I think that the answers to both the concern about 7 elements, and the desire to have questions depend of previous questions come out of thinking about FFS models, rather than FFS.
If you want to have 7 elements in Ω, that just means you will probably have more than 7 elements in S.
If I want to model a situation where some questions I ask depend on other questions, I can just make a big FFS that asks all the questions, and have the model hide some of the answers.
For example, Let’s say I flip a biased coin, and then if heads I roll a biased 6 sided die, and if tails I roll a biased 10 sided die. There are 16 outcomes in Ω.
I can build a 3 dimensional factored set 2x6x10, which I will imagine as sitting on my table with height 2. heads is on the bottom, and tails is on the top.f:S→Ω will then merge together the rows on the bottom, and the columns on the top, so it will look a little like the game Jenga.
In this way, I am imagining there is some hidden data about each world in which I get heads and roll the 6 sided die, which is the answer to the question “what would have happened if I rolled the 10 sided die. Adding in all this counterfactual data gives a latent structure of 120 possible worlds, even though we can only distinguish 16 possible worlds.
I think that the answers to both the concern about 7 elements, and the desire to have questions depend of previous questions come out of thinking about FFS models, rather than FFS.
If you want to have 7 elements in Ω, that just means you will probably have more than 7 elements in S.
If I want to model a situation where some questions I ask depend on other questions, I can just make a big FFS that asks all the questions, and have the model hide some of the answers.
For example, Let’s say I flip a biased coin, and then if heads I roll a biased 6 sided die, and if tails I roll a biased 10 sided die. There are 16 outcomes in Ω.
I can build a 3 dimensional factored set 2x6x10, which I will imagine as sitting on my table with height 2. heads is on the bottom, and tails is on the top.f:S→Ω will then merge together the rows on the bottom, and the columns on the top, so it will look a little like the game Jenga.
In this way, I am imagining there is some hidden data about each world in which I get heads and roll the 6 sided die, which is the answer to the question “what would have happened if I rolled the 10 sided die. Adding in all this counterfactual data gives a latent structure of 120 possible worlds, even though we can only distinguish 16 possible worlds.