sandfort

Correction:

It seems that in general, the less certain any counterfactual oracle is about its prediction, the more self-confirming it is. This is because the possible counterfactual worlds in which we have or acquire self-confirming beliefs regarding the prediction will have a high expected score

This is actually only true in certain cases, since in general many other counterfactual worlds could also have high expected scores. Specifically, it is true to the extent that the oracle is uncertain mostly about aspects of the world that would be affected by the prediction, and to the extent that self-confirming predictions lead to higher scores than any alternative.

Submission (LB). The post's team-choosing example suggests a method for turning any low-bandwidth oracle $O$ into a counterfactual oracle $O^{\prime }$: have $O^{\prime }$ output $o$ from the same set of possible outputs $L$; in case of erasure calculate $R\left(l\right)$ for a randomly chosen $l\in L$ and set $R^{\prime }\left(o\right)=R\left(l\right)$ if $o=l$ and to$-\infty$ otherwise. Although the counterfactual low-bandwidth oracle is not any safer${}^1$, it has the advantage of almost never requiring us to evaluate its score. Thus, by running multiple oracles in sequence (stopping the process after the first erasure event) we can (with ... (read more)

Submission (CF). Use a counterfactual oracle to send a message to ourselves with a time delay. We choose an episode length $T$ and set of possible messages $M$. The oracle outputs a time $t_o<T$ and message $m_o\in M$. We are automatically sent $m_o$ at time $t_o$ unless erasure occurs, in which case at the end of the episode we input a time $t^{\ast }$and message $m^{\ast }$ which we wish we had received at $t^{\ast }$. The oracle's reward is then $-(t^{\ast }-t_o{)}^2$ if $m_o=m^{\ast }$ and $-\infty$ otherwise. We do not find out that erasure has occurred until the end of the episode, ensuring that events before $t_o$ are ... (read more)