I like the analogy. Here’s a simplified version where the ticket number is good evidence that the shop will close sooner rather than later.
There are two types of shop in Glimmer. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Glimmer use a numbered ticket system that starts at #1 for the first customer after they open, and resets when the shop closes.
I walk into a shop in Glimmer at random and get a ticket.
If the ticket number is #20 then I update towards the shop being a 9-5 shop, on the grounds that otherwise my ticket number is atypically low. If the ticket number is #43,242 then I update towards the shop being a 24⁄7 shop.
The argument also works with customer flow evidence:
Like Glimmer, there are two types of shop in Silktown. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Silktown experience increasing customer flow over time, starting with a few customers an hour, rising over time, and capping at hundreds of customers an hour after about ten hours of opening.
I walk into a shop in Silktown and observe the customer flow.
If the customer flow is low then I update towards the shop being a 9-5 shop, on the grounds that otherwise there will most likely be hundreds of customers an hour. If the customer flow is high then I update towards it being a 24⁄7 shop.
Reading through your hypothetical, I notice that it has both customer flow evidence and ticket number evidence. It’s important here not to double-update. If I already know that customer flow is surprisingly low then I can’t update again based on my ticket number being surprisingly low. Also your hypothetical doesn’t have strong prior knowledge like Silktown and Glimmer, which makes the update more complicated and weaker.
I like the analogy. Here’s a simplified version where the ticket number is good evidence that the shop will close sooner rather than later.
There are two types of shop in Glimmer. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Glimmer use a numbered ticket system that starts at #1 for the first customer after they open, and resets when the shop closes.
I walk into a shop in Glimmer at random and get a ticket.
If the ticket number is #20 then I update towards the shop being a 9-5 shop, on the grounds that otherwise my ticket number is atypically low. If the ticket number is #43,242 then I update towards the shop being a 24⁄7 shop.
The argument also works with customer flow evidence:
Like Glimmer, there are two types of shop in Silktown. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Silktown experience increasing customer flow over time, starting with a few customers an hour, rising over time, and capping at hundreds of customers an hour after about ten hours of opening.
I walk into a shop in Silktown and observe the customer flow.
If the customer flow is low then I update towards the shop being a 9-5 shop, on the grounds that otherwise there will most likely be hundreds of customers an hour. If the customer flow is high then I update towards it being a 24⁄7 shop.
Reading through your hypothetical, I notice that it has both customer flow evidence and ticket number evidence. It’s important here not to double-update. If I already know that customer flow is surprisingly low then I can’t update again based on my ticket number being surprisingly low. Also your hypothetical doesn’t have strong prior knowledge like Silktown and Glimmer, which makes the update more complicated and weaker.