I am using a future light cone whereas your alternatives seem to be formulated in terms of a past light cone.
I was assuming that the "vertex" of your light cone is situated at or shortly after the Big Bang (e.g. maybe during the first few minutes of nucleosynthesis). In that case, the radius of the light cone "now" (at t = 13.8 billion years since Big Bang) is the same as the particle horizon "now" of the observable universe (roughly 45 billion light-years). So the light-cone so far (starting at Big Bang and running up to 13.8 billion years) will be bigger than Earth's past light-cone (starting now and running back to the Big Bang) but not massively bigger.
This means that there might be a few expanded simulations who are outside our past light-cone (so we don't see them now, but could run into them in the future). Still if there are lots of civilisations in your light cone, and only a few have expanded, that still implies a very strong future filter. So my main point remains: given that a super-strong future filter looks very unlikely, most of the probability will be concentrated on models where there are only a few civilisations to start with (so not many to get filtered out; a modest filter does the trick).
The effective time discount function is of rather slow decay because the sum over universes includes time translated versions of the same universe. As a result, the effective discount falls off as 2^{-Kolmogorov complexity of t} which is only slightly faster than 1/t.
Ahh... I was assuming you discounted faster than that, since you said the utilities converged. There is a problem with Kolmogorov discounting of t. Consider what happens at t = 3^^^3 years from now. This has Kolmogorov complexity K(t) much much less than log(3^^3) : in most models of computation K(t) will be a few thousand bits or less. But the width of the light-cone at t is around 3^^^3, so the utility at t is dominated by around 3^^^3 Boltzmann Brains, and the product U(t) 2^-K(t) is also going to be around 3^^^3. You'll get similar large contributions at t = 4^^^^4 and so on; in short I believe your summed discounted utility is diverging (or in any case dominated by the Boltzmann Brains).
One way to fix this may be to discount each location in space and time (s,t) by 2^-K(s,t) and then let u(s,t) represent a utility density (say the average utility per Planck volume). Then sum over u(s,t).2^-K(s, t) for all values of (s,t) in the future light-cone. Provided the utility density is bounded (which seems reasonable), then the whole sum converges.
I was assuming that the "vertex" of your light cone is situated at or shortly after the Big Bang (e.g. maybe during the first few minutes of nucleosynthesis).
No, it can be located absolutely anywhere. However you're right that the light cones with vertex close to Big Bang will probably have large weight to low K-complexity.
...given that a super-strong future filter looks very unlikely, most of the probability will be concentrated on models where there are only a few civilisations to start with.
This looks correct, but it is different from y...
The 'Irrationality Game' posts in discussion came before my time here, but I had a very good time reading the bits written in the comments section. I also had a number of thoughts I would've liked to post and get feedback on, but I knew that being buried in such old threads not much would come of it. So I asked around and feedback from people has suggested that they would be open to a reboot!
I hereby again quote the original rules:
I would suggest placing *related* propositions in the same comment, but wildly different ones might deserve separate comments for keeping threads separate.
Make sure you put "Irrationality Game" as the first two words of a post containing a proposition to be voted upon in the game's format.
Here we go!
EDIT: It was pointed out in the meta-thread below that this could be done with polls rather than karma so as to discourage playing-to-win and getting around the hiding of downvoted comments. If anyone resurrects this game in the future, please do so under that system If you wish to test a poll format in this thread feel free to do so, but continue voting as normal for those that are not in poll format.