   3.  Hyperreal Brouwer   post by Scott Garrabrant 503 days ago  Vadim Kosoy and Stuart Armstrong like this  2 comments  
 This post explains how to view Kakutani’s fixed point theorem as a special case of Brouwer’s fixed point theorem with hyperreal numbers. This post is just math intuitions, but I found them useful in thinking about Kakutani’s fixed point theorem and many things in agent foundations. This came out of conversations with Sam Eisenstat.  
  4.  Conditioning on Conditionals   post by Scott Garrabrant 553 days ago  Abram Demski likes this  discuss  
 (From conversations with Sam, Abram, Tsvi, Marcello, and Ashwin Sah) A basic EDT agent starts with a prior, updates on a bunch of observations, and then has an choice between various actions. It conditions on each possible action it could take, and takes the action for which this conditional leads the the highest expected utility. An updateless (but nonpolicy selection) EDT agent has a problem here. It wants to not update on the observations, but it wants to condition on the fact that its takes a specific action given its observations. It is not obvious what this conditional should look like. In this post, I agrue for a particular way to interpret this conditioning on this conditional (of taking a specific action given a specific observation).  
       10.  The Ubiquitous Converse Lawvere Problem   post by Scott Garrabrant 681 days ago  Marcello Herreshoff, Sam Eisenstat, Jessica Taylor and Patrick LaVictoire like this  discuss  
 In this post, I give a stronger version of the open question presented here, and give a motivation for this stronger property. This came out of conversations with Marcello, Sam, and Tsvi.
Definition: A continuous function \(f:X\rightarrow Y\) is called ubiquitous if for every continuous function \(g:X\rightarrow Y\), there exists a point \(x\in X\) such that \(f(x)=g(x)\).
Open Problem: Does there exist a topological space \(X\) with a ubiquitous function \(f:X\rightarrow[0,1]^X\)?
 
    13.  Entangled Equilibria and the Twin Prisoners' Dilemma   post by Scott Garrabrant 739 days ago  Vadim Kosoy and Patrick LaVictoire like this  2 comments  
 In this post, I present a generalization of Nash equilibria to nonCDT agents. I will use this formulation to model mutual cooperation in a twin prisoners’ dilemma, caused by the belief that the other player is similar to you, and not by mutual prediction. (This post came mostly out of a conversation with Sam Eisenstat, as well as contributions from Tsvi BensonTilsen and Jessica Taylor)  
             
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There should be a chat icon
Apparently "You must be
There is a replacement for
Regarding the physical
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
I think that we should expect
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
I think I understand your
by Jessica Taylor on The LearningTheoretic AI Alignment Research Agend...  0 likes 
This seems like a hack. The
by Jessica Taylor on The LearningTheoretic AI Alignment Research Agend...  0 likes 
After thinking some more,
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
Yes, I think that we're
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
My intuition is that it must
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
To first approximation, a
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
Actually, I *am* including
by Vadim Kosoy on The LearningTheoretic AI Alignment Research Agend...  0 likes 
Yeah, when I went back and
by Alex Appel on Optimal and Causal Counterfactual Worlds  0 likes 
> Well, we could give up on
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