A “coincidence” is an a priori improbable event in your model that has to happen in order to create a situation containing a “copy” of the observer (which roughly means any agent with a similar utility function and similar decision algorithm).
Imagine two universe clusters in the multiverse: one cluster consists of universe running on fragile physics, another cluster consists of universes running on normal physics. The fragile cluster will contain much less agent-copies than the normal cluster (weighted by probability). Imagine you have to make a decision which produces different utilities depending on whether you are in the fragile cluster or the normal cluster. According to UDT, you have to think as even you are deciding for all copies. In other words, if you make decisions under the assumption you are in the fragile cluster, all copies make decisions under this assumption, if you make decisions under the assumption you are in the normal cluster, all copies make decisions under this assumption. Since the normal cluster is much more “copy-dense”, it pays off much more to make decisions as if you are in the normal cluster (since utility is aggregated over the entire multiverse).
The weighting comes from the Solomonoff prior. For example, see the paper by Legg.
I’ll dig a little deeper but let me first ask these questions:
What do you define as a coincidence?
Where can I find an explanation of the N 2^{-(K + C)} weighting?
A “coincidence” is an a priori improbable event in your model that has to happen in order to create a situation containing a “copy” of the observer (which roughly means any agent with a similar utility function and similar decision algorithm).
Imagine two universe clusters in the multiverse: one cluster consists of universe running on fragile physics, another cluster consists of universes running on normal physics. The fragile cluster will contain much less agent-copies than the normal cluster (weighted by probability). Imagine you have to make a decision which produces different utilities depending on whether you are in the fragile cluster or the normal cluster. According to UDT, you have to think as even you are deciding for all copies. In other words, if you make decisions under the assumption you are in the fragile cluster, all copies make decisions under this assumption, if you make decisions under the assumption you are in the normal cluster, all copies make decisions under this assumption. Since the normal cluster is much more “copy-dense”, it pays off much more to make decisions as if you are in the normal cluster (since utility is aggregated over the entire multiverse).
The weighting comes from the Solomonoff prior. For example, see the paper by Legg.