The teapot comparison (to me) seems to be a bad. I got carried away and wrote a wall of text. Feel free to ignore it!

First, lets think about normal probabilities in everyday life. Sometimes there are more ways for one state to come about that another state, for example if I shuffle a deck of cards the number of orderings that look random is much larger than the number of ways (1) of the cards being exactly in order.

However, this manner of thinking only applies to certain kinds of thing - those that are in-principle distinguishable. If you have a deck of blank cards, there is only one possible order, BBBBBB.... To take another example, an electronic bank account might display a total balance of $100. How many different ways are their for that $100 to be "arranged" in that bank account? The same number as 100 coins labelled "1" through "100"? No, of course not. Its just an integer stored on a computer, and their is only one way of picking out the integer 100. The surprising examples of this come from quantum physics, where photons act more like the bank account, where their is only 1 way of a particular mode to contain 100 indistinguishable photons. We don't need to understand the standard model for this, even if we didn't have any quantum theory at all we could still observe these Boson statistics in experiments.

So now, we encounter anthropic arguments like Doomsday. These arguments are essentially positing a distribution, where we take the exact same physical universe and its entire physical history from beginning to end, $U$ (which includes every atom, every synapse firing and so on). We then look at all of the "counting minds" in that universe (people count, ants probably don't, aliens, who knows), and we create a whole slew of "subjective universes", $U_1$ , $U_2$, $U_3$, $U_4$, etc, where each of of them is atomically identical to the original $U$ but "I" am born as a different one of those minds (I think these are sometimes called "centred worlds"). We assume that all of these subjective universes were, in the first place, equally likely, and we start finding it a really weird coincidence that in the one we find ourselves in we are a human (instead of an Ant), or that we are early in history. This is, as I understand it, The Argument. You can phrase it without explicitly mentioning the different  $U$s, by saying "if there are trillions of people in the future, the chances of me being born in the present are very low. So, the fact I was born now should update me away from believing there will be trillions of people in the future". - but the  $U$s are still doing all the work in the background.

The conclusion depends on treating all those different subscripted  $U$s as distinguishable, like we would for cards that had symbols printed on them. But, if all the cards in the deck are identical there is only one sequence possible. I believe that all of the $U_1$ , $U_2$, $U_3$, $U_4$'s etc are identical in this manner. By assumption they are atomically identical at all times in history, they differ only by which one of the thinking apes gets assigned the arbitrary label "me" - which isn't physically represented in any particle. You think they look different, and if we accept that we can indeed make these arguments, but if you think they are merely different descriptions of the same exact thing then the Doomsday argument no longer makes sense, and possibly some other anthropic arguments also fall apart. I don't think they do look different, if every "I" in the universe suddenly swapped places - but leaving all memories and personality behind in the physical synapses etc, then, how would I even know it? I would be a cyborg fighting in WWXIV and would have no memories of ever being some puny human typing on a web forum in the 21s Cent. Instead of imaging that I was born as someone else I could imagine that I could wake up as someone else, and in any case I wouldn't know any different.

So, at least to me, it looks like the anthropic arguments are advancing the idea of this orbital teapot (the different scripted  $U$s, although it is, in fairness, a very conceptually plausible teapot). There are, to me, three possible responses:

1 - This set of different worlds doesn't logically exist. You could push this for this response by arguing "I couldn't have been anyone but me, by definition." [Reject the premise entirely - there is no teapot]

2 - This set of different worlds does logically make sense, and after accepting it I see that it is a suspicious coincidence I am so early in history and I should worry about that. [accept the argument - there is a ceramic teapot orbiting Mars]

3 - This set of different worlds does logically make sense, but they should be treated like indistinguishable particles, blank playing cards or bank balances. [accept the core premise, but question its details in a way that rejects the conclusion - there is a teapot, but its chocolate, not ceramic.].

So, my point (after all that, Sorry!) is that I don't see any reason why (2) is more convincing that (3).

[For me personally, I don't like (1) because I think it does badly in cases where I get replicated in the future (eg sleeping beauty problems, or mind uploads or whatever). I reject (2) because the end result of accepting it is that I can infer information through evidence that is not causally linked to the information I gain (eg. I discover that the historical human population was much bigger than previously reported, and as a result I conclude the apocalypse is further in the future than I previously supposed). This leads me to thinking (3) seems right-ish, although I readily admit to being unsure about all this.].

I found this post to be a really interesting discussion of why organisms that sexually reproduce have been successful and how the whole thing emerges. I found the writing style, where it switched rapidly between relatively serious biology and silly jokes very engaging.

Many of the sub claims seem to be well referenced (I particularly liked the swordless ancestor to the swordfish liking mates who had had artificial swords attached).

Other Ant-worriers are out there!

""it turned out this way, so I guess it had to be this way" doesn't resolve my confusion"

Sorry, I mixed the position I hold (that they maybe work like bosons) and the position I was trying to argue for, which was an argument in favor of confusion.

I can't prove (or even strongly motivate) my "the imaginary mind-swap procedure works like a swap of indistinguishable bosons" assumption, but, as far as I know no one arguing for Anthropic arguments can prove (or strongly motivate) the inverse position - which is essential for many of these arguments to work. I agree with you that we don't have a standard model of minds, and without such a model the Doomsday Argument, and the related problem of being cosmically early might not be problems at all.

Interestingly, I don't think the weird boson argument actually does anything for worries about whether we are simulations, or Boltzmann brains - those fears (I think) survive intact.

I suspect there is a large variation between countries in how safely taxi drivers drive relative to others.

In London my impression is that the taxis are driven more safely than non-taxis. In Singapore it appears obvious to casual observation that taxis are much less safely driven than most of the cars.

At least in my view, all the questions like the "Doomsday argument" and "why am I early in cosmological" history are putting far, far too much weight on the anthropic component.

If I don't know how many X's their are, and I learn that one of them is numbered 20 billion then sure, my best guess is that there are 40 billion total. But its a very hazy guess.

If I don't know how many X's will be produced next year, but I know 150 million were produced this year, my best guess is 150 million next year. But is a very hazy guess.

If I know that the population of X's has been exponentially growing with some coefficient then my best guess for the future is to infer that out to future times.

If I think I know a bunch of stuff about the amount of food the Earth can produce, the chances of asteroid impacts, nuclear wars, dangerous AIs or the end of the Mayan calendar then I can presumably update on those to make better predictions of the number of people in the future.

My take is that the Doomsday argument would be the best guess you could make if you knew literally nothing else about human beings apart from the number that came before you. If you happen to know anything else at all about the world (eg. that humans reproduce, or that the population is growing) then you are perfectly at liberty to make use of that richer information and put forward a better guess. Someone who traces out the exponential of human population growth out to the heat death of the universe is being a bit silly (lets call this the Exponentiator Argument), but on pure reasoning grounds they are miles ahead of the Doomsday argument, because both of them applied a natural, but naïve, interpolation to a dataset, but the exponentiator interpolated from a much richer and more detailed dataset.

Similarly to answer "why are you early" you should use all the data at your disposal. Given who your parents are, what your job is, your lack of cybernetic or genetic enhancements, how could you not be early? Sure, you might be a simulation of someone who only thinks they are in the 21st centaury, but you already know from what you can see and remember that you aren't a cyborg in the year 10,000, so you can't include that possibility in your imaginary dataset that you are using to reason about how early you are.

As a child, I used to worry a lot about what a weird coincidence it was that I was born a human being, and not an ant, given that ants are so much more numerous. But now, when I try and imagine a world where "I" was instead born as the ant, and the ant born as me, I can't point to in what physical sense that world is different from our own. I can't even coherently point to in what metaphysical sense it is different. Before we can talk about probabilities as an average over possibilities we need to know if the different possibilities are even different, or just different labelling on the same outcome. To me, there is a pleasing comparison to be made with how bosons work. If you think about a situation where two identical bosons have their positions swapped, it "counts as" the same situation as before the swap, and you DON'T count it again when doing statistics. Similarly, I think if two identical minds are swapped you shouldn't treat it as a new situation to average over, its indistinguishable. This is why the cyborgs are irrelevant, you don't have an identical set of memories.

I remember reading something about the Great Leap Forward in China (it may have been the Cultural Revolution, but I think it was the Great Leap Forward) where some communist party official recognised that the policy had killed a lot of people and ruined the lives of nearly an entire generation, but they argued it was still a net good because it would enrich future generations of people in China.

For individuals you weigh up the risk/rewards of differing your resource for the future. But, as a society asking individuals to give up a lot of potential utility for unborn future generations is a harder sell. It requires coercion.

I think we might be talking past each other. I will try and clarify what I meant.

Firstly, I fully agree with you that standard game theory should give you access to randomization mechanisms. I was just saying that I think that hypotheticals where you are judged on the process you use to decide, and not on your final decision are a bad way of working out which processes are good, because the hypothetical can just declare any process to be the one it rewards by fiat.

Related to the randomization mechanisms, in the kinds of problems people worry about with predictors guessing your actions in advance its very important to distinguish between [1] (pseudo-)randomization processes that the predictor can predict, and [2] ones that it cannot. 

[1] Randomisation that can be predicted by the predictor is (I think) a completely uncontroversial resource to give agents in these problems. In this case we don't need to make predictions like "the agent will randomise", because we can instead make the stronger prediction "the agent will randomize, and the seed of their RNG is this, so they will take one box" which is just a longer way of saying "they will one box". We don't need the predictor to show its working by mentioning the RNG intermediate step.

[2] Randomisation that is beyond the predictor's power is (I think) not the kind of thing that can sensibly be included in these thought experiments. We cannot simultaneously assume that the predictor is pretty good at predicting our actions and useless at predicting a random number generator we might use to choose our actions. The premises: "Alice has a perfect quantum random number generator that is completely beyond the power of Omega to predict. Alice uses this machine to make decisions. Omega can predict Alice's decisions with 99% accuracy" are incoherent.

So I don't see how randomization helps. The first kind, [1] doesn't change anything, and the second kind [2], seems like it cannot be consistently combined with the premise of the question. Perfect predictors and perfect random number generators cannot exist in the same universe.

Their might be interesting nearby problems where you imagine the predictor is 100% effective at determining the agents algorithm, but because the agent has access to a perfect random number generator that it cannot predict their actions. Maybe this is what you meant? In this kind of situation I am still much happier with rules like "It will fill the box with gold if it knows their is a <50% chance of you picking it", [the closest we can get to "outcomes not processes" in probabilistic land], (or perhaps the alternative "the probability that it fills the box with gold is one-minus the probability with which it predicts the agent will pick the box".). But rules like "It will fill the box with gold if the agents process uses either randomisation or causal decision theory" seem unhelpful to me.

I see where you are coming from. But, I think the reason we are interested in CDT (for any DT) in the first place is because we want to know which one works best. However, if we allow the outcomes to be judged not just on the decision we make, but also on the process used to reach that decision then I don't think we can learn anything useful.

Or, to put it from a different angle, IF the process P is used to reach decision X, but my "score" depends not just on X but also P then that can be mapped to a different problem where my decision is "P and X", and I use some other process (P') to decide which P to use.

For example, if a student on a maths paper is told they will be marked not just on the answer they give, but the working out they write on the paper - with points deducted for crossings outs or mistakes - we could easily imagine the student using other sheets of paper (or the inside of their head) to first work out the working they are going to show and the answer that goes with it. Here the decision problem "output" is the entire exame paper, not just the answer.

I like this framing.

An alternative framing, which I think is also part of the answer is that some art is supposed to hit a very large audience and give each a small amount of utility, and other art is supposed to hit a smaller, more specialized, audience very hard. This framing explains things like traditional daytime TV, stuff that no one really loves but a large number of bored people find kind of unobjectionable. And how that is different from the more specialist TV you might actually look forward to an episode off but might hit a smaller audience.

(Obviously some things can hit a big audience and be good, and others can be bad on both counts. But the interesting quadrants two compare are the other two).