SIA is the Self Indication Assumption, an anthropic theory about how we should reason about the universe given that we exist. I used to love it; the argument that I've found most convincing about SIA was the one I presented in this post. Recently, I've been falling out of love with SIA, and moving more towards a UDT version of anthropics (objective probabilities and total impact of your decision being of a specific type, including in all copies of you and enemies with the same decision process). So it's time I revisit my old post, and find the hole.

The argument rested on the plausible sounding assumption that creating extra copies and killing them is no different from if they hadn't existed in the first place. More precisely, it rested on the assumption that if I was told "You are not one of the agents I am about to talk about. Extra copies were created to be destroyed," it was exactly the same as hearing  "Extra copies were created to be destroyed. And you're not one of them."

But I realised that from the UDT/TDT perspective, there is a great difference between the two situations, if I have the time to update decisions in the course of the sentence. Consider the following three scenarios:

• Scenario 1 (SIA):

Two agents are created, then one is destroyed with 50% probability. Each living agent is entirely selfish, with utility linear in money, and the dead agent gets nothing. Every survivor will be presented with the same bet. Then you should take the SIA 2:1 odds that you are in the world with two agents. This is the scenario I was assuming.

• Scenario 2 (SSA):

Two agents are created, then one is destroyed with 50% probability. Each living agent is entirely selfish, with utility linear in money, and the dead agent is altruistic towards his survivor. This is similar to my initial intuition in this post. Note that every agents have the same utility: "as long as I live, I care about myself, but after I die, I'll care about the other guy", so you can't distinguish them based on their utility. As before, every survivor will be presented with the same bet.

Here, once you have been told the scenario, but before knowing whether anyone has been killed, you should pre-commit to taking 1:1 odds that you are in the world with two agents. And in UDT/TDT precommitting is the same as making the decision.

Suppose there is a diagnostic procedure that allows to catch a relatively rare disease with absolute precision. If left untreated, the disease if fatal, but when diagnosed it's easily treatable (I suppose there are some real-world approximations). The diagnostics involves an uncomfortable procedure and inevitable loss of time. At what a priori probability would you not care to take the test, leaving this outcome to chance? Say, you decide it's 0.0001%.

Enter timeless decision theory. Your decision to take or not take the test may be as well considered a decision for the whole population (let's also assume you are typical and everyone is similar in this decision). By deciding to personally not take the test, you've decided that most people won't take the test, and thus, for example, with 0.00005% of the population having the condition, about 3000 people will die. While personal tradeoff is fixed, this number obviously depends on the size of the population.

It seems like a horrible thing to do, making a decision that results in 3000 deaths. Thus, taking the test seems like a small personal sacrifice for this gift to others. Yet this is circular: everyone would be thinking that, reversing decision solely to help others, not benefiting personally. Nobody benefits.

Obviously, together with 3000 lives saved, there is a factor of 6 billion accepting the test, and that harm is also part of the outcome chosen by the decision. If everyone personally prefers to not take the test, then inflicting the opposite on the whole population is only so much worse.

Or is it?