I will not reply to the first paragraph, because we clearly disagree about what "ceteris paribus" means, while this disagreement has little to no relevance to the original problem.
effectively infinite
If it is finite, the logic behind choosing torture works. If it is infinite, you have other problems. But you can't have it both ways.
Where am I mistaken? What am I mistaking you on?
You have said "[y]ou are assuming that u(n) != s(n) + Z(n) in my formulation", I had been assuming no such thing.
Why would you declare a topic that you are unable to even describe interesting? You are the one who brought it up... provide examples of scenarios that fulfill your description.
Recall that you are probably reacting to this:
I haven't seen anybody propose a coherent general decision algorithm which returns "specks" for this dilemma and doesn't return repugnant or even paradoxical answers to different questions. This is the hard part, which if you engaged, it would be much more interesting.
No mention of any scenarios. If you want me to describe a consistent decision theory which returns "specks" and has no other obvious downsided, well, I can't, because I have none. Neither I believe that such a theory exists. You believe that "specks" is the correct solution.
I will not reply to the first paragraph, because we clearly disagree about what "ceteris paribus" means, while this disagreement has little to no relevance to the original problem.
If you are not stipulating the relevance of secondary consequences to the original hypothesis then this conversation is at an end, with this statement. Either they are relevant, as is my entire argument, or they are not. Claiming via fiat that they are not will earn you no esteem on my part, and will cause me to consider your position entirely without merit of any ki...
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.