In (a) you’ve drawn a ball but not looked at it yet. SSA says this gives you no info about which urn you have. SIA says you can draw twice as many balls from the Heads urn so you’re twice as likely to have the Heads urn conditional on making a successful draw at all. Under SIA, if you want to estimate how many balls there are in total, you’ll have a prior expectation of 1/2 + 2/2 = 3/2, but a posterior expectation – with no additional info than that you’ve drawn a ball from one of two urns, both of which contain balls – of 1/3 + 2 * 2/3 = 5/3. (SSA refuses to update here.)

Bostrom is arguing that drawing a black ball from an urn shouldn’t do anything to your probability distribution over urns, even though one has only black balls and in the other half the balls are white.

]]>This *also* applies equally well to Solomonoff induction.

]]>This objection applies equally well to Solomonoff induction.

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