Okay, let's look at the "selfish" anthropic preference laid out in your paper, in two different problems.
In both of these problems there are two worlds, "H" and "T," which have equal "no anthropics" probabilities of 0.5. There are two people you could be in T and one person you could be in H. Standard Sleeping Beauty so far.
However, because I like comparing things to utility, I'm going to specify two sets of probabilities. In Problem 1, the probability of being each person is 1/3. In Problem 2, the probability of being the person in H is 1/2, while the probability of being a person in T is 1/4 each.
( These probabilities can be manipulated by giving people evidence of which world they are in - for example, you could spontaneously stop some H or T sessions of the experiment, so the people in the experiment can condition on the experiment not being stopped. The point is that both problems are entirely possible. )
And let's have winning each bet give 1 hedonic utilon (you get to eat a candybar).
ADT makes identical choices in both problems, because it just interacts with the "if there were no anthropics" probabilities. The selfish preference just says to give each world the average utility of all its inhabitants. To calculate the expected-utility-ish thing for betting on Tails, we take the average bet won in the winning side (1 candybar) and multiply it by the probability of the winning side if there were no anthropics (0.5). So our "selfish" ADT agent pays up to 0.5 candybars for a bet on Tails in both problems.
Now, what are the expected hedonic utilities? (in units of candybars, of course)
In problem 1, the probability of being a winner is 2/3, so a utility maximizer pays up to 2/3 of a candybar to bet on Tails.
In problem 2, the probability of being a winner is 1/2, so a utility maximizer pays up to 1/2 of a candybar to bet on Tails.
So in problem 2, the "selfish" ADT agent and the utility maximizer do the same thing. This looks like a good example of selfishness. But what's going on in problem 1? Even though the utilon is entirely candybar-based, the "selfish" anthropic preference seems to undervalue it. What anthropic preference would maximize expected hedonic utility?
Well, if you added up all the utilities in each world, rather than averaging, then an ADT agent would do the same thing as a utility maximizer in problem 1. But now in problem 2, this "total utility" ADT agent would overestimate the value of a candybar, relative to maximum expected utility.
There are in fact no ADT preferences that maximize candybars in both problems. There is no analogue of utility maximization, which makes sense because ADT doesn't deal with the subjective probabilities and expected utility does.
However, because I like comparing things to utility, I'm going to specify two sets of probabilities. In Problem 1, the probability of being each person is 1/3. In Problem 2, the probability of being the person in H is 1/2, while the probability of being a person in T is 1/4 each.
To translate this into ADT terms: in problem 2, the coin is fair, in problem 1, the coin is (1/3, 2/3) on (H, T) (or maybe the coin was fair, but we got extra info that pushed the postiori odds to (1/3, 2/3)).
Then ADT (and SSA) says that selfish agents should bet up to 2/3 of ca...
A few weeks ago at a Seattle LW meetup, we were discussing the Sleeping Beauty problem and the Doomsday argument. We talked about how framing Sleeping Beauty problem as a decision problem basically solves it and then got the idea of using same heuristic on the Doomsday problem. I think you would need to specify more about the Doomsday setup than is usually done to do this.
We didn't spend a lot of time on it, but it got me thinking: Are there papers on trying to gain insight into the Doomsday problem and other anthropic reasoning problems by framing them as decision problems? I'm surprised I haven't seen this approach talked about here before. The idea seems relatively simple, so perhaps there is some major problem that I'm not seeing.