The probability must add to one. There are exponentially more possibilities with linearly more complexity, so the probability would have to decrease exponentially on average. You can base it on something other than complexity, but whatever you use will still correlate to complexity.
Equally weight all hypotheses that explain the data.
There are infinitely many of them. Now what?
The likelihood of a hypothesis is inversely proportional to the number of observations it purports to explain.
How does that work? Saying the coin will land on heads or tails explains two observations. Saying it will land on heads explains one. Is it twice as likely to land on heads than land on heads or tails?
The likelihood of a new hypothesis that explains the data is proportional to the Solomonoff prior for the Kolmogorov complexity of the code that transforms the previously accepted hypothesis into the new hypothesis.
I don’t think you could do this without violating the axioms of probability. Also, what’s your first hypothesis?
If your first hypothesis is nothing, then until your first observation, you have the Solomonoff prior. If you do manage to obey the axioms of probability, you will have to use Solomonoff induction.
My aesthetics prefers the O’Neill way over the Carter way: the Goldpan over the Razor.
If that’s your razor, you’re doing it wrong. Everything is possible. The simplest explanation is just most likely. Preparing for your death may be the most likely action to be relevant, but it also doesn’t do much to help.
In addition, the show skews the results by making O’Neill right much more often than reasonable. Of course it will look like it’s a good idea to assume you have a good chance of survival if they only ever show the characters surviving.
The probability must add to one. There are exponentially more possibilities with linearly more complexity, so the probability would have to decrease exponentially on average. You can base it on something other than complexity, but whatever you use will still correlate to complexity.
There are infinitely many of them. Now what?
How does that work? Saying the coin will land on heads or tails explains two observations. Saying it will land on heads explains one. Is it twice as likely to land on heads than land on heads or tails?
I don’t think you could do this without violating the axioms of probability. Also, what’s your first hypothesis?
If your first hypothesis is nothing, then until your first observation, you have the Solomonoff prior. If you do manage to obey the axioms of probability, you will have to use Solomonoff induction.
If that’s your razor, you’re doing it wrong. Everything is possible. The simplest explanation is just most likely. Preparing for your death may be the most likely action to be relevant, but it also doesn’t do much to help.
In addition, the show skews the results by making O’Neill right much more often than reasonable. Of course it will look like it’s a good idea to assume you have a good chance of survival if they only ever show the characters surviving.