Hope it’s okay to piggyback on an existing thread. Eli, if what I’m about to write doesn’t represent your question, please say so (and I’ll open a new question).

Seemingly, every moral theory also has a consequentialist component, and it needs to define its utility-damage function—that is, what exactly it wants to maximize or minimize, and how. Two people each suffering 3 units, or one person suffering 5 units? The generalizations are of course many and immediate.
For example, in defining variance, we use squaring in order to prioritize many small deviations over a few large ones. In training a neural network too (a quintessentially consequentialist entity), a standard error function (MSE) uses squaring to define the value one tries to minimize in training.
This question seemingly forces the addition of another principle (of course on a moral basis) to the clear and lucid principle of consequentialism, and personally it troubles me as a moral lacuna that I don’t know how to decide. Even as a single individual, it’s hard for me to say what I would prefer (twice suffering 3 or once suffering 5), and maybe one could use a person’s preferences about himself as an empirical means for determining the utility function (I don’t see a naturalistic fallacy here).

I don’t know how to answer that, but I repeat what I said: it isn’t right to discuss this in general. It depends on the circumstances and on the question before us. In the question of what to do, other components are involved, such as how directly I am causing the bad outcome, and even on the consequentialist level there are components of suffering versus danger to life (which do not always go together). Dealing with something this general and amorphous is, in my opinion, futile.

Clearly there is no naturalistic fallacy here, since you are asking a factual question, not a value question: which is a worse outcome (in the sense of suffering). If you are asking a value question—how one should relate to different kinds of suffering—that brings us back to the problems I described in the previous answer.

I thought the question “what is worse” was seemingly independent of circumstances. Just as in any possible circumstance it is preferable to cause unnecessary suffering of level 3 rather than unnecessary suffering of level 5. But let’s indeed assume someone is threatening me with a gun (or threatening to kill all three people) and forcing me to choose. Additional components (like danger to life) can surely be filtered out in examples. Why is this amorphous? Suppose we defined units of suffering for each individual event (two whip lashes = 3 units, three whip lashes = 5 units), we still need to define the weighting function (two lashes to two people or three lashes to one person).

You have before you two people: one intends to torture someone for fifty years, and the other intends to get dust into the eyes of a great many people. If we ignore side effects (for example, that the person might die from the torture, or that the dust in the eyes happens exactly while driving and causes traffic accidents), and you are able to stop one of them, whom would you stop?

Joshua,
Since you do not know how to quantify the degree of suffering, and it is doubtful whether there is any quantification at all (after all, there is the basic question of psychophysics; see column 99, and a bit in column 20). For example, the number of lashes does not correspond to the amount of accumulated suffering (it is not necessarily linear. On the contrary, in psychophysics it is accepted that the relation is not linear but either logarithmic or some kind of power law). In my opinion the question still does not lend itself to systematic discussion and answer.

Eli,
I think getting dust in the eyes simply does not enter into comparison with one person being tortured for life. If you ask me for a justification, it will be hard for me to give one, but I assume that each of those suffering would tell you he is willing to get dust in his eyes in order to prevent another person from being tortured for life. And since each one of them is willing, the number of people is of no importance (it does not accumulate).

[In the example I gave there is no linearity (intentionally), but rather increasing marginal suffering. I used the vulgar example of lashes because I seem to recall there is discussion of non-linearity in the Talmud in Tractate Makkot or in the commentators there.]

You are right that one cannot quantify. I thought that was not a critical point, because it is enough if one can give an order relation of what suffering is greater than what (as with different intensities of desire, for example, since in the end a person decides. I think there is an illuminating remark in Two Carts about the quantification of sensations and also about a common axis in the background?). For moral decision-making, an order relation is obviously enough.
For such an order relation I have a reasonable intuition (for example, what is preferable: a pinch in the stomach or accidentally turning on the cold water in the shower), because each event produces a specific sensation with which I somehow have experience, and I am able to compare sensations and say which I prefer. But I have no such order relation over a collection of different sufferings, because there one has to compare sets of sensations, and toward that—at least for me—I have no feeling at all.
In the lashes example above, it is clear that the order relation follows the number of lashes (one lash is less bad than two lashes, which are less bad than three, etc.), but it is still not clear what the order relation is in the example above (two lashes to two people or three lashes to one person).

I’m adding a short example (although it was probably obvious) to clarify the independence between the question of individual quantification (or an order relation between pairs) and the question of weighted quantification (an order relation among n-tuples). For example, in linear regression, the distance of the line from each and every point is well defined (individual quantification), but there is also a definition of the total distance of the line from all the points together (weighted quantification) in order to evaluate the quality of fit. If one uses “least squares,” then even in the weighted quantification there is no linearity (two distances of 3 are preferable to one distance of 5). Here it is easy to see that the distance function for an individual point is entirely independent of the function that weights the overall distance (one could also choose any other even power besides the square). And it is not at all clear that the units of the weighted function are “suffering” (and therefore it is not entirely clear to me that this can be tested empirically within consequentialism).
Even if instead of quantifying the individual distance one had only an order relation (whether when the line moves it is “getting closer” to the point or “moving away” from the point), one would still have to define a general order relation as well (whether the line is closer to set of points A or closer to set of points B).

In the end, there are two questions:
A. If it were possible to quantify suffering, would one indeed still need to choose a weighting method?
B. If an order relation is enough in place of quantification, does one in fact still need, theoretically, to define an order relation that performs the weighting?

B. I completely agree that an order relation is enough, but once you combine several sufferers together, the order relation is no longer relevant. At that point actual quantification is required. How would you rank two people getting three lashes versus three people getting two lashes? You yourself pointed this out. The question of whether two or three lashes are preferable for the same person is not difficult. The entire discussion is about the difficult questions, and there an order relation will not suffice.
A. I didn’t understand the question.

I understand more now, thanks. It’s still not completely sharpened for me, but it seems I’ve imposed enough already.

1) If someone intends to punch one person, and someone else intends to punch five people with the same force, would you stop the five, or because suffering is subjective there is no preference?
2) Would you stop a person who intends to kill five people rather than a person who wants to kill one person?

1. I assume that if it is the same intensity, the number would decide.
2. Yes. In the trolley dilemma, saving the many requires an action, while by inaction the one will die. But when both sides require action, I would save the five.

2. Is that because the combined blood of the five is “redder” than the blood of the individual?

I don’t understand the wording. It’s the same redness of blood, just more gallons of it. It is better to help five than one. What is unclear about that?

What do you actually think about the trolley dilemma? Seemingly, the reasoning is like the obligation to be killed rather than commit murder—maybe the blood of the one is redder than the combined blood of the five.
I’m trying to clarify the difference between the quality of the blood and its quantity. (Sorry if the wording isn’t so clear. It’s much easier for me to ask face to face than to formulate it in writing.)

A great deal has already been written about the trolley dilemma. It is not relevant here, because there the choice is between an action (killing one) and an omission (not saving several). Here the dilemma is between action and action, or omission and omission. Therefore here quantity matters, and there, according to all halakhic decisors, quantity has no significance (although some permit it for the sake of a public collective, but not because of a quantity of individuals). The question is not the redness of blood, but an act of murder versus omission.

From the straightforward meaning of the Talmudic passage, the reason one must die rather than murder is that we do not know whose blood is redder, and there is no reference to the fact that this is murder.

Then why, in the canteen of water case, don’t I have to give the other person my water? Why don’t I commit suicide to save another person? Clearly, in the background stands the fact that this is murder, set against the priority of my own life.