Wei Dai wrote:
> 
> 
> The thing is, we need a decision theory, otherwise it's not clear what
> predictions mean. To be cute about it, I could say that without a decision
> theory, a prediction is no more than a number (probability) attached to a
> statement, devoid of other meaning. Once you think in terms of decision
> theory, it seems that measure only has meaning if you give it meaning by
> making it part of your utility function.

Wei, you have been asking about a decision theory for a long time.  

It seems to me that if utility function is defined as your own
probability (or possibly measure) of existence then all decision process
becomes based on conditional probability given your own existence. Your
decision theory is just based on conditional probabilities. Most of the
time you assume that the probability of the continuation of your own
existence is one. In these cases the conditional probability approach
reverts to plain probability. 

Thus if you consider your own measure only, the probability that (you
continue living AND that (you shoot yourself if you don't win the
lottery) given that (you continue living) is one... and leading a life
of leisure and quantum suicide are justified; working overtime is not. 

On the other hand, if you consider the measure of, and utility to your
family, the probability that (their measure and utility is not
decreased) AND that (you shoot yourself if you don't win the lottery) is
definitely smaller than one... and you should buy a life insurance and
work overtime to make the payments. Leading a life of leisure is not
justified. So depending on the point of view you reach different and
sometimes opposite results.

I have been superficially following your discussion with Juergens, Hal
and Russell. I assume that  by "prior" you mean prior probability
distribution of universal states as defined by some universal algorithm
or machine. It seems to me that such distributions are totally
irrelevent because what actually matters TO AN OBSERVER is the specific
subsets of disconnected state vectors necessary to make that OBSERVER
conscious. The state vector in that subset could be widely separated and
therefore not at all related or ordered according to the originating
prior. Their ordering and/or relationship to each other depends on the
physical and mental processes governing that OBSERVER consciousness. The
linkage from state vector to state vector that gives rise to
consciousness is purely subjective in a relativistic way to the
observer.

George

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