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).
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.
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.