This privileges the hypothesis. You're claiming that there will be no secondary consequences and therefore secondary consequences need not be considered. This is directly antithetical to the notion of treating these questions in an "all other things being equal" state.
What? Which hypothesis do I privilege? How does assuming no secondary consequences of either variant contradict treating the other things as being equal?
There is an error in your reasoning here, but I can understand why it would be non-obvious. You are assuming that u(n) != n + Z(n) in my formulation. ...
If n refers to either X or Y, I certainly don't assume that u(n) != n + Z(n), because such a thing has no sensible interpretation ("u(X) = X" would read "utility of torture is equal to torture"). If n refers to number of people dust-specked or some other quantity, I still have no idea what you mean by Z(n). In my notation, Z was not a function, but a change of state of the world (namely, that society begins tolerating torture). So, maybe there is an error in my reasoning, but certainly you are not understanding my reasoning correctly.
As for your demanded examples, I am still not sure what do you want me to write.
Edit: seems to me that I made the same reply as paper-machine, even accidentally using the same symbols X, Y and Z, but in his use these are already utilities, while in my use they are situations. So, paper-machine.X = prase.u(X).
How does assuming no secondary consequences of either variant contradict treating the other thing as being equal?
Because, in order to achieve that state, you must impose special conditions on the implementation of the hypothetical. Ones the hypothetical itself is agnostic to. The only way to eliminate secondary consequences from consideration, in other words, is to treat the hypotheticals unequally.
I also began by stating, if you'll recall, that if you do so isolate the query to first-consequences only, all that you practically achieve is a comparison ...
For those not familiar with the topic, Torture vs. Dustspecks asks the question: "Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?"
Most of the discussion that I have noted on the topic takes one of two assumptions in deriving their answer to that question: I think of one as the 'linear additive' answer, which says that torture is the proper choice for the utilitarian consequentialist, because a single person can only suffer so much over a fifty year window, as compared to the incomprehensible number of individuals who suffer only minutely; the other I think of as the 'logarithmically additive' answer, which inverts the answer on the grounds that forms of suffering are not equal, and cannot be added as simple 'units'.
What I have never yet seen is something akin to the notion expressed in Ursula K LeGuin's The Ones Who Walk Away From Omelas.If you haven't read it, I won't spoil it for you.
I believe that any metric of consequence which takes into account only suffering when making the choice of "torture" vs. "dust specks" misses the point. There are consequences to such a choice that extend beyond the suffering inflicted; moral responsibility, standards of behavior that either choice makes acceptable, and so on. Any solution to the question which ignores these elements in making its decision might be useful in revealing one's views about the nature of cumulative suffering, but beyond that are of no value in making practical decisions -- they cannot be, as 'consequence' extends beyond the mere instantiation of a given choice -- the exact pain inflicted by either scenario -- into the kind of society that such a choice would result in.
While I myself tend towards the 'logarithmic' than the 'linear' additive view of suffering, even if I stipulate the linear additive view, I still cannot agree with the conclusion of torture over the dust speck, for the same reason why I do not condone torture even in the "ticking time bomb" scenario: I cannot accept the culture/society that would permit such a torture to exist. To arbitrarily select out one individual for maximal suffering in order to spare others a negligible amount would require a legal or moral framework that accepted such choices, and this violates the principle of individual self-determination -- a principle I have seen Less Wrong's community spend a great deal of time trying to consider how to incorporate into Friendliness solutions for AGI. We as a society already implement something similar to this, economically: we accept taxing everyone, even according to a graduated scheme. What we do not accept is enslaving 20% of the population to provide for the needs of the State.
If there is a flaw in my reasoning here, please enlighten me.