blog post day, at the end of the week of readings, dicussions, and exercises about epistomology for doing good conceptual research.
(/with courtesy to Adam Shimi who suggested the title and idea. )
Rationality, Probability, Uncertainty, Reasoning
Failures of The Aumann Agreement Theorem
The famous Aumann Agreement Theorem states that rational reasoners can never agree-to-disagree. In day-to-day life we clearly have many situations where rational reasoners cannot agree-to-disagree. Are people just bad rationalist or are there more fundamental reasons that the Aumann Agreement Theorem can fail.
I review all the ways in which the Aumann Agreement Theorem can fail that I know of - including failures based on indexical information, computational-complexity obstacles, divergent-interpretations-of-evidence, Hansonian non-truth-seeking and more.
Warren Buffet: The Alpha of Wall Street
If we observe a trader that consistenly beat the market that should be evidence against the Efficient Market Hypothesis.
A trader could also just have been lucky. How much should we update against the EMH and how much should we expect the trader to beat the market in the future?
Can we quantify how much information the market absorbed? This is very reminiscent of Wows Bayesian surprise in Bayesian statistics.
The Bid-Ask Spread and Epistemic Uncertainty/ Prediction Markets as Epistemic Fog of War
If you know A will resolve you should buy shares on A, if you know not A will happen you should buy shares on not A. If you think A will not resolve you should sell shares on A. The Bid-ask Spread measures bet resolution uncertainty
Suppose an adversary has an interest in showing you A and t. There is a -> selective reporting
When an earnings call come in.. bid-ask spread increases.
Where Forecasting goes Wrong...
Forecasting is now a big deal in the rationalist community. I argue that a slavish adherence to Bayesian Orthodoxy leads to missing most of the value of prediction markets.
What do we mean when we talk about Probability?
Possibility theory is prior to Probability Theory. Probability theory is possibility theory + Cournot's principle.
Cournot's principle that an epsilon/zero probability possible event will never happen is the fundamental principle of probability theory.
cf Shafer on history of Cournot's principle.
But what happens when we observe a epsilon/zero probability event? We obtain a contradiction requiring belief revision.
Wow!1! I made a productive mistake
An exposition of 'Bayesian Surprise attract Human Attention', focused on the notion of 'Bayesian surprisal' measured in wows. There has been a ton of interest in Predictive Processing and Friston's Free Energy Principle. The discussion is often hampered by equivocation between different quantitites that are the log of something. This post will try to clearly disambiguate between these notions and give both mathematical and intuitive explanations.
I argue that the notion of a 'productive mistake' can be formalized as the choice to engage with a high wow high entropy source.
Compare risk-seeking behaviour in MaxCausalEnt and Schmidthuber's Artificial Curiosity?
Foundations of Reasoning
Atocha Aliseda's Axioms of Abduction
A book review of Aliseda's underappreciated 'Abductive Reasoning'.
From SEP: In the philosophical literature, the term “abduction” is used in two related but different senses. In both senses, the term refers to some form of explanatory reasoning. However, in the historically first sense, it refers to the place of explanatory reasoning in generating hypotheses, while in the sense in which it is used most frequently in the modern literature it refers to the place of explan...