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KatjaGrace comments on An empirical test of anthropic principle / great filter reasoning - Less Wrong
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What settlers have really seen also depends on whether your prior is correct in our world of real islands (implicitly 1/4 to each possibility). But you can easily model what people would see in a world with that distribution of islands:
e.g. Let an easy to get to island have 100 visitors and a hard to get to one 10 visitors. Let visitors to disaster prone islands die before the next people arrive. Let there be ten of each type of island
Total observers:
From each island type 1: 1 arrives to an uninhabited island, 99 to an inhabited one
Island type 2: 1 arrives to an uninhabited island, 9 to an inhabited one
Island type 3: 100 arrive to uninhabited island
Island type 4: 10 arrive to an uninhabited island
Of the 1120 observers arriving at uninhabited islands (ten of each of the above islands), 1000 will be on type 3 islands, consistent with SIA. In this case the alternative anthropic principle preferred by others, the self sampling assumption (SSA), can come to the same conclusion because the possible islands you are considering are actual. If real islanders have seen something other than this, it is because there were different frequencies of islands.
The prior for reaching a hard-to-reach island should be lower than the prior for an easy-to-reach island. The prior for a hard-to-reach island existing may be the same as the prior for an easy-to-reach island existing. So you have to state your terms clearly before you can state your priors.
(Maybe the prior for an existing island being hard-to-reach is higher, since "easy-to-reach" should mean "easier than considerably more than half of all islands.").
That's not how I understood it. These are just types of islands that are supposed to exist in some hypothetical world. Arbitrarily, we say there are 10 islands of each type. That's all that 1/4 means here.
Small correction: The ten islands of type 1 have a total of 10 immigrants encountering an uninhabited island, and 90 an inhabited one. This doesn't substantially change your conclusion (121 observe uninhabited islands, 100 of which are on type 3).
the OP's last sentence suggests a way to test the hypothesis that islands prone to disaster are just as likely to be encountered as islands not prone to disaster. If the hypothesis is true, then island colonization attempts should have failed 83% of the time.
Of course, such a finding would imply the attempts succeeded 17% of the time. A similar conclusion can be made about galaxy colonization - a small percentage of these attempts will be successful - i.e., the galaxy will be colonized.
fixed I think