Yeah, extra dimensions. See the link to the CERN guy in Van Rijn's post above, and scroll down to the bottom where he addresses the safety concerns. He seems to think extra dimensions are highly unlikely despite the fact that they've been the rage in physics for the last twenty years at least. He thinks it's less probable than no Hawking radiation, so let's rate that at 0.1% or 0.001.
That's right, these are all conditional probabilities. What you do is rate each probability, and then combine them in the end to get the total probability. And let me reiterate that cosmic rays have not in fact done the "same experiment". The products of cosmic rays are 1-way affairs. Put an 8-ball on the little dot, then aim the cue ball directly at it, and shoot with all your might, and you will see what I mean. At the LHC, however, it's more like two cars getting in a high speed, direct head on. The two cars kind of fuse together, and stop moving. So any mBH's formed at the LHC will be at rest with respect to the Earth. That would be quite unprecedented were that to happen. No one disagrees with this one, so let's keep it at 90%, or 0.9

One step at a time my lad. Let's take Hawking radiation. Although the CERN guy was quick to mention that extra dimensions have never been observed, he failed to mention that Hawking radiation has never been observed. It is in fact controversial within the physics community. Out of a pool of 15 physicists, their probabilities ranged from 0 to 0.5. The median, however, was 2%, so let's go with that.
I wish you were right, my friend. But in fact that part of the equation is poorly constrained. That is why they had to bring in the whole neutron star/white dwarf argument. The laws of physics--as they are known now-- cannot constrain the growth of mBH's. They might not grow; but then again they just might. I called it a coin flip myself, because I specifically want to choose conservative, worst case scenarios, because after all Mother Earth is at stake. But we can put a fairly low probability on it if you want. How about 2%--the same as Hawking radiation.
Again, I wish you were correct. However, you may at least take comfort in the thought that this is not my original idea (well actually I've got that backwards, don't I). The fact is, we have no empirical evidence of what the quantum gravitational regime is like. This was pointed out in Plaga's paper (sec. 5) and was not discussed at all by M &G's rebuttal, because M&G admitted as much in their first paper, when they said that they did not use "worst case" assumptions for every uncertainty. This is the big one here. The worst case scenario is that the semiclassical approximation breaks down for multidimensional mBH's deep within the quantum gravitational regime and that cosmic ray produced mBH's will pass harmlessly through both the Earth as well as neutron stars and white dwarfs. Moreover, the CERN guy says that the most unlikely possibility is that we exist in 5 or 6 dimensions, so we need a higher probability than we chose for #1, so how about 1/2 of a percent that maybe such an extrapolation is unwarranted by the eventual empirical facts that we do not yet have in hand. So that would be 0.005.

You are quite correct that each of the uncertainties reinforce each other so when combined they produce a probability much smaller than any single one of them. So shall we?


So our total probability is about 2 out of 1 billion. So you can see how each of the probabilities reinforced each other to come up with the tiny total probability. And you were also correct in your earlier post that drew attention to important disanalogies between lotteries and the kind of probability we are dealing with here. The probability that Mother Earth will die because of the LHC is not a statistical probability like lotteries, or even repeatable disasters in nature like hurricanes and floods. Rather, it's a subjective, Bayesian probability; it's more of a bet, really. It's more like what the British oddsmakers do. Like betting on whether Sarah Palin will be President in 2016. (BTW, they had her in 2nd place right behind Romney, though most people had never heard of her, so this process works when many people pool their subjective probabilities. Stock markets are based on the same principle.) What it really represents are the odds you would demand if you took the other side of the bet and bet on world destruction. That is, if you bet $1 USD that the world will be destroyed within the next twenty years because of an LHC induced mBH (assuming of course that you had a nice condo on the Moon so you could survive to collect the bet), then you should get paid $1.8 billion USD for the $1 USD you put up. What's going to happen is going to happen. Mother Earth will either live or she will die. There are no statistical ifs, ands, nor buts about it.
Once again, I wish you were right my friend, but there's no way you can equate a 2 in 1 billion probability with the probability that a burrito in a microwave will destroy the planet.

Now you calculate the net expected utility by multiplying the probability of destruction by the value of the Earth. Assuming the Earth is worth $10¹⁰⁰ USD:

1.8 x 10^-9 x $10¹⁰⁰ = $1.8 x 10⁹¹ USD

So to make it worth it, the benefit of the LHC should be greater than $1.8 x 10⁹¹ USD. Do you think it will?