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prase comments on Applying utility functions to humans considered harmful - Less Wrong
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Depends on what you want to predict. I throw dice and have a model which says that number 5 is the result, deterministically. Now I will be right in 1/6 cases. If I am rewarded for each correct guess, then by introducing randomness into the model I will gain nothing - this is what Eliezer was arguing for. But if I am rewarded for correctly predicting the distribution of results after many throws, any random model is clearly superior to the five-only one.
The random model is better than the five-only one but a non-random model that directly predicts the distribution would be better still. If your goal is to predict the distribution then a model that does so by simulating random dice throws is inferior to one that simply predicts the distribution.
And if you want to do both, i.e. predict both the individual throws and the overall distribution? The "model" which directly states that the distribution is uniform doesn't say anything about the individual events. Of course we can have model which says that the sequence will be e.g. 1 4 2 5 6 3 2 5 1 6 4 3 and then repeated, or that the sequence will follow the decimal expansion of pi. Both these models predict the distribution correctly, but they seem to be more complex than the random one and moreover they can produce false predictions of correlations (like 5 is always preceded by 2 in the first case).
Or do I misunderstand you somehow?
A model that uses a sequence is simpler than one that uses a random number, as anyone who has implemented a pseudo random number generator will tell you. PRNGs are generally either simple or good, rarely both.
Depends on what hardware you have got. Having a computer with access to some quantum system (decaying nuclei, spin measurement in orthogonal directions) there is no need to specify in a complicated way the meaning of "random". Or, of course, there is no need for the randomness to be "fundamental", whatever it means. You can as well throw dice (though it would be a bit circular to use dice to explain dice, but it seems all right to use dice as the random generator for making predictions in economy).
A hardware random number generator isn't part of an algorithm, it's an input to an algorithm. You can't argue that your model is algorithmically simpler by replacing part of the algorithm with a new input.
So, should quantum mechanics be modified by removing the randomness from it?
Now, having a two level spin system in state ( |0> + |1> ) /sqrt[2], QM says that the result of measurement is random and so we'll find the particle in state |1> with probability 1/2.
A modified QM would say, that the first measurement reveals 1, the second (after recreating the original initial state, of course) 1, the third 0, etc., with sequence 110010010110100010101010010101011110010101...
I understand that you say that the second version of quantum mechanics would be simpler, and disagree.