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drnickbone comments on SIA won't doom you - Less Wrong
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That's why you don't see any worlds where the filter happens after where we are - these worlds are not in our reference class (to use outdated SSA terminology). We can't use SIA on them.
There still is a way of combining SIA with the filter argument; it goes something like:
1) Use SIA on the present time to show there are lots of civilizations at our level around now.
2) Use a distribution on possible universes to argue that 1) implies there were lots of civilizations at our level around before.
3) From 2), argue that the filter is in our future.
The problem is 2). There are universes in which there is no great filter, but whose probability is boosted by SIA - say, slow-start simultaneous worlds, where it takes several billion years for life to get going, but life is never filtered at all, and now the galaxy is filled with civilizations at approximately our level. This world is very unlikely - but SIA boosts its probability!
So until we have some sensible distributions over possible worlds with filters, we can't assert SIA+great filter => DOOM. I feel it's intuitively likely that SIA does increase doom somewhat, but that's not a proof.
This dispute about 2) seems a little desperate to me as a way out of doom.
Surely there is high prior probability for universes whose density of civilizations does NOT rise dramatically at a crucial time close to our own (such that at around our time t/o ~ 13 billion years the density of civilizations at our level is high, whereas at times very slightly before t/o in cosmological terms, the density is very low)? If you assume that with high probability, lots of civilizations now implies lots of civilizations a million years ago (but still none of them expanded) then we do get a Doomish conclusion.
Incidentally, another approach is to argue that SIA favours "Big Worlds" (ones containing a spatially-infinite universe, or infinitely many finite universes). But then, among the Big Worlds, SIA doesn't further favour a high density of civilizations at our level (since all such Big Worlds have infinitely many civilizations anyway, SIA doesn't "care" whether they appear on the order of once per star system, or once per Galaxy, or less than once per Hubble volume). This approach removes Katja's particular argument to a "late" filter, but unfortunately it creates another argument instead, since when we now apply SSA we get the usual Doomsday shift - see http://lesswrong.com/lw/9ma/selfindication_assumption_still_doomed/
Broadly I've now looked at a number of versions of anthropic reasoning: SSA with and without SIA, variations of reference class a la Bostrom, and attempts to avoid anthropic reasoning completely (such as "full non-indexical conditioning"). Whichever way I cut it, I'm getting a "Doom" conclusion. I'm thinking of putting together a main post on this at some point.