
Sure-thing principle - denzil_correa
https://en.wikipedia.org/wiki/Sure-thing_principle
======
vpribish
"the sure-thing principle states that a decision maker who would take a
certain action if he knew that event E obtained, and also if he knew that the
negation of E obtained, should also take that same action if he knows nothing
about E."

using "obtain" in it's archaic, old-french, meaning of roughly "succeed".
Wikipedia math pages are generally useless for non-experts, but this is a new
one!

~~~
hinkley
It now says occurred instead of obtained.

No set of pages in Wikipedia imply “we hate everybody else” quite like the
math pages. It’s like the math folks have either forgotten that Wikipedia is
for communicating with people, they just don’t care, or they don’t know how.

Every time I read a math page on Wikipedia I want to go watch a Feynman
lecture as eye bleach.

~~~
striking
I'm very thankful for Simple English Wikipedia for this reason. Compare the
vanilla Set page
[https://en.wikipedia.org/wiki/Set_(mathematics)](https://en.wikipedia.org/wiki/Set_\(mathematics\))
with
[https://simple.wikipedia.org/wiki/Set](https://simple.wikipedia.org/wiki/Set).

It's too bad there aren't more of these pages, as they are honestly excellent
quick resources.

------
fwdpropaganda
Is this trivial, or am I missing something?

~~~
taneq
I guess I'm missing it too.

action(x) = a if x

    
    
            = a if not x
    

Does action(x) not just equal a?

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

~~~
a-nikolaev
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?

~~~
TezlaKoil
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.

~~~
taneq
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();

~~~
TezlaKoil
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.

------
vpribish
lousy wikipedia math culture aside, this is critical bit of logic for Sudoku
players :)

------
lactau
Sounds like dilemma:
[https://en.wikipedia.org/wiki/Dilemma#Use_in_logic](https://en.wikipedia.org/wiki/Dilemma#Use_in_logic)

~~~
a-nikolaev
Disjunction elimination rule of inference:
[https://en.wikipedia.org/wiki/Disjunction_elimination](https://en.wikipedia.org/wiki/Disjunction_elimination)
(plus, the law of excluded middle that either E or not E holds)

~~~
thaumasiotes
Wow, that rule is stated horribly.

You'd get much more value from phrasing it as

    
    
        ((p implies r) and (q implies r)) iff ((p or q) implies r).
    

No need to have a special rule stating that when you also have (p or q), you
can resolve all three to just "r" in one step instead of two steps.

~~~
a-nikolaev
Well, then it would be a different rule. The one I referred to, eliminates
disjunction, and so that's where its name is coming from.

~~~
thaumasiotes
No, it would be the same rule, just phrased better. The rule works by
introducing a disjunction (to match the one you already have), not by
eliminating one.

Given

    
    
        a implies p
        b implies p
        a or b
    

you can conclude ((a or b) implies p) from my statement of the rule, and then
conclude "p" from modus ponens. And if you're feeling really obscurist, you
can rename modus ponens to "proposition elimination".

But notice that if you have

    
    
        a implies p
        b implies p
        c implies p
        a or b or c
    

then my statement of the rule will still allow you to conclude "p", whereas
the statement on wikipedia won't.

~~~
a-nikolaev
You misunderstand my comment. I'm not saying that your interpretation is
wrong. I'm fine with it. Better or not, either result can be used in the right
context. I'm saying that your interpretation does not eliminate disjunction,
so it should be called differently. It's a different rule, that's all I want
to say.

~~~
thaumasiotes
> Better or not, either result can be used in the right context.

This is most of the point I'm making -- there is no context where the brittle,
overspecified version is useful but the more general version isn't. But there
are lots of contexts where the overspecified version is useless.

And again, it's not a different rule. Brittle "disjunction elimination" is a
special case of the rule I state. Similarly, the Pythagorean Theorem is a
special case of the Law of Cosines, not a different rule.

It gets worse, though, because where the Pythagorean Theorem is simpler to
state than the Law of Cosines, brittle disjunction elimination is _more
complex_ to state than the more general result is.

Think about exportation. We say:

    
    
        (a implies (b implies p)) iff ((a and b) implies p)
    

We don't say:

    
    
        ((a implies (b implies p)) and (a and b)) implies p
    

That second version, which is the equivalent of brittle disjunction
elimination for _and_ instead of _or_ , is harder to state, is less
informative, and doesn't generalize.

