The sure things principle comes from decision theory and economics. It's obvious in the sense that it constitutes one of the axioms that define rational behavior.

In decision theory, we try to define behavioral axioms in a way that choices under uncertainty can be encoded in mathematical functions (utility functions or reward functions as Machine Learning has renamed/rediscovered these things). Connecting properties of these "preference orders" with utility functions and probabilities is the basis of a lot (but not all!) of modern economics.

Check for example Savage's proof of the existence of a subjective probability measure and a utility function based on only handful of "trivial" axioms. If these axioms hold, we can do meaningful mathematical social science.

The issue is of course that people don't actually behave rationally. The examples (or paradoxes) by Ellsberg and Allais show that most people violate the sure things principle.

If you are interested to learn more, here are some excellent notes by Gilboa http://www.econ.hit-u.ac.jp/~makoto/education/Gilboa_Lecture...

I can answer questions as well.

It's supposed to be trivial; it's one of the axioms of decision theory from which other (less obvious) things are derived. For example the vNM Theorem (that every rational agent acts as though it were maximising some utility function) follows from a set of assumptions including the sure thing principle.

I guess I'm missing it too.

action(x) = a if x

        = a if not x

Does action(x) not just equal a?

It depends on whether evaluating x leads to non-termination. In that case, action(x) should also not terminate.

Yeah, I would be curious of a different scenario when:

  - If E then I would take action A
  - If not E then I would take A also
  - However when the outcome of (E vs not E) is undetermined, hesitate from action A.

Does anyone know a real world example of such a situation?

Scientists say that there's a considerable but not overwhelming chance that the volcano on my island might erupt in the next few days.

If I knew that the volcano is going to erupt, then I would drive to the airport (with all my belongings, and leave).

If I knew that the volcano on my island is not going to erupt this month, then I would drive to the airport (to go on a package holiday that I had planned).

However, if the outcome is undetermined, I might prefer to cancel my holiday (I would not enjoy it while worrying about all my stuff potentially being destroyed in a fiery inferno) and wait to see what happens. So I should hesitate from driving to the airport.

In this example the two "drive to airport" actions are different.

    If (volcano_status == GONNA_BLOW)
        pack_everything_and_run();
    else if (volcano_status == NO_WORRIES)
        pack_suitcase_and_leave_for_holiday();
    else if (volcano_status == UNKNOWN)
        cancel_holiday();

It depends on what you treat as a complete action. One could equally well decompose it as two actions and two conditionals:

if (volcano_status == GONNA_BLOW) refuel_car(); else if (volcano_status == NO_WORRIES) refuel_car(); else if (volcano_status == UNKNONW) nop();

then later

if (volcano_status == GONNA_BLOW) pack_everything_and_run(); else if (volcano_status == NO_WORRIES) pack_suitcase_and_leave_for_holiday(); else if (volcano_status == UNKNONW) call_to_cancel_holiday();

Then refueling the car is definitely the same action, even if it's followed by different actions later on.

I don't think things in real life lead to non-termination, because humans are flexible and get bored. (In fact I'm pretty sure this is the evolutionary advantage behind boredom - it's a mechanism for breaking out of loops.)

It's fairly trivial, but related to Simpson's paradox, which isn't. There is a hidden assumption that's worth pointing out.

It was probably posted due to recent discussion of casual inference. Judea Pearl talks about it in The Book of Why.

you mean causal? though I'm intrigued about casual inference now that you mention it. would this be a branch of behavioral economics where actors investing only a little effort come to a different conclusion than those looking at it formally? Could this explain the wealth gap?

Yes, causal. :)