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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