I got an improved reality-filter that blocks a certain class of environments that lead conjecture 1 to fail, although it isn’t enough to deal with the provided chicken example and lead to a proof of conjecture 1. (the t subscripts will be suppressed for clarity)
Instead of the reality-filter for E being |E(E(ADT))−E(U)|<ϵ
it is now
∑F∈EP(ADT=amF)⋅|E(E(ADT)|ADT=amF)−E(U|ADT=amF)|<ϵ
This doesn’t just check whether reality is recovered on average, it also checks whether all the “plausible conditionals” line up as well. Some of the conditionals may not be well-formed, as there may be conditioning on low-or-zero probability events, but these are then multiplied by a very small number, so no harm is done.
This has the nice property that for all “plausibly chosen embedders” F that have a probability sufficiently far away from 0, all embedders E and E′ that pass this reality filter have the property that E(E(ADT)|ADT=amF)≃tE(E′(ADT)|ADT=amF)
So all embedders that pass the reality filter will agree on the expected utility of selecting a particular embedder that isn’t very unlikely to be selected.
I got an improved reality-filter that blocks a certain class of environments that lead conjecture 1 to fail, although it isn’t enough to deal with the provided chicken example and lead to a proof of conjecture 1. (the t subscripts will be suppressed for clarity)
Instead of the reality-filter for E being |E(E(ADT))−E(U)|<ϵ
it is now
∑F∈EP(ADT=amF)⋅|E(E(ADT)|ADT=amF)−E(U|ADT=amF)|<ϵ
This doesn’t just check whether reality is recovered on average, it also checks whether all the “plausible conditionals” line up as well. Some of the conditionals may not be well-formed, as there may be conditioning on low-or-zero probability events, but these are then multiplied by a very small number, so no harm is done.
This has the nice property that for all “plausibly chosen embedders” F that have a probability sufficiently far away from 0, all embedders E and E′ that pass this reality filter have the property that E(E(ADT)|ADT=amF)≃tE(E′(ADT)|ADT=amF)
So all embedders that pass the reality filter will agree on the expected utility of selecting a particular embedder that isn’t very unlikely to be selected.