The first paragraph of this comment is a nitpick, but I felt impelled to it: there is no way that 10^14 dust specks is anywhere near enough to equal one torture victim. Maybe if you multiplied it by a googolplex, then by the number of atoms in the universe, you'd be within a few orders of magnitude.
And now for the meaty response.
You're making the whole case extremely arbitrary and ignoring utility metrics, which I will now attempt to demonstrate.
Eliezer chose the number 3^^^3 so that no calculation of the disutility of the torture could ever match it, even if you have deontological qualms about torture (which most humans do). It simply doesn't compare. Utilitarianism in the real world doesn't work on fringe cases because utility can't actually be measured. But if you could measure it, then you'd always pick the slightly higher value, every single time. In your example,
We breath a huge sigh of relief - you don't have to torture anybody, because the math worked out in your favor by a vanishingly small fraction! Then Omega suddenly tells you he's changing the deal - he's going to be putting dust speck in YOUR eye, as well.
you ignore that part of my utility function that includes selflessness. Sacrificing something that means little to me for sparing intense suffering by someone else leads to positive utility for me, and I'm assuming other people. (This interestingly also invalidates the example you gave earlier where you polled the 3^^^3 people asking what they wanted - you ignored altruism in the calculation).
Your problems with the Torture vs. Dust Specks dilemma all boil down to "Here's how the decision changes if I change the parameters of the problem!" (and that doesn't even work in most of your examples).
Here's the real problem underlying the equation, and invulnerable to nitpicks:
Omega comes to you and says "I will create 3^^^3 units of disutility, or disutility equal or lesser to the destruction of a single galaxy full of sentient life. Which do you choose?"
As has been said before, I think the answer is obvious.
The device allows for certain issues like slavery and income distribution to be determined beforehand. Would one vote for a society in which there is a chance of severe misfortune, but greater total utility? e.g, a world where 1% earn $1 a day and 99% earn $1,000,000 vs. a world where everyone earns $900,000 a day. Assume that dollars are utilons and they are linear (2 dollars indeed gives twice as much utility). What is the obvious answer? Bob chooses $900,000 a day for everyone.
But Bob is clever and he does not trust himself that his choice is the rational choice, so he goes into self-dialogue to investigate:
In the insurance industry, purchasing insurance comes with a price. Perhaps 1.5% premium of the cost of reimbursing you for your house that may burn down. The actuaries have run the probabilities and determine that you have a 1% chance that your house will burn down. Assume that all dollar amounts are utilons across all assets. Bob once again is a rational man. Every year Bob is chooses to pay 1.5% in premium even though his average risk is technically a 1% loss, because Bob is risk adverse. So risk adverse that he prefers a world in which he has less wealth, the .5% went to the insurance companies making a profit. Once again Bob questions his rationality on purchasing insurance:
Eliezer's post on Torture vs. Dust Specks [Here] has generated lots of discussion as well as what Eliezer describes as interesting [ways] of [avoiding] the question. We will do no sort of thing in this post, we will answer the question as intended; I will interpret that eye specks is cumulatively greater suffering than the suffering of 50 years.
My PVG tells me that I would rather have a speck in my eye, as well as the eye's of 3^^^3 people, than to risk to have one (perhaps me) suffer torture for 50 years, even though my risk is only 1/(3^^^3) which is a lot less than 50 years (Veil of ignorance). My PVG is what I will maximize, and doing so is the definition of instrumental rationality.
In short, the rational answer is not TORTURE or SPECKS, but depends on what your preference, values and goals are. You may be one of those whose preference is to let that one person feel torture for 50 years, as long as your actions that steer the future toward outcomes ranked higher in your preferences, you are right too.
Correct me if I am wrong but I thought rationality did not imply that there were absolute rational preferences, but rather rational ways to achieve your preferences...
I want to emphasize that in no way did I intend for this post to declare anything. And want to thank everyone in advance for picking apart every single word I have written. Being wrong is like winning the lottery. I do not claim to know anything, the assertive manner in which I wrote this post was merely a way to convey my ideas, of which, I am not sure off.