Is God’s coin toss with equal numbers a counterexample to mrcSSA?
I feel confused as to whether minimal-reference-class SSA (mrcSSA) actually fails God’s coin toss with equal numbers (where “failing” by my lights means “not updating from 50/50″):
Let H = “heads world”, W_{me} = “I am in a white room, [created by God in the manner described in the problem setup]”, R_{me} = “I have a red jacket.”
We want to know P(H | W_{me}, R_{me}).
First, P(R_{me} | W_{me}, H) and P(R_{me} | W_{me}, ~H) seem uncontroversial: Once I’ve already conditioned on my own existence in this problem, and on who “I” am, but before I’ve observed my jacket color, surely I should use a principle of indifference: 1 out of 10 observers of existing-in-the-white-room in the heads world have red jackets, while all of them have red jackets in the tails world, so my credences are P(R_{me} | W_{me}, H) = 0.1 and P(R_{me} | W_{me}, ~H) = 1. Indeed we don’t even need a first-person perspective at this step — it’s the same as computing P(R_{Bob} | W_{Bob}, H) for some Bob we’re considering from the outside.
(This is notthe same as non-mrcSSA with reference class “observers in a white room,” because we’re conditioning on knowing “I” am an observer in a white room when computing a likelihood (as opposed to computing the posterior of some world given that I am an observer in a white room). Non-mrcSSA picks out a particular reference class when deciding how likely “I” am to observe anything in the first place, unconditional on “I,” leading to the Doomsday Argument etc.)
The step where things have the potential for anthropic weirdness is in computing P(W_{me} | H) and P(W_{me} | ~H). In the Presumptuous Philosopher andthe Doomsday Argument, at least, probabilities like this would indeed be sensitive to our anthropics.
But in this problem, I don’t see how mrcSSA would differ from non-mrcSSA with the reference class R_{non-minimal} = “observers in a white room” used in Joe’s analysis (and by extension, from SIA):
In general, SSA says P(Wme|H)=# observers in a white room in ref class R given H# observers in ref class R given H.
Here, the supposedly “non-minimal” reference class R_{non-minimal} coincides with the minimal reference class! I.e., it’s the observer-moments in your epistemic situation (of being in a white room), before you know your jacket color.
The above likelihoods plus the fair-coin prior are all we need to get P(H | R_{me}, W_{me}), but at no point did the three anthropic views disagree.
In order words: It seems that the controversial setup in anthropics is in answering P(I [blah] | world), i.e., what we do when we introduce the indexical information about “I.” But once we’ve picked out a particular “I,” the different views should agree.
(I still feel suspicious of mrcSSA’s metaphysics for independent reasons, but am considerably less confident in that than my verdict on God’s coin toss with equal numbers.)
It seems that what I was missing here was: mrcSSA disputes my premise that the evidence in fact is “*I* am in a white room, [created by God in the manner described in the problem setup], and have a red jacket”!
Rather, mrcSSA takes the evidence to be: “Someone is in a white room, [created by God in the manner described in the problem setup], and has a red jacket.” Which is of course certain to be the case given either heads or tails.
Is God’s coin toss with equal numbers a counterexample to mrcSSA?
I feel confused as to whether minimal-reference-class SSA (mrcSSA) actually fails God’s coin toss with equal numbers (where “failing” by my lights means “not updating from 50/50″):
Let H = “heads world”, W_{me} = “I am in a white room, [created by God in the manner described in the problem setup]”, R_{me} = “I have a red jacket.”
We want to know P(H | W_{me}, R_{me}).
First, P(R_{me} | W_{me}, H) and P(R_{me} | W_{me}, ~H) seem uncontroversial: Once I’ve already conditioned on my own existence in this problem, and on who “I” am, but before I’ve observed my jacket color, surely I should use a principle of indifference: 1 out of 10 observers of existing-in-the-white-room in the heads world have red jackets, while all of them have red jackets in the tails world, so my credences are P(R_{me} | W_{me}, H) = 0.1 and P(R_{me} | W_{me}, ~H) = 1. Indeed we don’t even need a first-person perspective at this step — it’s the same as computing P(R_{Bob} | W_{Bob}, H) for some Bob we’re considering from the outside.
(This is not the same as non-mrcSSA with reference class “observers in a white room,” because we’re conditioning on knowing “I” am an observer in a white room when computing a likelihood (as opposed to computing the posterior of some world given that I am an observer in a white room). Non-mrcSSA picks out a particular reference class when deciding how likely “I” am to observe anything in the first place, unconditional on “I,” leading to the Doomsday Argument etc.)
The step where things have the potential for anthropic weirdness is in computing P(W_{me} | H) and P(W_{me} | ~H). In the Presumptuous Philosopher and the Doomsday Argument, at least, probabilities like this would indeed be sensitive to our anthropics.
But in this problem, I don’t see how mrcSSA would differ from non-mrcSSA with the reference class R_{non-minimal} = “observers in a white room” used in Joe’s analysis (and by extension, from SIA):
In general, SSA says P(Wme|H)=# observers in a white room in ref class R given H# observers in ref class R given H.
Here, the supposedly “non-minimal” reference class R_{non-minimal} coincides with the minimal reference class! I.e., it’s the observer-moments in your epistemic situation (of being in a white room), before you know your jacket color.
The above likelihoods plus the fair-coin prior are all we need to get P(H | R_{me}, W_{me}), but at no point did the three anthropic views disagree.
In order words: It seems that the controversial setup in anthropics is in answering P(I [blah] | world), i.e., what we do when we introduce the indexical information about “I.” But once we’ve picked out a particular “I,” the different views should agree.
(I still feel suspicious of mrcSSA’s metaphysics for independent reasons, but am considerably less confident in that than my verdict on God’s coin toss with equal numbers.)
It seems that what I was missing here was: mrcSSA disputes my premise that the evidence in fact is “*I* am in a white room, [created by God in the manner described in the problem setup], and have a red jacket”!
Rather, mrcSSA takes the evidence to be: “Someone is in a white room, [created by God in the manner described in the problem setup], and has a red jacket.” Which is of course certain to be the case given either heads or tails.
(h/t Jesse Clifton for helping me see this)