On 4/21/2022 3:03 PM, George Kahrimanis wrote:
In my current way of thinking, the disagreement between Alan Grayson
and John K. Clark is about two subtly different concepts under the
same name, "probability". For example, when I read "80% chance of rain
today", I may think that in some possible futures it will not rain (so
probability is meaningless), yet I feel an instinctive urge for
protection from bad weather, so I take my umbrella. We are programmed
to act in this way, due to Darwinian selection -- but it is a
different matter to claim that QM (without collapse) issues a
probability for each possible outcome so that then we are rationally
obliged to apply Maximisation of Expected Utility. I grant the former
but not the latter.
Part of the trouble is that serious philosophical issues about
probability are still debated, so that there are traps for anyone who
deals with these things. Here is an example.
> [...] until Alan Grayson sees the end of the race, or somebody tells Alan Grayson about it, Alan
Grayson can't be certain what world Alan Grayson is in. Alan Grayson
could be in a world where horse X won or Alan Grayson could be in a
world where horse Y won, until Alan Grayson receives more information
Alan Grayson would have to say the odds are 50-50.
If you mean that on sheer ignorance the odds are 50-50, we need some
clarifications. Strictly speaking, zero information implies "undefined
probability", or "imprecise probability between 0 and 1". The reason
it is commonly mistaken as 50-50 is an implied strategy, flipping a
coin in case of ignorance, but then the odds are of the coin instead
of the object of the bet. (This strategy works only if the agent is
free to choose which side of the bet she underwrites.)
If the odds 50/50 can apply to the coin...because you don't know which
way it will come down...then the same concept applies to the horse race.
For the instrumentalists among us (glad to have you, BTW): the
question of interest to me is not about which way is best to derive
probability from QM -- that would be a pointless discussion, I agree!
The question is whether all of them beg the question, so that we have
to think of a rational decision theory without probability.
Rational decision theory only exists because of uncertainty. If there
were no uncertainty one wouldn't need theory to inform your choice, you
would directly by value.
Brent
Although Everett's argument (whose improvement I have proposed) grants
that in the long run (that is, large samples) the Born Rule is
practically certain to apply, this is not technically the same as
probability for each single outcome -- though I admit that it works
the same, to trigger an instinctive impulse. But for a RATIONAL
decision theory this probability is not granted, IMO.
I can give examples of a decision theory w/o probability, but they
would dilute the focus of this message.
George K. --
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