UDASSA
UDASSA (sometimes also written UD+ASSA to make the two components clear) is a theory of anthropics(? is it just anthropics, or is it also decision theory or a bunch of other things?).
Etymology
The name "UDASSA" comes from "universal distribution + absolute self-selection assumption".
History
UDASSA was first proposed by wei dai on everything-list.
If I am not mistaken, Paul Christiano reinvented UDASSA in 2011. Why do I think this? See this post from 2011-04-02. In comments, Wei says "Seems like we have a lot of similar ideas/interests. :) This is was my main approach for solving anthropic reasoning, until I gave it up in favor of UDT." and then links to the UDASSA page. Then on 2011-04-11, paul posts a second post, which mentions UDASSA: "In this article I will discuss UDASSA, a framework for anthropic reasoning due to Wei Dai."
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). As paul says in a different post, "It is typical to use some complexity prior to select a universe, and then to appeal to some different notion to handle the remaining anthropic reasoning (to ask: how many beings have my experiences within this universe?). What I am suggesting is to instead apply a complexity prior to our experiences directly."
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.
the shortest program that produces my current OM and the shortest program that produces the OM of someone else on earth right now probably have the same "physical law" part, so the difference is in locating the two of us. now, the weird thing is, one of us will be closer to some "natural" location from which to specify coordinates (e.g. maybe "where the big bang started", if that's even a well-defined location? idk any physics). the upshot is that probably the location part will have a different length (i'm imagining that you use something like a binary search, where each extra bit gets you halfway to where you are; is there a more efficient way to specify coordinates?). and each extra bit means you incur a penalty of 1/2. so even though my OM and their OM "feel just as real" (whatever that means..), one of us will have possibly something like 2k times as much measure, where k is the difference in number of bits needed to locate the two OMs. this sounds pretty crazy, especially considering the fact that we shouldn't expect either OM to occur in a larger number of possible worlds. i.e. the only difference between the two OMs is that one happens to be easier to find in the physical world. this is sort of like the "big people matter more" thing that people have brought up, but i find it much more unintuitive. this might be mostly the same problem as "people who are next to black holes matter more"/"people with a giant arrow pointing at them matter more", but the difference seems to be that any difference in distance changes the measure, not just being super close to a big important thing.
shortest way of finding each OM separately vs shortest way of finding all the OMs of a single human's life. the latter will presumably get some efficiency gains by e.g. not needing to keep specifying the time period in full each moment. like, you specify the initial OM in the usual way (like how udassa would specify each OM), but then you can just "follow the consciousness" starting from that OM. so i think it would still take linear complexity to track, but it wouldn't be as complex as finding each om independently?
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, ...).
