UDASSA

UDASSA (sometimes also written UD+ASSA to make the two components clear) is a theory of anthropics.

Etymology

The name "UDASSA" comes from "universal distribution + absolute self-selection assumption".

Description

i think it's useful to compare UDASSA to solomonoff induction first. what does solomonoff induction tell us? it takes in some bit string, and then gives you a probability distribution over the next bit, i.e. it takes in some data and then predicts what you're likely to see.

udassa makes use of the universal distribution (the same one that solomonoff induction uses). so how is it different? well, in udassa, instead of interpreting the bit strings as just "abstract objects" or "camera inputs that a robot sees", we instead interpret them as "observer moments". how is this even possible? well, if you take a snapshot of your brain at the current moment, and then scan it/encode it in some standard format, you get some long sequence of bits. so we can take an observer moment and convert it to some bit string. the probability that this bit string appears in the universal distribution is the "measure" of that observer moment. so that's the UD part.

what's the ASSA part? i think the ASSA part just says that this measure under the UD is how likely we are to experience that OM.

actually a better order of introduction might be going from ASSA, and then UD. that's how paul does it here: the idea is, first we leave the measure unspecified. and we say that how likely we are to experience an OM is the measure of that OM under some measure. finally at the end, we decide that UD would be a fine measure to use here.

here's an alternative that paul mentions, just to show something different so that you know udassa is doing something different: we could have used the measure to find the probability of each world. then in each world, we could find all the OMs (within each world, we weigh each OM equally).

so what does UDASSA get us? make decisions; explain anthropics; ...

so how can we use UDASSA to make decisions? well, i'm slightly confused here myself. i can think of two possibilities:

• define some relevant reference class, like "human observer moments".
• you don't define a reference class. instead, you just define some utility function. and it's the utility function that defines what matters and what doesn't. for example, there will be an observer moment that corresponds to the integer 3. and it's a really simple OM, so it will have high measure! but we don't care about it, so the utility function will just ignore it.

Comparison to UDT

Does UDASSA give any different decisions from UDT? i think one example might be https://riceissa.github.io/everything-list-1998-2009/14037.html where UDT seems to give the intuitively-correct answer, but UDASSA doesn't.

what does udassa say about probability of heads in sleeping beauty? well, if each of the three OMs takes an equal complexity to specify, then i think we just get the thirder position, because a randomly selected OM has probability 1/3 of being in a heads world.

but what if the measures of the three OMs are not equal? e.g. maybe it takes 1 bit to specify heads or tails world, then in the tails world, a second bit to specify first or second OM. so now out of all four two-bit strings, two of them are heads and two of them are tails. (by the same reasoning, out of all infinite bit strings, half of them start with "1", a quarter start with "00", and a quarter start with "01".) so p(heads)=1/2.

as you can see, it seems like with udassa, what we decide is the measure of the OM (which depends on what is the shortest program to output that OM) sways the outcome. it's not clear to me what's the right answer (i.e. what udassa ends up saying in the end, after you set up the sleeping beauty problem in some "neutral" way).

or maybe i've gotten all of this wrong. what udassa actually gives you is the measure of the OM. but in sleeping beauty, we've stipulated that the beauty can't tell what world she's in. so the OMs in all three spots are the same. they all get counted toward the same OM in the output of udassa. and udassa just tells you the measure of an OM, i.e. how likely you are to experience that OM. but it doesn't tell you the probability of heads. but maybe we could modify the sleeping beauty problem slightly: we change the OM so that in some subconscious part of the beauty's brain is stored the "index" of which copy she is, but she doesn't have conscious access to this index. so the OMs are now distinguished, but beauty can't make use of the information.

what does UDT say? well, you can read the stuart armstrong paper. basically, udt refuses to give you probabilities! because what matters is the decisions. and you can't make a decision without some sort of bet, and some sort of utility function (e.g. selfish, altruistic, ...).