Hi there. First post; be kind please.
I'm looking to present a short talk on the Sleeping Beauty problem in our maths/computing group at work. So far, I've just sketched an incomplete outline:
- Start by describing SB and the halfer, thirder & double-halfer arguments. Note that there seem to be two types of uncertainty here: (1) the coin outcome and (2) the day of the week. These types "feel" different, and it should not be a foregone conclusion that you can treat each the same.
- Describe the Absent-Minded Driver and how his choice of mixed strategy appears consistent only with certainty that he is approaching the first junction, i.e. the planning-optimal decision. At first glance, this looks like bad news for type-2 day-of-the-week / position-on-the-road uncertainty.
By this point, the audience (maths/computing folk, remember) will be starting to conclude that type-2 uncertainty is just a load of old touchy-feely nonsense and that all the world needs is cold hard classical probability. I would like to counter that on two fronts:
- Though we didn't achieve it when scratching the surface of the SB & AMD problems, consistent theories of rational decision making that include type-2 uncertainties do exist, such as XXX.
- There is a philosophical need for such theories (you cannot just rely on cold hard classical probability), as shown for example by YYY.
I'm stuck for what to say on XXX and YYY. Can you help?
Comments also welcome on appropriate terminology (not "type-2"!) and anything else that strikes you as being egregiously wrong. Please do not assume any prior knowledge. Thank you.